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Studies of charmed baryons decaying to lambda+C (n pi)

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Studies of charmed baryons decaying to lambda+C (n pi)
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Average linear density ( jstor )
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Mass ( jstor )
Momentum ( jstor )
Pions ( jstor )
Quark models ( jstor )
Quarks ( jstor )
Signals ( jstor )
Systematic errors ( jstor )
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Thesis:
Thesis (Ph.D.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 128-130).
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Typescript.
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Vita.
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The original title contains the following designation: "<Greek letter lambda> <superscript +> <subscript c> ( n <Greek letter pi> )"
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by Jiu Zheng

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STUDIES OF CHARMED BARYONS DECAYING TO A+ (n7r)


By

JIU ZHENG


















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1999














ACKNOWLEDGMENTS


Most of all, I would like to thank my adviser, John Yelton. He taught me from scratch how to do physics analysis in CLEO, introduced me to charmed baryon studies, and suggested a research topic which turned into this dissertation. Over five years he has been always very supportive in my work in physics and with many other aspects of my life.

I thank Paul Avery, who has taught me much about high energy physics, data analysis, and CLEO software. I gained a large part of my knowledge of elementary particles from his one year introductory course. The magnificent KNLIB he provided has given tremendous help to my analysis.

I am greatly indebted to my former college classmate, Song Yang, who influenced me to pursue the study of high energy physics. When he was a research associate at the University of Florida, he gave me much help with Monte Carlo simulations, Unix, C++, and GNU Make.

Thanks go to Craig Prescott for answering many of my questions about CLEO software and for engaging in much useful discussion about physics. My life in CLEO would have been much more difficult without him. His longtime maintenance and support of the CLEO software library have helped everybody in CLEO do better analyses. I used his Vee-finding library and primary-vertex-finding routine directly in my analysis.

I enjoyed lectures on "the Standard Model" by Pierre Sikivie and on "the Experimental High Energy Physics" by Guenakh Mitselmakher. I also thank Zongan Qui, Sergei Obukhov, and Charles Hooper for their first-year courses. I appreciate


ii









the help provided by my former colleagues, Jorge Rodriguez and Fadi Zeini. The Latex template provided by Youli Kanev and Mike Jones saved me a lot of time on writing this dissertation.

I would like to express my gratitude for the entire CLEO collaboration and all staff members in the Cornell Electron Storage Ring. I wish happiness and success to all high energy physicists. The world is a much better place with these people's dedication to answer the big, important questions.

Finally, I would like to thank my wife, Hongyan Yan. This work would have been impossible without her love and support. Much credit for this work goes to my mother, Chunyu Xu, my father, Zhiyi, and my father-in-law, Boxun. I have learned many things about life from my little son, David.


iii




























To my grandmothers















TABLE OF CONTENTS


ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . .ii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

CHAPTERS

1 THEORY OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Quark Model ...... . . . . . .. . . .. . .. .*. .. .. .. 1
1.2 Heavy-Quark Effective Theory ...................... 3
1.2.1 Q C D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Potential Models. .. .................... 5
1.2.3 Heavy-Quark Chiral Perturbation Theory ... ........... 7
1.3 Introduction to Charmed Baryons decaying to Aj(n7r) ........ 8
1.3.1 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Strong Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 HQET Predictions on E(*) and A . . . . . . . . . . . . . . . . . . . . 12

2 EXPERIMENTAL FACILITIES . . . . . . . . . . . . . . . . . . 17

2.1 CESR ........ ................................... 17
2.2 C LE O -II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Time-of-Flight System . . . . . . . . . . . . . . . . . . . . . . 26
2.2.3 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . 28

3 A+ RECONSTRUCTION . . . . . . . . . . . . . . . . . . . . . 29

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Data and Monte Carlo Sample . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.3 y and 7r Finding . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.4 Event Vertex Finding . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.5 Vee Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.6 E and E Finding . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 A+ Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


v









4 STUDIES OF A+ BARYONS . . . . . . . . . . . . . . . . . . . 52

4.1 Introduction....... ................................ 52
4.2 Monte Carlo Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3 Signals and Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 A +ir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 A tw 070 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Substructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.1 A+ -+ +r- and A+ -+ Ec7r+ . . . . . . . . . . . . . . . . . 66
4.4.2 A + E.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5 Search for Other Decays . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6 Masses and Widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.6.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 80
4.6.2 A+(2625) Mass and Width Limit . . . . . . . . . . . . . . . . 83
4.6.3 AC!c (2593) Mass and Width . . . . . . . . . . . . . . . . . . . . 84
4.7 Fragmentation Functions . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.8 Decay Ratios and Production Ratios . . . . . . . . . . . . . . . . . . 88
4.8.1 Systematic Errors on Yields and Efficiencies . . . . . . . . . . 88
4.8.2 A 0 r0, A+70, and A+y Decays . . . . . . . . . . . . . . . . . 89
4.8.3 E.7 Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.8.4 A+ Production Ratios . . . . . . . . . . . . . . . . . . . . . . 92

5 STUDIES OF Ec AND E' BARYONS . . . . . . . . . . . . . . . 94

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2 Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2.1 A wr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.2 A + 7r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3 M asses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4 W idths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.5 Fragmentation Functions . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.6 Production Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.7 New Measurements of A+ (2593)-A +r - . . . . . . . . . . . . . . . . 116

6 SUMMARY AND DISCUSSION . . . . . . . . . . . . . . . . . . 124


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . 131


vi














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

STUDIES OF CHARMED BARYONS DECAYING TO A+(n7r) By

Jiu Zheng

May 1999


Chairman: J. Yelton
Major Department: Physics


This dissertation presents studies of charmed baryons the A+i, E, and E*. The two A+i baryons are the L = 1 excited states of the A+, and they decay to a A+ and two pions; the Ec triplet is the spin 1/2 I = 1 state corresponding to the A+; and E* is the spin 3/2 excitation of the Ec. Both Ec and E* decay to a A+ and a pion. We performed comprehensive measurements on the masses, widths, fragmentation functions, and the production ratios of these particles from 10 GeV/c2 e+e- annihilations.

A new decay channel of the A+i, A+707r0, is first observed and its decay ratio relative to A7r+7r- is reported. A detailed study of A+i decays through the intermediate Ec is performed.

The Ec intrinsic widths are first measured with consistency with theoretical predictions. The relative production ratios among the three Ec's are measured to be consistent with 1. The first evidence of the existence a new particle, the E*+, is reported.


vii














CHAPTER 1
THEORY OVERVIEW


1.1 Quark Model


Tremendous progress has been made in high energy physics since the beginning of this century. We now have a simple picture about the ultimate constituents of matter: All matter is composed of quarks, which carry fractional electric charges, and leptons, such as the electron and neutrino. A quark does not exist individually and strong interactions hold quarks together in hadrons, which are built from two types of quark combination: a baryon consists of three quarks and a meson consists of a quark and an antiquark.

Quarks come in six flavors (called d, u, s, c, b, and t), as do leptons (three types of charged and three of neutral). Each quark has spin 1/2 and baryon number 1/3. Table 1.1 shows the additive quantum numbers (other than baryon number) of the three generations of quarks. By convention each quark is assigned positive parity, so each antiquark has negative parity. The masses of quarks vary largely for different


Table 1.1: Additive quantum numbers of quarks.


1


Flavor d u s c b t
Charge 7- -} + -} +T
Isospin z-component -5 +2 0 0 0 0 Strangeness 0 0 -1 0 0 0
Charm 0 0 0 +1 0 0
Bottomness 0 0 0 0 -1 0
Topness 0 0 0 0 0 +1






2


flavors,* ranging from a few MeV/c2 for u and d quarks to about 170 GeV/c2 for t quark. Since u and d are very light, the isospin SU(2) symmetry is a very good approximation. In the limit that isospin is an exact symmetry, the u and d quarks are considered identical except the charge difference.

Analogous to the photon in electromagnetic interactions, a strong coupling happens via a mediating boson, call a gluon. In the theory of quantum chromodynamics (QCD), there are six types of strong charge, called "color," representing an internal degree of freedom. A quark can carry one of the three red, blue, or green colors, and an antiquark can carry one of the corresponding anticolors. The quark-quark force is independent of quark color, so the color symmetry, SU(3), is exact.

All baryons are three-quark (qqq) states, and each such state is an SU(3) color singlet, a completely antisymmetric state of the three possible colors. Since quarks are fermions, the state function for any baryon must be antisymmetric under interchange of any two equal-mass quarks (up and down quarks in the limit of isospin symmetry). The state function of a baryon can be written as


I qqq)A = color)A x |space, spin, flavors,


where the subscripts S and A indicate symmetry or antisymmetry under interchange of any two of the equal-mass quarks.

For baryons made up of u, d, and s quarks, the three flavors imply and approximate flavor SU(3). This flavor SU(3) symmetry requires that a corresponding group of baryons belong to the multiplets on the right side of


3 9 3 3 = 10s e 8m e 8m E 1A,
*The values of quark masses depend on precisely how they are defined. The quark masses we referred to here follow the meanings defined by the Particle Data Group [1], which are different from the constituent quark masses.






3


where the subscript M indicates mixed-symmetry states under interchange of any two quarks. Taking spin symmetry, SU(2), into account, the two 8' s will end up with one octet of baryon states of Ispin, flavor)s. This octet is shown as the bottom layer of Figure 1.1(a) In the ground state of the multiplet, the SU(3) flavor singlet 1 is forbidden by Fermi statistics. The decuplet formed by 10s, shown as the bottom layer in Figure 1.1(b), contains the states with the three quark spins aligned to the same direction (spin J = 3/2).

If we add the c quark to the three light quarks, the flavor symmetry is extended to SU(4). The SU(4) multiples are shown in Figure 1.1(a) and Figure 1.1(b). All the particles in a given multiplet have the same spin and parity. Since the mass of the c quark is large, this SU(4) symmetry is very badly broken.


1.2 Heavy-Quark Effective Theory


1.2.1 QCD

In QCD, the Lagrangian describing the interactions of quarks and gluons is


1
LQCD = F a)F(a) + (D) - (1.1)
4 'Lv


Fa) = a A"a - aA a + 9sfabcA bA'

(D,)ij = 6ij1, - ig Aa
a 2 A
where g, is the QCD coupling constant (a= g /47r), and the fabc are the structure constants of the SU(3) algebra. The 0'(x) are the 4-component Dirac spinors associated with each quark field of color i and flavor q, and the Aa(x) are the Yang-Mills gluon fields.







4


+cc

(a)

cc +




Q0+ '=cc





Y++++ 0~










C+
AA














S



Figure 1.1: SU(4) multiplet of baryons made of u, d, s, and c quarks shown in (Ii, S, C) coordinates. (a) The 20-plet with an SU(3) decuplet. (b) The 20-plet with an SU(3) octet.






5

QCD is believed to be the fundamental theory of strong interactions. But to date, there are no practical means to do full QCD calculations of hadron masses and their decay widths. and a variety of different approximate methods have been introduced. Potential models have been well recognized to be the most useful in understanding the mass spectrum and the decay patterns of heavy-flavor hadrons. The correlation between flavor and spin wave functions is outside the realm of QCD. Some assumptions can be made using the empirical evidence of the constituent quark model. Heavy-hadron perturbation theory can be used to predict the decay widths.


1.2.2 Potential Models

Although the details of modern potential models have evolved greatly since the discovery of J/#, the essential features remain unchanged. The potential between two quarks is often taken to be of the form


V = a, + kr,
3 r

where r is the inter-quark separation, and a, - 1, about two orders larger than a, represents the magnitude of the strong coupling. The factor 4/3 holds for the interaction between a quark and an antiquark. It is 2/3 for the interaction between two quarks. The first term dominating at small distance r arises from a single gluon exchange, and the linear term is associated with the confinement of quarks and gluons inside hadrons at large r. Because of the linear term, attempts to free a quark from a hadron simply result in the production of new qq quark-antiquark pairs. The annihilation process e+e- - hadrons is viewed in terms of the process e+e -+ qq followed by "fragmentation" of the quark and antiquark into hadrons. One important feature of potential models is that, except for mass dependencies, the inter-quark potential is independent of quark flavor.






6


Potential models cannot be formally derived from QCD, but they can be interpreted by it. In QCD, the short-distance behavior is dominated by one gluon exchange described in the lowest-order perturbation theory. The linear behavior at large r can be seen by considering that a qq pair are attracted to each other and a color flux tube forms between them. Lattice calculations suggest that the tension per unit length in this flux tube is a constant[2, 3], and therefore the energy stored in the tube is proportional to the separation of the charges. Finally, couplings described in QCD are flavor independent.

The most well-known and successful potential model is described Isgur, et al. [4, 5, 6]. Early models[5, 6] are non-relativistic and later they are improved by adding some relativistic terms[4]. The Hamiltonian of a baryon is,

3 2
H =E(mi + i) + E(Hj + HB"F, (1-2)
i=1 2mi i

H = 2a"+ +
3r---+ a +br,
3 r

HBF Ciij ' i + Ci - ?j + CT(3 i' j'- F -i ) + CH i j,

where i, j run over all quarks inside the baryon, and


1 1 4 a, 1 b
Ck = 2 + _) - i k
mk mimj 3 r 2mT r

1 4 a,
CT =-3
mj 3 r'

87r 1 4 a,
3 mimj3 r

H, is the confinement term, and the spin-dependent term HjF is very similar to the Breit-Fermi Hamiltonian of atomic and nuclear physics. It is very crucial that in H, the a, and b terms have opposite signs, and the two contributions to the









spin-orbit coupling cancel almost exactly. Since this model does not perform a full relativistic treatment, it is called a "relativized" quark potential model. Compared with non-relativistic models, it has slightly different values of a and b.

In the limit of mQ -- oc, where Q indicates the heavy quark, the Hamiltonian is simplified and a new good quantum number I+, the total angular momentum of the light degrees of freedom, is introduced. J Iis the direct analogy with the total angular momentum of the electron in a hydrogen atom.


1.2.3 Heavy-Quark Chiral Perturbation Theory

The quark contribution to the QCD Lagrangian in equation 1.1 can be considered to have two parts. The first comes from the light degrees of freedom, and the second part is from heavy quarks. Each of the two parts has distinct symmetry.

The light-quark part of the Lagrangian has a flavor SU(3)LxSU(3)R chiral symmetry in the limit that the light-quark masses are set to zero. SU(3)L xSU(3)R is only an approximate symmetry since the quark masses explicitly break it. This chiral symmetry is spontaneously broken and leads to eight massless Goldstone bosons, the 7r's, K's, and q. Their couplings to hadrons are determined by PCAC (partial conservation of axial-vector current) and current algebra, or, alternatively, by the nonlinear chiral Lagrangians.

For the heavy-quark part, in the limit of infinite quark masses, the dynamics of a heavy quark in QCD depends on its velocity and is independent of its mass and spin. As a consequence, a new flavor and spin symmetry appear for hadrons containing one heavy quark. This symmetry is called heavy-quark symmetry. Many models based on different approaches have been proposed by theorists from [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. This new symmetry implies that the excitation spectrum and the transition form factors in weak decays of heavy hadrons are independent of the






8


heavy-quark species and heavy-quark spins. This is similar to a hydrogen-like atom in QED having an excitation spectrum and transition matrix elements independent of the mass and spin of the nucleus.

Since heavy hadrons contain both heavy and light quarks, both the chiral symmetry of the light quarks and heavy-quark symmetry affect the low-energy dynamics of heavy hadrons interacting with the Goldstone bosons. Experimentally, strong decays such as E, - A+ir involving soft pions give such examples.


1.3 Introduction to Charmed Baryons decaying to At(n7r)


1.3.1 Spectroscopy

The charmed baryons which are covered in this work are those containing a c quark and two u or d quarks. The two light quarks are often referred to as a diquark. In the mc -+ oc limit, the total angular momentum of the light constituents,






become a good quantum number. Here is the total spin of the two light quarks

and L is the orbital angular momentum between the c quark and the two light quarks. In potential models, j, has an analogy with the total angular momentum of an electron in a hydrogen atom. Therefore, the properties of a charmed baryon are mostly dictated by its light-quark contents. In HQET, the final angular momentum of the baryon is given as



where 9c is the spin of the c quark.*

*For L = 0, we simply have I = -9 + Ic. But when L is non-zero, the angular momenta can be coupled as either 7 = (C + -9) + ? or I = -c + (9 + ?). Although the final physics






9


Table 1.2: The s-wave (both L and L, are 0) and p-wave (either L or L, is 1) charmed baryons and their quantum numbers: isospin (I), orbital angular momentum between the diquark and the c quark (L), orbital angular momentum between the two light quarks (LI), total spin of the diquark (SI), total angular momentum of the light degree of freedom (j,), and spin-parity of the baryon (JP). S, and j, are good quantum numbers in the limit of me -* oo.


The properties of all L = 0 (s-wave) and L = 1 (p-wave) baryons of cuu, cud, and cdd states are listed in Table 1.2. The lowest-lying L = 0 state is the A+, a cud state in which the ud diquark has isospin of I = 0. The state is antisymmetric under the exchange of the u and d quarks. Since it is required that the total Ispin, flavor) be symmetric, the spin state has to be antisymmetric. The the ud diquark must be in a S, = 0 state. Combining S with the spin of the c quark gives a total spin of J= 1/2. By convention, the A+, like all spatial ground state baryons, has positive parity.

For Ec states, which have I = 1, the diquark must have S, = 1 to satisfy the requirement of |spin, flavor) being symmetric. Adding S, = 1 with the spin of the does not depend on the order of coupling, the latter choice leads to a lar er amount of algebra in the calculations of most of the HQET models. The choice of i = + J I coupling also helps us derive the physical states more easily.


State I L L, S jI JP A+ 0 0 0 0 0 +
EC 1 0 0 1 1 + +
Aci 0 1 0 0 1
EcO 1 1 0 1 0 1
Ec1 1 1 0 1 1
Ec2 1 1 0 1 2 5
A' 0 0 1 1 0
0 0 1 1 1 A'c2 0 0 1 1 2
Ec 1 0 1 0 1






10


c quark results a doublet having JP = 1/2+ (Ec) and JP = 3/2+ (E*). A+, E,, and E* are called s-wave particles since there is no orbital angular momentum involved.

It is worthing mentioning that we have the similar L = 0 states in the strange baryon sector, A, E, and E*. An important fact is that


M(E*) -- M(Ec) m,
M(E*) - M(E) M

for the hyperfine splittings. Based on HQET, a hyperfine splitting arises from the color magnetic moment of the heavy quark. Since m,/mc ~ 1/3, the M(E*)-M(E,) is expected to be about one-third of M(E*) - M(E).

Now Let us consider the lowest-lying L = 1 (p-wave) particles. In the I 0 case, there must be S = 0 for the same reason as for the A+ baryon, so j= 1. The c quark brings hyperfine splitting to give two baryon states of JP = 1/2- and JP = 3/2-, where the negative parity comes from the one unit of the orbital angular momentum. This doublet is named A,,.

Same as Ec, for I = 1, we have S = 1. This gives j, = 0, 1, 2. Each of these is split by its hyperfine interaction with the c quark. This type of excitation ends up with five baryons: the Eco singlet, the Ec, doublet, and the E,2 doublet.

Another type of p-wave states come from one unit of the orbital angular momentum between the two light quarks, L, = 1. This implies that the I = 0 ud diquark must have S = 1. This produces j, = 0, 1, 2. Then the hyperfine splittings give five baryon states: the A' singlet, the A' doublet, and the A'2 doublet.

Finally, it can be easily derived that L, = 1 and I = 1 require S = 0. Then the hyperfine splitting gives a doublet of E'1 baryons. Note that the degeneracy of the L = 1 (Li = 1) and L, = 1 (L = 1) switches with the change from I = 0 to I = 1.






11


1.3.2 Strong Decays

All the charmed baryons we described in the last section will decay to the Al, since it is the lowest state of u, d, c compositions. The purpose of these research work is to get better understanding on how the E(*) baryons and even p-wave charmed baryons decay to A+.

To date, only the Ec triplet, two states of the E* triplet, and the A,, doublet have been found, and only strong decays through one or two pions have been observed. Based on the mass predictions by the relativized potential model[4], other p-wave baryons may decay strongly to the final states containing a A+ and one, two, or three pions, but this work failed see any more p-wave states higher than the A,,. In general, the higher states which have the same decay modes are expected to be wide and difficult to observe. So this dissertation only reports the studies of the E(*) and Ac, baryons. This subsection gives a brief review of the strong decays of these baryons.

The selection rules of these decay can be easily derived from conservation of parity and angular momentum. For a strong decay A -+ BC, where the spinparities of these particles are denoted by JP', J'B and 'C, and a possible orbital angular momentum between B and C is denoted by LBC, it is required that L must satisfy

1A = LBC+ B + C,

and

PA = PBPC 1)LBC

in order to decay with a partial wave corresponding to LBC. In addition, isospin has to be conserved in all strong decays.






12


Table 1.3: Allowed partial waves for strong decays of the E(*) and A,, baryons. The At7r7r mode listed in the table only represents the non-resonance decay mode.


Table 1.3 lists the all the possible decay channels for strong decays of the E(*) and Ac, baryons. The E(*) baryons do not have the Atlr7r decay because there is no phase space. They should entirely decay through Atir. The Ac, baryons do not have the A+7r decay because of isospin conservation. Based on the table, we should expect that the S-wave Ec7r would dominate the Ac1(1/2) decay. The Ac1(3/2) can only have D-wave Ec7r decay because of the conservation of total angular momentum; the Ac1(3/2)->E*7r decay would be S-wave, but is kinematically forbidden. Thus we should expect that P-wave non-resonance A+7r7r decay dominates the A,1(3/2) decay.


1.4 HQET Predictions on E(*) and A+i

Many quark models have the ability to make quantitative predictions on heavybaryon masses, and almost all of such models use the "constituent quark masses" which are derived from well-known hadron masses. Predictions vary from model to model, and they all fall in roughly the same range. Among all the models, the quark potential model developed by Isgur et al.[4, 6] is the most complete, and it covers all the baryons from the proton to bottom baryons.


Particle Decay Mode Allowed Partial Wave Ec A+ir P
A+7r P
Ac1(1/2) A77r P
Ac1(1/2) Ec7r S
A,1(3/2) A+1r7r P
Ac1(3/2) Ec7r D






13


Table 1.4: The constituent quark mass assumptions by the potential models. All numbers are in units of MeV/c2.


Table 1.5: Some charmed baryon mass predictions by the potential models in comparison with average values of experiments. All numbers are in units of MeV/c2. All uncertainties of the experiments measured numbers are less than 3 MeV/c2.


Quark Non-relativistic Model Relativized Model Experiment
A+ 2260 2265 2285
Ec 2440 2440 2453
E* 2510 2495 2518
A+(1/2) 2510 2630 2594
AC+(3/2) 2590 2640 2627


An important part of the potential models is to specify the constituent masses of quarks. Typical values used in both non-relativistic models and relativized models are listed in Table 1.4. Although they use different mass assumptions, both models work extremely well for light baryons and strange baryons, and their predictions on charmed baryons are also close. Table 1.5 lists some of the predictions[4, 6] compared with the average experimental values[1].

Potential model also predicted the masses of other p-wave charmed baryons. The masses of EcO (the next state higher than Aci) and Eci doublet are predicted to lie around 2770 MeV/c2, within 10 MeV/c2. Other nine states are also close to each other in masses and range from 2780 MeV/c2 to 2900 MeV/c2. Based on these predictions, unless some of these states have very narrow width, it would be


Quark Non-relativistic Model Relativized Model
u 350 220
d 350 220
s 550 419
c 1500 1628
b 5000 4977






14


difficult to see them. In our work, we looked at these mass ranges for A+7r' and Afw+7r-decays, and did not see any obvious signals.

The potential models can make calculations on decay widths but do not work very well. Their predictions are very rough and agree with experimental values only in their order of magnitude.

The most-recognized theoretical model which can predict heavy-hadron widths was developed by Yan et al.[16], who used the nonlinear chiral quark model[17] to calculate heavy-quark coupling to the Goldstone bosons. In a charmed baryon, the diquark with sP' = 1+ can be represented by an axial-vector field 0.; and the diquark with sP' = 0+ can be represented by a Lorentz scalar field 0. The decays 0, - 01+7r and 0, -> 0+7r can be described by two independent coupling constants gi and 92, respectively. For the decay E-+A+7r, the decay rate is determined by 92 and masses of the Ec, A+, and 7r. Their mode predicts


2
3

where gA is the coupling constant in the single-quark transition u -* d. gA is generally assumed to have a value of 1, but the experimental extracted value is 0.75[17]. g2 values are not very different from other theoretical predictions[18, 19, 20]. Their Lagrangian gives the following decay width:



r (EO A+ 7r-) = 922 AN 3(1) C C TflM~o(1.3)
27rff Mg''

F(E*0 E7r-) = g2 Mr
167f2 Mao""

where f, = 93 MeV/c2 is the pion decay constant and p, is the pion momentum in the center of mass frame. equation 1.3 predicts the total width of E since Ec decays 100% to Ap7r. equation 1.4, however, is invalid since the decay E*-*Ec7r is









kinematically forbidden. If we neglect the radiative decay width associated with the decay Z>a>c7,* the total width of E* is given by


F(E*) = g A MA+ 3 (1.5)
2 27r f,2 ME


92 = 0.612 (with gA= 0.75) will lead to


F(E,) = 2.45 MeV/c2,


F(E*) = 17.6 MeV/c2, if MIL; - MA+ = 233.5 MeV/c2.

Equations 1.3 and 1.5 show that the E, width is directly related to the E* width, which has been reported by CLEO collaboration[21]. This work includes the first attempt to measure that E, width. If these widths can be measured accurately, 92 can be derived from equation 1.3 or equation 1.4 and then further predicts the widths of other particles, for example, -.

Recently Pirjol and Yan[22] included all possible strong-interaction couplings (S-wave, P-wave, and D-wave) among and between s-wave and p-wave baryons in the chiral Lagrangian. This model contains 45 independent coupling constants up to and including D-wave interactions. Besides g, and g2, coupling constants h2, h3, h4, ... are involved, which correspond to the p-wave baryons. In this theory, they derived model-independent sum rules which contain these couplings and relate them to properties of the lowest-lying baryons. However, couplings h2 and h8, which correspond to lowest p-wave baryons, cannot be directly predicted from the constituent quark model. Using published A'+ masses[1] M(A'+(2593) - A+)
*A radiative decay can happen when the strong decay is largely suppressed. Since the widths of scst-+Ec7r decays have been measured to be around 16 MeV/c2, there should be almost no radiative decay.






16


308.6 MeV/c2 and M(A'i(2625) - A+) = 341.5 MeV/c2 together with 92 = 0.57,* and neglecting radiative modes A+ -+ At y, they calculated


F(A+ (2593)) = 11.9h2 + 13.8h2 - 0.042h2h8 (MeV/c2),


F(Aj (2625)) = 0.52h2 + (0.15 x 106)h2 - 5.2h2h8 (MeV/c2).

With F(A+ (2593)) and F(A+ (2625)), the values of h2 and h8 can be obtained, and they can be used to further estimate the width of other particles. Based on the published values of [(Aj(2593)) and F(A+(2625))[1], it can be estimated that h2 = 0.57_0 .3,


h8 < 3.5 x 10-3 (MeV/c2)1.

They further estimated that Eco and Ec1have widths larger than 100 MeV/c2, If these estimates are correct, it will be very diffucult to observe signals of next-level higher state baryons.

















*This value is the average value obtained from applying published masses[21] M(E*++ -A+) 234.5 MeV/c2 and M(E*0 - A+) = 232.6 MeV/c2 to equation 1.5.














CHAPTER 2
EXPERIMENTAL FACILITIES


2.1 CESR

The Cornell Electron Storage Ring (CESR) is an electron-positron collider with a circumference of 768 meters located on the campus of Cornell University, Ithaca, NY. It can produce collisions between electrons and positrons with center-of-mass energies between 9 and 12 GeV/c2. It serves both CLEO for the study of particle physics, and the Cornell High Energy Synchrotron Source (CHESS) for a variety of biological and surface physics studies.

A diagram of CESR's main components is shown in Figure 2.1. This accelerator consists of three major parts: (1) the linear accelerator (LINAC), (2) the synchrotron, and (3) the storage ring. Electrons are accelerated to 150 MeV/c2 by the 150-foot LINAC. Positrons are created by 50 MeV/c2 electrons colliding with a thin tungsten target part-way through the LINAC. The electrons and positrons are then boosted to the operating energy of about 5 GeV/c2 by the synchrotron and transferred into the storage ring, where they can be maintained in the storage ring for about 1 hour in order to achieve the highest integrated luminosity.

Electrons and positrons travel in opposite directions around the storage ring in evenly spaced bunches (currently there are 9) at 390,000 revolutions per second. Electrostatic separators hold the electron beam and the positron beam slightly apart from each other, and two beams only collide in one place - the center of the CLEOII detector.


17






18


CESR



SYNCHROTRON



WEST EAST
TRANSFER TRANSFER
LINE LINE






LINAC ee+






7s1 CLEO II $ Positron Bunch - Clockwise Electron Bunch - Counter Clockwise



Figure 2.1: CESR layout. The CESR lies in a tunnel 50 feet underground. CLEO-II and the LINAC reside in Wilson Lab.






19


2.2 CLEO-II


CLEO-1I is a multipurpose high energy physics detector incorporating excellent charged and neutral particle detection and measurement used to analyze electronpositron collision events generated by CESR. It is operated by the CLEO collaboration of over 200 physicists from many institutions, including the University of Florida.

Side and end views of the detector are shown in Figure 2.2 and Figure 2.3, respectively. The major components (going outward from the beam pipe) are the central detector (CD) which forms the tracking system, the time of flight (TOF) system, the electromagnetic calorimeter (CC), the 1.5-Tesla superconducting magnet, and muon chambers. The central detector comprises the Precision Tracking Layer (PTL), the Vertex Detector (VD), and the Drift Chamber (DR). CLEO-II is also equipped with timing, trigger, and data acquisition systems. Brief description of the CD, TOF, and CC are given in the following since they are the most important in this analysis.


2.2.1 Tracking System

Charged particle momentum is measured by three cylindrical, coaxial wire chambers sharing a common axis in the direction of the beams.

Figure 2.4 shows the structure of PTL and VD. The PTL is a cell-strawtubedrift-chamber which extends within 1 cm of the 3.5 cm beam pipe. The device consists of 6 layers of mylar tubes with 64 axial wires per layer. It is used to make precise measurement of the transverse position of the particle near the interaction point, with a resolution of 90 Mim; and it does not provide longitudinal information. The VD covers the radial region from 7.5 to 17.5 cm. It has 10 layers of hexagonal cells as shown in Fig. 2.4. arranged in 10 layers. The VD provides a tracking resolution of 150 pm in r - # and 0.75 mm in z.







20


Muon Chambers Outer Iron

Inner Iron

Return Iron


--


- Magnetic Coil Barrel Crystals


Time of Flight Central Drift Chamber L Endcap Crystals
Endcap Time of Flight Beam Pipe


FL


Figure 2.2: Side view of the CLEO-I Detector.


PTL and VD


W< NRY111 M\\\\\\\


I I i

_T_





















Muon Chambers



Inner Iron Magnetic Coil
Barrel Crystals Return Iron Time of Flight





Central
Drift Chamber











Beam Pipe PTLA and VD


Figure 2.3: End view of the CLEO-II detector.


21

















.Oute







16.cm - . ' . + . -* . * . ++

.4.-.. *4 -+ . ---!VD
- 4 . - .- .I




* - .
- - * . .
\. . T








- . -.*
4.. cm Be B










\* 4 .4
. I . VD.4



N. . + .+ Ac Inner



8.1 Cm'
PTL







4.5 cm'NNBe

3.5 cm


r Cathode Strips










- Field Wire + Sense Wire










* Cathode Strips


eampipe


0.0 cm + Interaction Point


Figure 2.4: The VD/PTL wires.


')9









23


DR Outer Shell


.~o ..

..


..o -


0. 0 . 0


.0.








..



..


-o


.-0


-.-


S * 0 * . . . * 051 S 0 . .0. * - -50



- -... ... -48



-o-o- .*-o 46

* . . . . . . * 45



.-.. ...0 43

-e.. ..*. 42
S-0 *-o*0 * ., 48 o 0 *0 *0 *0 .46


DR Outer Cathode Strips


- Field Wires
oStereo Sense Wires eAxial Sense Wires . .00.0-O-0.0..
.0 - .... - ..... - 12



S .10

0 0 9
. . . . . . . . . . . . . . 0 .

. . * . . . - 0 - 0 - . . . . * 0 9






o. 0 50
. 0 - . 0 -0 - 0 . ' . - 0 .





'.. -: .0 04
S .. 0 - .
.. 0 . 0




DR inner Cathodes DR Inner Shell

VD Outer Shell


Figure 2.5: The DR wires.






24


Transverse and longitudinal momentum are best measured by DR, shown in Figure 2.5. This 51-layer outer drift chamber extends from 17.5 cm to 95 cm, including 12,240 sense wires and 36,240 wires. One sense wire and three field wires make a rectangular cell structure. There are 40 axial (parallel to the beam line) layers and 11 stereo (not parallel to the beam line) layers. Axial layers measure transverse momentum, the radial distance of the closest approach to the beam line, and the azimuthal direction of tracks. The stereo layers and 2 cathode layers measure the polar angle and the longitudinal position of the intersection of the track with the beam axis. Sequential layers are offset in azimuth in order to resolve left-right ambiguity in drift distance. An r - # position resolution of 110 prm for the axial wires and a z position resolution of about 3 cm can be obtained with this chamber.

Particles can be identified from the specific ionization energy loss (dE/dx) in the DR. The characteristic bands of dE/dx quantity as a function of momentum for different species of particles are shown in Figure 2.6. Protons can be well separated from other particles at momenta below 1 MeV/c, and separation between pions and kaons is possible only below 400 MeV/c.

Track-reconstruction programs are used to find a charged-particle track in an event. First, the pattern of hits, which are the records of the wirescaused by the ionized gas molecules, are recognized; then these hits are fitted to obtain the trajectory of the original particle.

The data from all three chambers are combined to measure the momentum vector of charged particles. Two major factors limit the momentum resolution - multiple scattering and the position resolution of the track. Multiple scattering dominates the resolution at low momentum, and the position resolution dominates at high momentum, where the track curvature is small.













CLEO-II dE/dx








d PIPp
K





-e


I I I I


I I I I


0.5


1.0


Momentum (GeV/c)


1.5


Figure 2.6: dE/dx plotted against momentum for different particles.


25


15






10
E
C,
U


x

-o


0


0.0


I I I


Z)






26


The CLEO-II charged-track momentum resolution has been measured to be


6p/p = 0.0052 + (0.0015)2p2


where the momentum p is in GeV/c. The first term represents the contribution from multiple scattering, and the second term is the contribution from the curvature measurement error. The two terms give equal contributions at a momentum of 3.3 GeV/c.

Charged particles with a transverse momentum greater than 225 MeV/c and a polar angle less than 450 will reach the outer radius of the DR and pass through the TOF counters and crystal calorimeter. These tracks are the best measured in the CLEO-1I detector.


2.2.2 Time-of-Flight System

Besides dE/dx measurement in DR, the TOF device is also an important tool for particle identification. The TOF system has two major parts: a barrel system covering polar angles from 36' to 1440, and an endcap system covering polar angles from 15' to 360 on one side and 1440 to 1650 on the other side.

The barrel system, which is located immediately outside the DR, consists of 64 plastic rectangular scintillation counters, and an endcap system consists of the same but wedge-shaped counters. The scintillators are 5 cm thick and 2.5 m long. Lucite light pipes are attached at each end of the scintillators and connected to photomultiplier tubes.

It takes a 500 MeV/c pion about 3.5 ns to travel from the interaction region to the barrel TOF counters, while it takes a kaon about 4.5 ns. The time resolution for pions in hadronic events is about 150 ps. Figure 2.7 plots 1/0 (0 = v/c) against momentum. As we can see in the plot, the distinction in the bands separates K - 7r















3.0




2.5




S2.0




1.5


0.0


0.5


1.0


1.5


2.0


2.5


Momentum (GeV/c)


Figure 2.7: Time-of-flight of different particles plotted against momentum.


27


P

K-


7T


I I I I I I I I I I I I i I , , . 1 1 1


1.0






28


up to momenta of about 1.1 GeV/c, and protons can be separated up to momenta of about 1.5 GeV/c2. Like the energy loss information, particles can not be well identified by TOF at high momentum.


2.2.3 Electromagnetic Calorimeter

The CsI crystal calorimeter is used to detect photons and to measure the energies of tracks. It is composed of 7800 thallium-doped cesium iodide scintillating crystals, 6144 in the barrel region and 828 in each endcap, covering 95% of the solid angle. Each crystal is 30 cm long and 5 x 5 cm2 in cross section.

When a photon or a charged particle interacts with the atoms in the crystal, an electromagnetic "shower" is emitted by crystals, and it is recorded by 4 Si photodiodes at the back of each crystal. The device allows detection of photons with energy of 30 MeV/c2 to 5.3 GeV/c2 with excellent resolution.

Photon energy resolution in the barrel (endcap) is 1.5% (2.6%) at 5 GeV/c2, and 3.8% (5.0%) at 100 MeV/c2. The angular resolution in azimuth is 3 mrad (9 mrad) at 5 GeV/c2 and 11 mrad (19 mrad) at 100 MeV/c2.

A typical 7ro (from the decay ) finding efficiency is about 50%, and the width of the reconstructed 7r0 peak is roughly 5 - 10 MeV/c2.














CHAPTER 3
A+ RECONSTRUCTION


3.1 Introduction


In order to study the charmed baryons which decay to A+'s, we first need to obtain At candidates, then add additional pions (one or two in our study) to reconstruct heavier charmed baryons.

Fifteen hadron decay modes were used to reconstruct A+ candidates. They
-0 -0 0
are pK-7r+, pK-r+7r , pK, pK 7r07r, pK7ro, Alr+, Alr 7r+7, A7r+7ro, AK+R, E+7r+7r-, E+7ro, E+K+K-, E07r+, =-K+7r+, and =OK+. All these decay modes have good signal-to-noise ratios and reasonable statistics. The decay pK-7r+ has a very large branching fraction and contributes almost half of all A+ candidates. It important to check the consistency of measurements by comparing the results obtained by using the pK-7r+ mode with those obtained from other modes.


3.2 Data and Monte Carlo Sample CLEO data are taken on and off the T(4S) resonance. The beam energy is 5.187 to 5.280 GeV/c2 for off-resonance and 5.285 to 5.295 GeV/c2 for on-resonance. We performed our analysis using both on-resonance and off-resonance events in datasets 4S1-4SG,* corresponding to a luminosity of 4.8 f b-1.

All Monte Carlo events generated were with the A+ mass 2286.7 MeV/c2, which is our measured mean value over all the 15 decay modes. In order to optimize
*Each time CESR or CLEO is updated, the data are processed differently, and they become a new dataset. Conventionally, CLEO datasets are named 4S1, 4S2, ..., 4S9, 4SA, 4SB, ..., and so on. "4S" indicates the state T(4S).


29






30


Table 3.1: Monte Carlo (MC) generated branching fractions for A' and E(*) studies.


Decay mode Average B/B(pK-7r+) MC generated branching ratio
pK-rT+ 1 0.158
pK-7r+7r 0.67 0.04 0.11 0.106
pK 0.46 0.02 0.04 0.073
pR07r+7r- 0.52 0.04 0.05 0.082
pROr0 0.66 0.05 0.07 0.104
Ar+ 0.18 0.03 0.028
A7+7+7- 0.66 0.10 0.104
Ar+7r0 0.73 0.09 0.16 0.115
AK+KO 0.12 0.02 0.02 0.019
E+7r+r- 0.68 0.09 0.107
E+70 0.20 0.03 0.032
E+K+K- 0.07 0.01 0.01 0.011
E07+ 0.20 0.04 0.032
=-K+7r+ 0.10 0.02 0.016
=OK+ 0.08 0.01 0.01 0.013
All 1


the cuts* used to reconstruct each decay mode, 15 individual types of events are

generated by sufficient amounts (more than 100,000 events for each mode). In our

later study on the A+ or the E(*) decaying to the A+, we need the Monte Carlo to

provide the correct over-all efficiencies. Thus the decay ratios of A+ decay modes

were generated as shown in Table 3.1. In the table, the average relative branching

ratios for pK-7r7r, pK , pKo7r+7r-, and pRro are the values recently measured

by CLEO[23]. For other modes we used the PDG average values[1].
*A cut is an action to remove a certain fraction of the events which contribute mostly to the background. An optimized cut on a measured physical quantity is the one which gives the best signal-to-noise ratio after it is applied.






31


3.3 Event Selection


3.3.1 Track Selection

When a charged particle travels through the tracking chambers, a set of hits, caused by the passage of the track, is generated. The tracking program will fit each set of hits forming a "track," which is a curve representing a possible particle causing the hits. In CLEO, this task is accomplished by the track-finding and fitting program, DUET.

Each track is described by the following five track parameters: (1) CUCD: curvature of the track; (2) FICD: # of the direction of the track at point of closest approach to the center of the CLEO-II detector; (3) DACD: impact parameter of track with respect to the center of the detector; (4) CTCD: cotangent of the polar angle, 9 (i.e. CTCD = 0 for tracks in the r - 0 plane and infinite for tracks pointing down the beam pipe;) (5) ZOCD: z coordinate at point of closest approach to the center of the detector. All other information about the track can be calculated from these five parameters.

Before 1996, the track fitter in the CLEO DUET processor ignored the energy loss of a track in materials and included multiple scattering approximately. In 1996, the CLEO collaboration reprocessed the data from 4S1 to 4SG, and the new data are called the recompressed data. For the recompressed data, the old track fitter is replaced by a Kalman Filter. The new Kalman fitter optimally treats both multiple scattering and energy loss, so it gives improved error matrices of track parameters for all tracks and better-measured track parameters for low-momentum tracks. It also fits each track separately for each particle hypothesis.

To select a track as a candidate for a pion, a kaon, or a proton, which come from the r - # range of e+e- interaction points, we first require it to have not only r - #






32


also z information. We reject all tracks which are identified inward going. To ensure these tracks are close to the interaction point, we used the following "track quality" cuts:

JDBCDJ < 5 - 3.8|PI (mm) if JPJ < 1,
1.2 mm if 1PI > 1,

where DBCD is the radial distance of the point of closest approach to the beam line, P is the momentum of the charged track; and


JZ0CDJ < 5 cm.


Note that the DBCD cut changes from 5 mm at 0 momentum to 1.2 mm at 1 GeV/c and then becomes flat from 1.2 mm. This is because the low-momentum tracks are more poorly measured, but we still want to keep those having fairly good quality.

Such selected tracks are used as the charged track candidates which are directly decayed from At's. The A+ has a mean lifetime of about 2 x 10-'s, so its flight distance in the CLEO detector is within the range of interaction points and is negligible in the invariant mass reconstruction.


3.3.2 Particle Identification

As we discussed in the last chapter, two types of detectors are used for the identification of the charged tracks: the time-of-flight counters and the drift chamber for the dE/dx measurement. The information from each device, if present, is quoted as the number of standard deviations of the measurement from the expected value as a given particle hypothesis. For each charged track, we combine the TOF and the dE/dx information to define a joint


2 (dE/dx)meas - (dE/dx)xp 2 [(TOF)meas - (TOF)exp12
Xi OdEldx I TOFI






33


where i stands for pion, kaon, and proton hypothesis.

The x2 ranges from zero to infinity and it is not very convenient to use when we perform a track identification cut. So, a equivalent parameter, the x2 probability, PROB, is calculated for each hypothesis. PROB ranges from zero to one.* For data analysis, it has the advantage of being flat in the zero to one range for particles which are the right species and peaking at zero for particles which are the wrong species.

One particle identification information will be used if the other device does not have the measurement. If neither TOF nor dE/dx information is present, we assume the track is a pion and assign it a small PROB(7r) value.

In this work, we are more concerned about separating protons, kaons and pions from each other, so a normalized probability, called "PROB level," is used. To strongly identify a proton or a kaon, we make a cut on


PRLEV PROB(p)
PROB(p) + PROB(K) + PROB(7r)

or,

KALEV PROB(K)
PROB(p) + PROB(K) + PROB(r)

We do not use a PROB level cut for pions, since we take all the tracks selected as pion candidates.


3.3.3 -y and 7r0 Finding

Although the CsI electromagnetic calorimeters can measure the photon energy and angle, they also interact with hadrons. An electromagnetic shower generally has different lateral development than a hadronic shower. This provides us a way
*Note it does not really represent the probability of the track to be a specific particle hypothesis.






34


to distinguish them from each other. The quantity E9/E25 is measured as


Energy of 9 central crystals
Energy of 25 central crystals


Here the 9 crystals in the numerator are those in a 3 x 3 array, with the most energetic crystal at the center. The 25 crystals in the denominator are those in a 5 x 5 array. Since electromagnetic showers tend to be more narrowly contained than hadronic showers, they mostly have E9/E25 near 1. The most widely used cut on E9/E25 quantity in CLEO is to keep 99% photons* and get rid of most of the hadronic showers. A E9/E25 cut also gets rid of two photons which are close together. Also, as the high energy showers near to each other often deposit energy to the same crystals, we can use a program to "unfold" the nearby shower clusters. The unfolding routine works well to identify high energy photons but become less efficient when photon energy is low. When we select a photon in this analysis, we mostly use unfolded E9/E25 at 99% (this cut is called 99% E9E25U), and sometimes directly use E9/E25 at 99% (not unfolded, called 99% E90E25) when we are certain that the photon energy spectrum is low.

To 's are formed by taking two photon combinations and calculating the di-photon invariant mass. The di-photon combination must have at least one photon in the barrel region of the crystal calorimeters.

Unless otherwise stated, we always selected 7r0 candidates as just described. In addition, we require the mass of each candidate to be within 2.5 uM,0 of the known 7r0 mass, which is 134.976 MeV/c. However, to suppress combinational background, we will place cuts on 7r0 momenta in different situations.
*This cut value is actually obtained by a program which returns E9/E25 cuts for 1% efficiency loss in a given region of the detector. The 1% is nominal only from MC, and it is a loss in an event with no other showers. Actual efficiency losses are substantially more, e.g., 5-10% efficiency loss for photons in hadronic events from a 1% cut. Harsh cuts, like 5% or 10%, lose too many photon candidates, so they are not often used.






35


3.3.4 Event Vertex Finding

Finding the event vertex, which is the e+e- interaction point, can be very useful to improve the mass resolution of a reconstructed particle. Most of the charged tracks come from the event vertex or vertices extremely close to the event vertex, so we can obtain the event vertex with errors by performing a vertex fit using charged tracks. However, some tracks are not from anywhere close to the event vertex, and some tracks are not measured correctly. Using these tracks will increase the uncertainty of the event vertex. Therefore, to find the event vertex, we start with the two tracks which are the most consistent with the beam position and also not close to back to back, form a vertex, then add more tracks one by one in the order of their consistencies with the current found vertex, until further adding any track would make a poorer vertex fit. If the error of the final found vertex is not small enough to confine itself within the spread of the beam position, or if we do not have more than one charged track, the beam position will be used as the event vertex.


3.3.5 Vee Finding

A large fraction of A+'s decay to K0's or A's. In CLEO, the K0 is reconstructed by the decay Ks --+ +7r--* and the A is reconstructed by its decay to p7r-. Ks's and A's mostly fly a few centimeters away before they decay. The Ks has cr = 2.7 cm and the A has CT = 7.9 cm. Since in each case the shape of the two daughters' paths looks like the letter V, they are generally called Vees. The vertex of a Vee formed by the two charged tracks is called a secondary vertex, in distinction to the primary vertex, the event vertex.

To find Vee candidates, we first list the tracks which satisfy -DBCD/DDBCD > 3(DDBCD is the estimated uncertainty of DBCD) to exclude the tracks coming from the

*KO appears in the states of Ks (50%) or KL (50%). CLEO detector cannot detect the KL since it travels many meters long (cr = 15.5 m).






36


primary vertex. The tracks in the list, called the secondary tracks, are all possible daughters of Vees. Then we take every pair of tracks from the list and fit them to form a vertex. We discard the pair if the fit is very poor (X2 < 0.001) or if the significance of the three-dimensional flight distance is smaller than 30-. We require the total number of hits inside the found vertex for both daughters to be smaller than 2. Also, the reconstructed mass of a Vee should be within 3 aM of the known Ks or A mass. Note that the Kalman Filter only calculates the track parameters of the secondary tracks from the origin. We corrected these track parameters at the secondary vertex, then further recalculated the momentum and the position of the Vees. Details of the CLEO secondary vertex finding program are described by Prescott[24].

In this analysis, we made a few more cuts on Vee candidates to make the signal clearer with a tiny sacrifice of losing events: a Vee is required to come from the range of the beam position; the separation in z of the two daughters at the r - 0 intersection should not be large (the significance is required to be smaller than 5); for a Ks candidate, each daughter must satisfy PROB(7r) > 0.001; for a A candidate, the daughter which carries most of the momentum in the decay in the laboratory frame (according to special relativity, this almost guarantees that it is the proton if its parent is really a A) must satisfy PROB(p) > 0.001.


3.3.6 E and 7 Finding

The decays of the four E and 3 are shown in Figure 3.1. Because these particles are supposed to be the decay products from the A+, which has very short lifetime, it is very reasonable to assume that they all come from the event vertex.

E+ candidates are reconstructed through the decay E+ -+ pir0. The 7r' selection is described in Section 3.3.3. All charged tracks are taken as proton candidates.






37


(a)


IC0
I
I
I
I


I '
p I'I


A


(c) IV







A


YI


(. . . . . .


7C 0


I, I, I,


/


'0


Figure 3.1: Decay paths of (a) E+ -+ p'ro and 7r0 -4 Y, (b) EO - Ay and A -+ p7r,
(c):- - A7r- and A - p7r-, and (d) 70 -- Ar', A -+ p7r-, and 7r -* y. In each
figure, the solid curves indicate paths of charged particles; the dashed lines indicate paths of photons; and the dotted lines indicate paths of neutral hyperons. All E and E are assumed to be created at the event vertex, which is shown as .. The E+,
-, 0, and A travel for a distance before decay. The E and 7r0 decay immediately after being created.






38


A particle identification cut PRLEV > 0.5 is used. After adding the 4-momenta of the proton and the 7rw, the flight distance of E+ can be calculated by constraining the E+ coming from the event vertex, and, further, the E+ decay vertex can be obtained. Since the E+ has a long lifetime (cr = 2.4 cm), we require the transverse flight distance of the E+ to be bigger than 5 mm and DBCD of the proton to be bigger than 0.5 mm. In addition, to reduce the combinational background, we make a momentum cut of 300 MeV/c2 for the 7r0 and 500 MeV/c2 for the proton. We require the mass of each E+ candidate to be 20 MeV/c2 within the known E+ mass, 1189.4 MeV/c2.

E0 candidates are reconstructed through the decay EO -+ Ay, where selections of the A and -y are described in the previous sections. A 50 MeV/c2 photon energy cut is used to reduced the background. We require the mass of each E candidate to be 20 MeV/c2 within the known E0 mass, 1192.6 MeV/c2.

E- candidates are reconstructed through the decay -+ Ar-. All negativecharge tracks are used to be the 7r- candidates. The has CT = 4.9 cm so its decay vertex should be distinctly displaced from the event vertex. The initial guess of the -- vertex is at the intersection of the projected A path and the 7r- track. The combination is discarded if the vertex cannot be reasonably formed or the combined direction does not point back to the event vertex. The invariant mass of Ar- is required to be within 6 MeV/c2 of the known -- mass, which is 1197.4 MeV/c2. Then the track parameters of the A and the 7r- are recalculated at the new vertex by constraining the Air- invariant mass to be 1197.4 MeV/c2. The E- momentum and vertex are further obtained more accurately. The -- flight distance is required to be larger than 5 mm, and its r - # radial distance is required to be larger than 1mm.
=0 candidates are reconstructed by a -O * A70. We initially build the 30 vertex, then combine the 7r0 angle with the projected A path. The combined direction is






39


required to point back to the event vertex. We correct the 7rO 4-momentum by constraining it to come from the EE vertex. Then the EO 4-momentum is recalculated. The reconstructed 0 mass is required to be within 8 MeV/c2 of the known E. mass, which is 1315 MeV/c2. The r - 0 radial distance of the E vertex from the event vertex has to be larger than 5 mm. A 100 MeV/c2 7r0 momentum cut is used.


3.4 A+ Selection


A A+ is reconstructed by calculating its 4-momentum and decay vertex from the momentum, mass assumption, and vertex information of its direct daughters. The A+ signal can be measured by fitting its reconstructed mass spectrum using Mnyit.[25]* Mnlit is an interactive plotting and fitting package that uses MINUIT[26] to fit histograms or data read in from a file and to display the fitting results. It is widely used by high energy experimental groups to perform data analysis.

Although the purpose of reconstructing the A+ baryons is to observe the A' and the Ec which decay to the At, our At candidates are not selected by direct optimizing the At or E(*) signals. The A+ or E, signals should not be biased by At selection. In general, for each At decay mode we try to use cuts to get the best signal-to-background ratio at x, > 0.5. x, is the At momentum normalized to the maximum possible At momentum, defined as



E2 - M '


where E is the energy of the e+(e-) beam of CESR. Note that xP > 0.5 is only used to optimize the At selection cuts, and not for A+ selection. The momentum
*In this dissertation, all histograms, fitted curves and direct statistical results are obtained from Mn-Fit.






40


spectra of charmed hadrons from the e+e- annihilation have been shown to be hard compared to the combinational background. Therefore a cut on x, is a very good way to improve the signal-to-background ratio. For most of the decay modes, the X, > 0.5 cut makes the signal be roughly same large as the background. Later, when we look at A+ or E(*) signals, we make x, cuts on these heavier baryons, and there will be no cut on the x, of the A+.

Since a A+ travels at a distance of the order of 100 pm before it decays, its vertex can be slightly displaced from the event vertex. We find that constraining all direct A+ daughters (except 7ro's which do not have position information) to come from an unknown vertex significantly improves the mass resolution of the A+. Thus for each of the 15 decay modes, the A+ candidate is built at its vertex.

For the decay modes containing a proton, strong particle identification cuts are needed. Since the proton momentum spectrum are different for different decay modes (generally higher for two-body decays and lower for three-body and fourbody decays), the cut value on PRLEV does not correspond to the same efficiency for the different modes of background rejection. The numbers we used - 0.3 for pR0, 0.6 for pK-7r+, and 0.8 for pK-7r+7r, pI7r07r , and pROrO- have roughly the same efficiencies. For the two modes containing a proton and a K-, the identification cuts are relatively softer since the proton is already strongly identified. Since the signals of E+K+K-, W-K+7r+, and 2OK+are already very clean, very soft PROB(K) cuts are used to keep the highest efficiencies. To suppress combinational background, Monte Carlo optimized momentum cuts on charged tracks or 7ro's are used. For charged particles, we generally cut at high values for two-body decays and lower values for multi-body decays. All decay modes containing a 7r0 have very high backgrounds, so we always need restrictive cuts on 7r0 momenta.






41


Table 3.2: Particle Identification and Momentum cuts used in the 15 decay modes for the A+ selection. The values of physical parameters in the table are required to be larger than the corresponding numbers listed. The momenta PK+, P, , and Pro are in units of MeV/c.


The cuts used to reconstruct Ar's for each decay mode are listed in Table 3.2. Note that the vertex constraint routines are common for all modes. The selection criteria of all immediate A+ daughters have been described in previous sections.

Figures 3.2 to 3.16 show the reconstructed mass of A+ for the 15 idividual decay modes, and Figure 3.17 shows the sum over all modes. For the purpose of display a XP > 0.5 cut is applied to the A+ momentum.

The measurements on all 15 modes and their summation are tabulated in Table 3.3. All parameters are obtained by fitting the signal with a single Gaussian. The Gaussian width of each decay mode reflects the detector resolution of the A+ mass. The table shows that the fitted widths agree very well with those of the Monte Carlo, except some modes with a Tr and "All." For the modes with a TrO, we found that the widths are all wide and the signals could not be fitted well by a single Gaussian.


Decay PRLEV KALEV PROB(K) PK P, Pro
pK-7r+ 0.6 0.2 100
pK-7r+7r0 0.8 0.5 200 500
PKO 0.3
pR r+ir- 0.8 500
pK7r0 0.8 500
Ar+ 300
A7+7r+ir- 200
Ar+TO 300 500
AK+K' 0.3
7r+7r- 100
E+70 300 E+K+K- 0.02 100
E07+ 400
=-K+7r+ 0.01 100
=OK+ 0.01 300








42





5000



4000



3000




100
0
~Z20001000




2.10 2.20 2.30 2.40 2.50
GeV/c2 Figure 3.2: Invariant mass of pK-7r+







400




300




200
Lfl









0
2.10 2.20 2.30 2.40 2.50
GeV/c2 Figure 3.3: Invariant mass of pK-7r+7r.















600 500



400 300



200 100


F









K . . . I . . . . . .


2.10 2.20 2.30
GeV/c2

Figure 3.4: Invariant mass


400 300


200 100


2.40


of pK.


L;
2.10 2.20 2.30 2.40 2
GeV/c2

Figure 3.5: Invariant mass of pK7r7ro.


2.50


.50


43


U UN


U
N


0
N (6
C
a,


- -


'







44


160




120



N,

80
c -,



40




0
2.10 2.20 2.30 2.40 2.50
GeV/c2 Figure 3.6: Invariant mass of pK 7r.









500



400



300

4,
0
21 2002



100




2.10 2.20 2.30 2.40 2.50
GeV/c2

Figure 3.7: Invariant mass of A7r+.








45


1000 750




2 500250




0 ' ' ' ,' '
2.10 2.20 2.30 2.40 2.50
GeV/c2 Figure 3.8: Invariant mass of A7r++7r-.









500



400 300


0
200 .



100



0 ' ' '
2.10 2.20 2.30 2.40 2.50
GeV/c2 Figure 3.9: Invariant mass of A7r+7r'.















50



40 30



20



10


0
2.10


2.20


2.30
GeV/c2


2.40


Figure 3.10: Invariant mass of AK+RO.


300


2001


100


"I


2.20


2.30
GeV/c2


2.40


U
2.10


Figure 3.11: Invariant mass of E+7r+r .


46


0 LJ


2.50


U? bJ


-


2.50


-~








47


30




U
> 20U?,



10






2.10 2.20 2.30 2.40 2.50


Figure 3.12: Invariant mass of E+7r'.













30





U
2






U. ,





2.10 2.20 2.v 22
FeV/C Figure 3.13: Invariant mass of Z+K K-.















240 200 160


120


80


40


2.10


2.20


2.30
GeV/c2


2.40


Figure 3.14: Invariant mass of E07r+


160


120




80




40


5.10


2.20


2.30
GeV/c2


2.40


Figure 3.15: Invariant mass of E-K+7r+


48


L.J


. ..I.. ..


2.50


0
M
Vq




LJ


2.50


0


--

















-
















60


40 20


01
2.10


2.20


2.30
GeV/c2


2.40


Figure 3.16: Invariant mass of 'oK+


2.20


2.30
GeV/c2


2.40


Figure 3.17: Invariant mass of A+ candidates reconstructed by Although the distribution overlaid by 15 different Gaussians is Gaussian shape, we fit it by a single Gaussian to roughly check value and the signal-to-background ratio.


15 decay modes. not exactly in a the central mass


49


4,

0
N
C 4' LU


2


2.50


6000


4000


U?
>


0

-W
C

b>


I I I I-


2000!


I.'


2.10


2.50


I . . I , , , I I . I I . I I






50


Table 3.3: Masses, Monte Carlo widths (om (MC)), Fitted widths (Um(Fit)) together with the number of Ar's found with x > 0.5. The mass for all modes is the errorweighted mean value over all modes and the same value is obtained when we fit Figure 3.17. The signal the background shown in the table are the fitted areas within 1.6am (Fit) around 2286.7 MeV/c2. Masses and widths are in units of MeV/c2. Only statistical errors are shown. The statistical errors on Monte Carlo width are all 0.01 MeV/c2.


Decay Mode Mass um(MC) I um(Fit) Signal [ Background
pK-7+ 2286.7 0.1 5.20 5.26 0.11 9650 11660
pK-7r+7r 2286.4 0.6 8.11 9.04 0.62 1252 1928
pKO 2287.1 0.2 6.51 6.33 0.23 1716 1019
pk7r+7r- 2287.1 0.3 3.98 4.07 0.30 568 690
pK7r0 2285.2 0.6 8.61 7.63 0.63 514 490
A7r+ 2287.8 0.3 7.03 7.15 0.31 1368 658
A7r+7+7r- 2287.0 0.2 5.28 5.37 0.21 1916 1812
A7r+70 2285.0 0.4 10.38 11.18 0.56 2007 1864
AK+K 2286.5 0.4 2.91 2.51 0.32 70 25
E+7r+7r- 2287.6 0.3 7.41 6.96 0.38 947 696
E+70 2284.0 1.7 10.32 9.80 0.23 95 101
E+K+K- 2287.0 0.4 2.61 2.54 0.31 65 18
E07r+ 2286.5 0.6 7.54 7.79 0.59 707 896
-K+7r+ 2286.7 0.1 3.50 3.27 0.25 317 171
=0K+ 2286.9 0.5 6.73 6.10 0.51 221 173
All 2286.7 0.1 20675 22160


If we fit them by a double-Gaussian, the data and the Monte Carlo are in better

agreement (about half way closer). Thus we can conclude that the Monte Carlo can

predict the mass resolution of the A+ very well.

Note that our measured mean value of A+ mass, 2286.7 MeV/c2, is slightly

larger than the PDG mean value 2284.9 0.6 MeV/c2, which is partially determined

by the result of CLEO-I.5[27]. CLEO-II has measured many more decay modes

with much better mass resolutions and tiny statistical errors, and has constantly

shown a higher value. So in this work, we decided to use the CLEO-I value as

the "known" A+ mass. As we will show in later chapters, as we look at A+ or E(*)






51

mass by mass differences with A+, the error on A+ mass contributes little to the systematic errors of our measurements. The purpose of this work does not include the A+ mass measurement. It should be a separate research work which will require a comprehensive study of the systematic uncertainties of the mass scale.













CHAPTER 4
STUDIES OF A+ BARYONS


4.1 Introduction


Two particles have been found decaying to A+ and two charged pions. They have been named A+(2625) and A+(2593) by the Particle Data Group[1]. The first observation of the A+(2625) was made by the ARGUS Collaboration[28]. The E687[29] and CLEO[30] Collaborations subsequently confirmed this charmed state. CLEO also reported the first observation of A+(2593), and E687[31] and ARGUS[32] published the confirmation of these states. Since hese particles were seen only in A++7r- modes but not in A+70 mode, they are believed to be the excited A+ baryons rather than higher states of E, baryons, which decay through both A+ir and A>+7rx channels but should prefer Afr modes. Proposed by the previous experiments and strongly confirmed in this work, the two states are a fine structure doublet of the excited A+ baryons in which the light diquark ud has an orbital angular momentum L = 1 with respect to the c quark, Therefore, even though they were called A*+ in previous experimental publications just referred above, we prefer to call them the A+(2593) and A+j(2625),* where subscript 1 refers to the total spin of the light degrees of freedom.

The A+ (2593) decays largely, and perhaps entirely, into EXr. As explained in Chapter 1, this is the expected dominant decay channel. The quark model predicts that E, has JP = 1/2+, so almost certainly the A+(2593) has JP = 1/2-. The
*They are called A+ (1/2) and A+ (3/2) in Chapter 1 in order to conviently distinguish the spin difference. But the general convention to name a excited state particle is to used the particle name followed by its first observed mass.


52






53


JP of the A+(2625) is expected to be 3/2-. The A+(2593) and the A+(2625) are presumably the charm counterparts of the strange particles the A(1405) and the A(1520).

Since the last publication of these states in 1995, the CLEO-II detector has collected 60% more data, and the recompress made in 1996 significantly improved the resolution of low-momentum tracks, which is very important in order to observe A+ -+A+r+7r decays. We think it is time to confirm or update our previous results and look for a new decay channel, A7r070.

In this chapter, we first describe Monte Carlo simulation of A+ decays. This is followed by the observations of A+7r+7r- and Ar 07r 0 signals. Then we present our measurements on Ec7r decay substructures and the search for the decays of A+7r0 and At-y. In later sections, we report the results on masses, widths, fragmentation functions, branching ratios, production ratios, together with a detailed discussion on estimating systematic errors. We also compare our results with theoretical predictions.


4.2 Monte Carlo Studies


In order to determine the detector resolution of signals and estimate the reconstruction efficiencies, large amounts (more than 100,000 events for each decay mode) of Monte Carlo events were generated. Therefore, statistical errors on all quantities directly derived from Monte Carlo can always be neglected in the numerical calculations.

The A+(2593) events are first generated with a mass of 2593.9 MeV/c2 and zero width to obtain the mass resolution of the detector. After a preliminary measurement of the natural width using the real data, more A+(2593) events with the measured natural widths were generated. We found that our invariant mass recon-






54

struction program can extract the Monte Carlo generated natural width very well, and efficiencies calculated from 0 width events and events with a finite width are very close.

The A+(2625) events are generated with a mass of 2626.6 MeV/c2 and zero width.

To study the substructure of A+ decays, we generated samples with both Ec7r and non-resonance decay modes. The non-resonance modes are simply the decays A+ - A+ur7r and A+ -+A+ r0r0. The Ec7r modes are (1) the mixed 50% A -E++7rand 50% A+-Ei7r+, with E+-A+7r+ and E�A+7r-, and (2) the A+ - Ew7r with E-+Au7r0. TheA - Ec7r and A+ -+A+ r7r modes are used for the A+ (2593) and the A+ (2625), respectively, to evaluate the corresponding efficiencies and resolutions, as the data show us that these are the dominating decay modes.

Determination of the detector resolution by the Monte Carlo is very crucial for extracting the intrinsic width of a particle when its intrinsic width is close or smaller than the resolution. As stated in the last chapter, we have checked for all 16 A+ decay modes, and the Monte Carlo predicted widths are all in good agreement with the fitted widths of the data signal. However, the charged daughters of A+'s are all at quite high momentum ranges, but the two independent pions in A+-+ A+7r7r decays are both soft. It is possible that the CLEO-II official Monte Carlo program overestimates the performance of the detectors on measurements of low-momentumtrack parameters. This can make the Monte Carlo predicted resolutions smaller than actual resolutions of A+ -- A7r7r signals.

Measuring the signal of the D*+, which has I < 0.13 MeV/c2 at 90% confidence level[1], can be used to check the accuracy of the resolution of the low-momentum pions by the Monte Carlo. To do this, we looked at the mass difference M(D*+) M(D0) of decay D*+ -+ D07r+ (and D0 -* K-7r+) in which the momentum spectrum of the independent pion is close to those of the two independent pions from A+






55


decays. The fitted width of the signal of M(D*+) - M(D0) distribution is (0.550

0.001) MeV/c2 for the Monte Carlo, but about 0.63 MeV/c2 for the real data in the worst case,* about 15% larger. We think the actual detector resolution is in the 0 - 15% range larger than the Monte Carlo predicted one. The D*+ width is largely affected by the angular resolution of the soft pion. This is not the case for A+ widths based on our study of comparing the Monte Carlo widths with the data at different decay angle. So the amount of the disagreement between real data and the Monte Carlo for D*+ may not reflect the same amount of the disagreement for A+ widths. But it appears that the Monte Carlo prediction of the resolution is too optimistic. This was not noticeable in the previous research in CLEO since the mass resolution itself was poor. For the CLEO-II recompressed data, this effect should be seriously considered as a big source of systematic uncertainties for particles whose natural widths and mass resolutions are small.

Some studies are performed to check the correctness of Monte Carlo determined efficiencies of particle reconstruction. We calculated the decay ratios of each A+ decay mode relative to pK-7r+ based on the actual yields from the data and Monte Carlo predicted efficiencies, and they all agree within 10% with the Monte Carlo generated ratios. As we measure all production and branching fractions by ratio relative to A+, the effect of the error of A+ reconstruction efficiency mostly cancels in the ratio.
*For the real data, the M(D*+) - M(DO) spectrum is difficult to fit due to the uncertain background shape near the peak, which is very close to the kinematic threshold. When we fitted the signal at a different pion momentum range, we found that fitted width is closer to the Monte Carlo predicted resolution at higher momentum pions. By using different fitting procedures to fit signals at different pion momentum ranges, 0.63 MeV/c2 is the largest fitted width. We believe that 15% is a conservative estimate of how much the Monte Carlo miscalculates the mass-difference resolution.






56


4.3 Signals and Fits


To observe Ai signals, we combine each A+ candidate with two pions (7+7.or 7r 0x 0), reconstruct the invariant mass with the At, then fit the spectrum of the mass difference M(Atir7) - M(At). A+ selection criteria are described in the last chapter, and the reconstructed masses of A+ candidates are required to be within 1.6UM of 2.2867 MeV/c2, our fitted mean value of the Atmass. As A+ decays are strong decays, their lifetimes are very short. We can assume that they decay at the interaction point of e+e~ annihilation. The event vertex finding procedure is described in Chapter 3. When we reconstruct the invariant mass of each Atirir combination, we constrain the three particles to be from the event vertex. We find that using vertex constraint improves the resolution of the At(2625) by more than 10% for the A+r-7r-case. In order to see very clean signals,* we require x, > 0.7 for each Atr ri combination. xP is defined as


PA+
Eeam - MA+

where PA+ is the total momentum of the At7rlr combination, Ebeam is the beam energy of the e+(e-), and MA+ is the mass of the At.


4.3.1 Ak 7+7rShown in Figure 4.1 is the mass-difference spectrum of A7r+7r- combinations. The large peak at 342 MeV/c2 is due to the decay A+ (2625) -*Air+x-, and the smaller peak at approximately 309 MeV/c2 is from A+ (2593)-Ati+7r-.

To fit the the mass-difference distribution, we used a second-order Chebyshev polynomial to fit the background and two signal functions to fit the peaks. Each
*As we can see in later sections, having low background is very important to measure the Ec7 substructure.






57


240 200


160


120

C4
80


40


0
0.290 0.315 0.340 0.365 0.390
GeV/c2


Figure 4.1: Mass difference M(A+7r+7r-) - M(A+)






58


signal function is a Breit-Wigner function with a floating width convoluted with a single Gaussian function with a fixed width. The Breit-Wigner widths reflect the intrinsic widths of the particles; while the Gaussian widths, which are 1.28 MeV/c2 for the A'(2593) and 1.62 MeV/c2 for the A'(2625) determined from the Monte Carlo studies, are used to parameterize the detector resolutions.

In order to prove that signals in Figure 4.1 are not artifacts of special selection criteria, we checked the backgrounds from two sources: one is the combination of a fake A+ candidate taken A+ sidebands and i+r-, the other is the combination of a A+ with two same-sign pions (7r 7*). As Figure 4.2 shows, these mass-difference distributions are smooth and similar to the Aft+w- background. These plots can be fitted very well using the fixed background parameterization as used in Figure

4.1.

As shown in Figure 4.1, it is obvious that the A+(2593) peak is not fitted well by a Breit-Wigner convoluted with a Gaussian. Fitting uncertainties on both the mass and the width are big. We will discuss this further in the next chapter after presenting the Ec mass measurements.*

The extracted Breit-Wigner width of the A+ (2625) with a 1.62 MeV/c2 Gaussian resolution is 0.7 0.3 MeV/c2, close to zero. But the question is, have we measured a finite width of the A+(2625)?

As we mentioned in the last section, for CLEO-II the actual detector resolution may be as much as 15% larger than the Monte Carlo predicted value. If we fit the A+ (2625) with a single Gaussian with a floating width, the fitted width is 1.76 0.12 MeV/c2, less than 10% larger than the Monte Carlo predicted value. So taking statistical errors into account, we cannot conclude that we have observed a finite natural width of the A+ (2625). Therefore, in the following study, we calculated the
*We also remeasured the A+(2593) signal by a new technique. This second method is only possible after a measurement of E, width and mass. The measurements give different mass and width values.






59







30

20

10

0
20 A1~T


0
20



-4-,
10
AC Sidebands 20

10

0
0.290 0.315 0.340 0.365 0.390
GeV/c2 Figure 4.2: The top plot shows the mass difference M(A+7r-7r-) - M(At) and the middle plot shows M(At7r+7r+)-M(At), and At's candidates are taken with masses with 1.6 aMA from 2.2867 MeV/c2. The bottom plot shows M(Aw7r+7r-) - M("At side"), where a "A+ side" is from A+ sidebands which are taken from 3.4 to 5.0 0M+ away from 2.2867 MeV/c2.






60


production rate of the A' (2625) by using the yield of the signal fitted by a single Gaussian, which is roughly 10% smaller than the yield obtained from the fit using a Breit-Wigner convoluted with a Gaussian. Corresponding systematic uncertainties were added in the final results of branching ratios and production ratios.

Table 4.1 shows the yields, mass differences, and widths obtained by using different fits to Figure 4.1. Fit Type 1 uses a Breit-Wigner convoluted with a Gaussian for the Aj(2593) peak and a single Gaussian for the A'(2625) peak. Type 2 fits the region right to 294 MeV/c2, excluding two entries from the plot. Type 3 uses a third-order polynomial to fit the background instead of the second-order one. Higher-order polynomials were also used, and the results are very similar. Types 4, 5, and 6 only fit the A' (2593) peak. Type 4 excludes the region from 325 MeV/c2 to 360 MeV/c2; Type 5 excludes from 335 MeV/c2 to 350 MeV/c2; Type 6 only fits the region from 290 MeV/c2 to 325 MeV/c2. Types 7 and 8 only fit the A' (2625) peak. Type 7 fits only from 335 MeV/c2 to 390 MeV/c2 and Type 8 excludes from 300 MeV/c2 to 325 MeV/c2. Type 9 uses a Breit-Wigner convoluted with a Gaussian to fit the A+ (2625) peak instead of a single Gaussian. The errors from Type 2 to Type 8 are not shown since they are roughly the same as in Type 1. We have performed more variations of fits other than listed in Table 4.1. Variations of the results are all within the range Table 4.1 shows.

Different values of xp and cut around the A+ mass may vary the results of the mass and the width. As we checked, the variation of the widths on both particles and the mass difference of the A' (2625) is less than the one shown in Table 4.1, but the mass of the A+(2593) varies from 308.2 MeV/c2to 309.1 MeV/c2.






61


Table 4.1: The measured yield, mass, and extracted width of A+--+A7r+7r- by various fits.


Fit Type Yield Mass(MeV/c2) Width(MeV/c2)
AX(2593) 1 191Ti4 308.8 0.4 4.7+1.3
2 204 308.7 5.2
3 175 308.6 4.2
4 209 308.9 5.3
5 194 308.7 4.9
6 181 308.7 4.4
A+ (2625) 1 431 23 341.80 0.10
2 428 341.78
3 428 341.81
4 433 341.84
7 429 341.77
8 431 341.86
9 475 t2 341.84 0.11 0.7 0.3


4.3.2 A+7r07r0

To search for A+ -4 Air07r0 signals, we combined each A+ candidate with two 7r0's and measured the mass difference with A+. 7r0 selection criteria are described in the last chapter. However, to suppress large background we need an additional cut on 7r0 momentum. We chose the cut based on the optimization of the Monte Carlo signal versus the background from the data. As Table 4.2 shows, the Monte Carlo predicts that 150 MeV/c gives best signal to background ratio for different momentum cuts. By fitting the signals in the M(A+7ro7r0) - M(Aj) spectrum of the data using different P(7r0) cuts, we have found the results are consistent with the Monte Carlo efficiencies.

The spectrum and its fit of the mass difference of A07r0r combinations are shown in Figure 4.3. As we expected, two A'i signals present at 309 MeV/c2 and 342 MeV/c2. Unlike the A+r- case in which we see a much larger A+1(2625) signal than A+(2593)'s, the two signals are roughly the same size. The A+(2593)






62


Table 4.2: Signal versus background of A7 i070 combinations for different r0 momentum cuts. Si and S2 in the table are the fitted areas of the A (2593) and the A' (2625), respectively, decaying into A+7070 from Monte Carlo studies; while B is the background from plotting A+7070 combinations of real data.


signal is three times as large as our estimation from Monte Carlo efficiencies and isospin symmetry. We will provide an explanation in the next chapter.

To fit the plot, we have used the same functions as in the A+irir mass-difference spectrum. Also shown in the plot as a histogram is the mass-difference spectrum obtained by using A+ sidebands instead of A+ candidates. Sidebands are picked from 3.4 to 5.0 am on both side of A+ mass. No evidence of peaks can be seen* in this A+ sideband mass-difference distribution and its shape is consistent with the M(A+ir0w0) - M(A+) background.

We have fitted Figure 4.3 in many different ways. Table 4.3 shows the results from some different fitting procedures.

Fit Type 1 uses a Breit-Wigner convoluted with a Gaussian with a fixed width of 2.4 MeV/c2 to fit the A+(2593) signal and a single Gaussian with a fixed width of 2.9 MeV/c2 to fit the A+(2625) signal. Both Gaussian widths are determined by Monte Carlo studies. Type 2 fixes the width of the A+(2593) signal using the measured value from the A7rir decay, with the Gaussian width floated. Types 3 and 4 only fit the A+ (2593) signal. Type 3 fits the region from 290 MeV/c2 to 320 MeV/c2, and Type 4 excludes the region from 230 MeV/c2 to 355 MeV/c2. Type 6

*By fitting it with the fixed masses and widths, we find yields of 23 14 at 307 MeV/c2 and
-9 14 at 342 MeV/c2.


P(70) (GeV/c2) S1 S2 B S/JB S2/vKB
0.50 747 661 6480 9.3 8.2
0.10 697 575 4380 10.5 8.7
0.15 518 424 2290 10.8 8.9
0.20 279 277 1078 8.5 7.2
0.25 69 109 414 3.4 5.4






63


120


100


80


:0 60N

- 4020


0
0.290 0.315 0.340 0.365 0.390
GeV/c2 Figure 4.3: Mass difference M(A7r070) - M(Aj) together with the rescaled histogram which is the mass difference M(A+7rr07) - M("Aj side"), where "A+ side" is the same as the one in Figure 4.2.






64


Table 4.3: The yield, mass difference(A (M)), Breit-Wigner width(F), and Gaussian width(o-) of signal events from various fits to A' -- A+7'r0. The numbers labeled by * are fixed values in the fit.


Fit Type Yield A(M)(MeV/c2) F(MeV/c2) o-(MeV/c2)
A+ (2593) 1 9 306.3 0.7 2.9 2.4*
2 113 306.4 0.7 4.7* 2.31-1
3 129I3 306.6 0.8 5.8 +3. 2.4*
4 109 +3 306.2 0.7 3.228 2.4*
- 6-2.1 24
5 102 +34 306.2 0.7 3.1 27 2.4*
-2 2.1 _ ______A,,(2625) 1 105 22 342.9 0.9 2.9*
5 150j4 342.2 1.1 4.61.
6 132 27 342.7+'-' 1.5* 2.9*
7 106 24 343.0 0.9 2.9*
8 107 23 342.8 0.9 2.9*


and further only fit the A+ (2625) signal. Type 6 fits the signal with a Breit-Wigner with a fixed width of 1.5 MeV/c2 convoluted with a Gaussian with a fixed with of 2.9 MeV/c2.* Type 7 fits the region to the right of 320 MeV/c2, and Type 8 excludes the region from 300 MeV/c2 to 315 MeV/c2.

Many other variations of fits like these are also performed. We find that using higher-order polynomials to fit the background gives almost the same results. Also, results are consistent with the ones in Table 4.3 if we fit only one peak by excluding the region of the other peak in the plot.

These fitting results show very strong evidence that the decay mode A+ -4 A+7r07r0 does exist for both the A+(2593) and the A+ (2625). The next point of interest is to calculate the branching ratio B(Aj -+ Airo7r0)/B(A -* A+7r+7r-). To do this we need to estimate the errors on the yields of At7r7r signals.

We not only have large statistical errors because of the poor signal, but also large systematic errors, mostly due to the uncertainties of the resolutions and the natural
*The reason we do this fit is that we do not trust the result on fit Type 5 since the width is too much wider than the Monte Carlo predicted resolution. Here we use this fit trying to estimate the upper limit of the yield






65


Table 4.4: Comparison of productions of A+7r07r0 for different momentum cuts. The A'(2593) yields are from the fits using a Breit-Wigner function with IF = 4.7 MeV/c2 convoluted with a Gaussian with fixed width from Monte Carlo studies. The A+ (2625) yields are from fits using a single Gaussian with fixed width from the Monte Carlo. The statistical errors on efficiencies are tiny.


Pro (GeV) Yield Efficiency(%) Yield/Efficiency(x100)
Al (2593) 0.05 133 30 2.35 57 13
0.10 145 28 2.19 66 13
0.15 115 20 1.63 70 12
0.20 59 13 0.88 67 15
0.25 11 9 0.22 50 41
A,',(2625) 0.05 107 34 2.46 43 14
0.10 95 30 2.31 41 13
0.15 105 22 1.78 59 12
0.20 65 17 0.95 68 18
0.25 38 11 0.37 103 30


width of the particle. Thus we have fitted the signals by varying the resolution

by 20% of the Monte Carlo predicted values, varying the width of the A+(2593)

from 2 MeV/c2 to 7 MeV/c2, and varying the width of the A+(2625) from 0 to 1.5

MeV/c2. We then estimate that the fitting uncertainties of the yields are -15 for the

A' (2593) and +27 for the A+ (2625).

Since a 150 MeV/c momentum cut on both independent 7r0's is a very hard cut, a

consistency check has been made by comparing the efficiency-corrected productions

for different 7r0 momentum cuts. As shown in Table 4.4, for the A+ (2593) decay,

the Monte Carlo and the data agree very well, but for the A+ (2625), we see some

disgreement. Thus we need to intoduce a corresponding systematic error when we

calculate the decay ratios.






66


4.4 Substructures


Studying A -+A->r7r decay substructures through intermediate Ec's is very useful to identify JP of the A+'s and gain more understanding of these two states. In this section, we describe the measurements on the number of Aj's which decay to Ec's. The ratio is defined to be


B(A -- Ec7r)/B(A+ -+ A+7rr).


4.4.1 A+ -+ E+7-r and A+ E'7+

Figure 4.4 plots the mass difference M(A7r-) - M(Aj) against M(Af ir+) M(Aj) for the same A7r+7r- combinations in Figure 4.1. By looking directly at the figure, it is easy to tell that there are two very prominent clusters which correspond to the decays through intermediate Ef+ and EZat the two ends of the diagonal band of A+(2593)'s in which all entries are shown as inverted triangles; in the diagonal band of A+ (2625)'s in which all entries are shown as triangles, no obvious clusters can be seen. Therefore, by simply inspecting this scatter plot, we can tell that the Ec7 mode dominates the A+ (2593) decay, and the non-resonant A7rwr mode dominates the A+ (2625) decay.

To determine the fraction fE++ and fgo of the A+ (2593), we first measured the A+(2593) yield as a function of A7r* submass. Figure 4.5 shows the mass enhancement of EZ and E++ from A+7r+r- combinations with the mass difference M(A+7r+7r-) - M(A+) between 304 MeV/c2 and 314 MeV/c2.

We fit each plot in Figure 4.5 with a bifurcated Gaussian* (left) and a single Gaussian (right) together with the same background function. The same combinations in the two plots are constrainted to have the same area.
*A bifurcated Gaussian is A Gaussian with different slopes on either side of the mean.







67


0.23 0 -J01 o00 0 00'r 0 % 0 I
C %~00 c~0 0 A0
COO 0 ~ 0 00 0 00
0 0 ~ o ~~0 0 cO ,,0 Cb14 0 0o C 0 o c6)5)0 C000 0 0.21 .01o0 00 XC' 0;0 0
, 00 %0 O b00
..0 0o 00 000 b
0.219 A C CO 008 00 00 00 0 0 0C b 6
A0 aP 0 0 06
9, 0 Q Q00 c600000 0 00 00 0~ 0

000 ~ 0 % 0- 0(,
0d A 0 C 0 0 0 0
1 'A & 0 00, 0 O 00 8 00 0 0 0 C
0> 1 A 0 C 0 00 0c 0
W A A 080 a 0 0 0
0~z AA?0 0 0 0000 0O8
0 A Cb0V 0 )~ 0 00 0 @00
AA 9 c) G O 0 0 0 0 0 ocP0 0.150 0 00 180
000 0 CO O 00

9)0 8 4 00 00 0
00A 0 0

0.13 - U AOIcR0s
0.1 0.1 01 0 0.2 0.2
0 0(~~ (beV/c2) Figure~~~~ 4.4: Scate plo of th mas difrec 0(~~ vs0h as ifr
ence ~ ~ ~ V MI~~ -V M(0l Shw in th plo ar010h etcl ada ~ms difference of)O abou 16 Ae/2 corsodn toZ +Ai 2 h oriona
band- at A as ifrf abu 168 0e/2 corsodn to 0 -2
(3) ~ ~ ~ ~ 0 th dignlbadetnin rm(.14 0.2) (0 .0 01) ocorepodn to0



diagonal badexedngfo1(.4 0.168 t(06,14) coresonin to.com


therer e.4 twoaloes alt othe nmatic liits:enc (a7( thvehncmnti the mabnder just Mabve the+) honi threhl fort are~ an1() the nanemet intel band, u+mst aboveenthe threshold for Apr. orepnigtoE+- +7 2 hehrzna






68


20 1
(a)'



) 100
(b)
-C 7TEC7
tC4

U)

' '1'
C',

0
0.135 0.145 0.155 0.165 0.175
GeV/c2

Figure 4.5: Events and fits of E 's and E+'s with the mass difference of M(A+7r+7r-) - M(A+) between 304 MeV/c2 and 314 MeV/c2 (the A+(2593) signal). Plot (a) shows the mass difference M(A7r-) - M(A+). The right peak centered at 167 MeV/c2 is the E' signal; and the left peak is the reflection of the Ef+ signal on the A+(2593) band. Plot (b) shows the mass difference M(A+ir+) - M(Af). The right peak centered at 167 MeV/c2 is the E+ signal; and the left peak is the reflection of the E signal on the A+(2593) band. Since plots (a) and (b) represent the same events projected in two different directions, they are fitted simultaneously by constraining the area of the left/right peak in (a) to be the same as the area of the right/left peak in (b) The left peaks in both (a) and (b) are fitted by bifurcated Gaussians, and the right peaks are fitted by single Gaussians. They are all constrainted to have the same widths.






69


Shapes of the bifurcated Gaussian and the single Gaussian are determined by Monte Carlo studies of A'-+Ec7r and Ec,-A+7 decays. The background is expected to be a mixture of two parts: random Afx+7r-- combinations and non-resonant A +(2593)+A ++r-- events. Alhough it is very difficult to predict what its exact shape is, we know this shape has cut-offs at phase space lower limit 139 MeV/c2 and upper limit about 172 MeV/c2,*. We used a "double-threshold" function y(x) with upper and lower thresholds at a and b (in this particular case a = 139 MeV/c2 and b = 172 MeV/c2),


y(x) = N(x - a)(b - x)es1(x-a)+s2(x-a e(b-x)+s4bx, (4.1)


to fit the background of Figure 4.5. Here N is a normalization factor and si, where i = 1, 2, 3, and 4, determines the shape of the function. The fitted background shape obtained by fitting the plot in Figure 4.5 with floating six's is very consistent with the shape from the Monte Carlo generated Alr+7r- non-resonance decay. As we tested, the fitted results are not sensitive to the variation of the background shape as far as a and b are fixed. Reasonably varying the parameters of the double-threshold function (reasonably means still giving a good fit) makes the yields of signals change within 5% of the mean value of fitted areas. We believe that statistical errors dominate the uncertainties of this measurement.

The areas of E' and F+ signal we measured from Figure 4.5 are 77 7 and 72 7, respectively. These values are obtained by fitting Figure 4.5 by fixing the background, with shape determined by the Monte Carlo studies of A+i(2593)-Ati7r+ non-resonance decay. To obtain the number of A+ (2593)'s which decay into Ec1r, these numbers need to be subtracted by the number of "independent" Ec's in the
*The lower limit is really the pion mass, and the upper limit, as we can tell in Figure 4.4 depends on the width of the A+ (2593) band.






70


sideband of the A'(2593) signal. Due to the kinematic limit, only the higher-mass A'(2593) sideband contains Ec's. Therefore we estimated the background as being half.

The number of Ec's in the A'(2593) sideband were measured similarly as we did with the number of Ec's in the A'(2593) peak except that the mass-difference range is wider and the kinematic reflections of the peaks are in different massdifference ranges. The sidebands were taken from the range of the mass difference M(A r+7-r) - M(A+) between 320 MeV/c2 and 330 MeV/c2. Figure 4.6 shows the histograms and the fits. The fitted yields are 19 4 of E++'s and 15 4 of E's.

After subtracting one-half of the yield from the sideband, we obtained the number of A+(2593)'s which decay to Ec's: 67 8 for the F+ and 65 8 for the E. Compared with the total number of A+(2593)'s in the mass-difference range between 304 MeV/c2 and 314 MeV/c2, which is 137 22 measured in Figure 4.1, we see that resonance via the Ec dominates these transitions.

The same methods were applied to measure f>,'s of the A+(2625) except that in this case there are two A+(2625) sidebands other than the one in the A' (2593) case. The numbers of E++'s and E's inside the A'(2625) signal are measured as shown in Figure 4.7, and the fitted yields are 46 9 for E+ and 36 9 for E0. The lower A+(2625) sideband is chosen to be between 320 MeV/c2 and 330 MeV/c2, which is the same as the one shown in Figure 4.6, and there are 19 4 E++'s and 15 4 E 's. The higher sideband is therefore in the range between 354 MeV/c2 and 364 MeV/c2, and the number of E++'s and E's is measured to be 13 3 and 6 4, respectively. The fit for the higher sideband is shown in Figure 4.8. After the sideband subtraction, the results are 30 10 Aj's decay to E+'s and 25 10 decay to E's. These numbers indicate that resonance through Ec is very small in the decay of the A+(2625), since the total number of A+(2625)'s between mass difference 354 MeV/c2 and 364 MeV/c2, 450 29, is much larger.






71


15 I , , i 1
(a)
c0 IT+


c7.5 - 7T(0


7.5
bJ
0





V7.5


Li


0.135 0.145 0.155 0.165 0.175
GeV/c2

Figure 4.6: Events and the fits of E 's and Ef+'s in the A+ (2593) sideband. Plot
(a) shows the mass difference M(A+7r-) - M(A+), and plot (b) shows M(A7r+) M(A+). The peaks in the right at about 168 MeV/c2 on both plots are the signals of the EO and the E++. In each plot a bump is centered at about 158 MeV/c2, representing reflections of the EI(E+) peak seen in the direction of E++(E). Each plot is fitted by two single Gaussians with fixed widths (3.4 MeV/c2 of the left bump and 1.1 MeV/c2 of the right peak) from E' -- A+7r- (Ef+ -- A7r+) Monte Carlo studies and a double-threshold function the same as the one used to fit Figure 4.5, with the lower threshold 140 MeV/c2 and the higher threshold 185 MeV/c2. The areas representing the same combinations are constrainted to be the same, and the two plots are constrained to have an identical background.






7-1


30 (a)






Z0T
NN











0
C I
~15



'I







0.15 0.16 0.17 0.18 0.19
GeV/C2
Figure 4.7: The mass difference of M(Af gr+7~) - M(A+) between 337 MeV/c2 and 347 MeV/c2 (the A+(2625) signal). The meanings of the signals are the analog to those in Figure 4.5. The reflection of the peak of one combination is overlaid with the peak of the other combination. These shapes are predicted by A'(2625)--Ec7r CC





Monte Carlo studies. Each plot is fitted by two single Gaussians and a second-order Chebyshev polynomial. The widths of the Gaussians are fixed by the values from thgue 4.7:Carlo (1.2 MeV/c2e of ain t Mfan3. between 33 the bump in the right). The areas representing the same combinations are constrained to be the same, and the two plots are constrained to have the same background.






73


8


N
U '1,

K
U) uJ


0


-

C bJ


4


0.15


0.17


0.19


0.21


GeV/c2


Figure 4.8: The mass difference of M(A+7r+7r-) - M(A+) between 354 MeV/c2 and 364 MeV/c2 (the A+(2625) sideband), fitted in the same way as fitting Figure 4.7. The widths of the Gaussians are fixed by the values from the Ec-+A+7r Monte Carlo studies (1.3 MeV/c2 in the left and 4 MeV/c2 in the right).


(a)


C ++ Too


ZcO1T+


(b)

S++ +T-


--I


4






74


After further considerations of systematic errors, we listed our results of fs++ and fyo, compared with the measurements with other experiments, in Table 4.13 and Table 4.14.


4.4.2 A+ a E7r0

The technique of measuring


fE. = B(A+ -4 E+7r )/B(A+ -- A+7070),



is similar to that of measuring fs++ and fro, and much simpler. Since Ar0 decay only has one substructure, which is A+Ur0, instead of two (EZ+i-- and E07r+), we do not need to do complicated fits to correlate E+ and E signals as we did in the Atlr+l- case.

The scatter plot of M(A+70ir0) - M(Aj) versus M(A+70) - M(Aj) shown in Figure 4.9 shows the evidence of A(2593)->+f0 substructure. In the plot, we can see two concentrated clusters of events in the A+(2593) mass-difference band around 306 MeV/c2: one at about 167 MeVc2 which is consistent with E mass difference, and another which is the kinematic reflection of the first, at about 140 MeV/c2 just above the kinematic threshold. We cannot see this phenomenon for the A+(2625) signal.

Low statistics and high background do not allow us to report the A+ (2625) -+Ec70 measurement (the upper limit would be 1). Thus only a fE+(A+ (2593)) measurement was performed.

Figure 4.10 shows the histogram and the fit of the E+ signal and its kinematic reflection at the A+ (2593) mass-difference band taken from the M(Air'0w0) - M(At) mass-difference range between 304 and 314 MeV/c2. The plot was fitted by two single Gaussians with fixed widths (2.9 MeV/c2 for the left signal and 2.4 MeV/c2






70





0.37




+ + ++~++

+ ++ * +.
+' 0.3 +
+ + +
__ + 4








0.29-




0.27 . A I
0.130 0.155 0.180 0.205 0.230
M(Ahv0*) -M(A) (GeV/c2)

Figure 4.9: Scatter plot of the mass difference M(Afwr0r) - M(Afj) vs. the mass difference M(Afir0)- M(Al). Very visible in the figure is a horizontal band at about 306 MeV/c2 of M(Afir0ir0) - M(Af), corresponding to Ajj(2593) -* Afwr0. It has two lobes at the kinematic limits: one at about 167 MeV/c2 of M(Af~r0) - MA) which is consistent with El mass difference; and the other just above the kinematic threshold which is 1r0 mass. We assume there are three other bands in the plot (visible but not obvious) which are not shown clearly: (1) a vertical band at about 167 MeV/c2 of M(Af ir0) - M(AZf), corresponding to El -+ Af~r0; (2) a diagonal band extending from (0.135, 0.308) to (0.2, 0.37), which is the kinematic reflection from band (1), corresponding to the single ir0's from the random Efir0 combinations(3) a horizontal band at about 342 MeV/c2 of M(Afir0wr0) - M(Af), in which no El clustering can be seen, corresponding to A3j(2625) -* Afir0ir0.






-6


50 , , , , i


40


30
> 30


C 20bJ I

10



0.130 0.140 0.150 0.160 0.170 0.180
GeV/c2 Figure 4.10: The mass difference M(A+7r07r0) - M(A 7r0) between 304 MeV/c2 and 314 MeV/c2 (the A'(2593) signal). The two peaks correspond to E's (left) and independent r's (right) in the A+ (2593) -+ E7r0 decay.









24


20


N u 1612
C:.

> 8


4


0 ' ' ' ' ' ' ' '
0.135 0.145 0.155 0.165 0.175
GeV/c2

Figure 4.11: The mass difference M(Afir70r0) - M(A+7rw) between 320 MeV/c2 and 330 MeV/c2 (the A+(2593) sideband). The positions and shapes of the two bumps are determined by the E-+A+r0 Monte Carlo. The signal at right corresponds to E+-A+ur0, and the left bump reflects single pro's from the E7' combinations. for the right signal) determined by the A+ (2593)-*E+7r0 Monte Carlo, and a doublethreshold function which is defined in equation 4.1. The shape of the doublethreshold function with the two thresholds 135 MeV/c2 and 176 MeV/c2 is determined by the non-resonance A'(2593)--A07r0 Monte Carlo. The areas of the the two Gaussians are constrained to be the same. Finally, the fitted yield is 89 11. Consistent fitting results were obtained when we fitted the background with a floating shape of the double-threshold function.

Figure 4.11 shows the M(A+7r0) - M(Aj) distribution at the A+(2593) side band and the fit to it. The sideband was taken from the M(A7r0r) - M(A+) range between 320 and 330 MeV/c2. The plot is fitted by two single Gaussians with









fixed mean values and shapes determined by the E+-A+7r' Monte Carlo, and a double-threshold function with fixed thresholds and other floating parameters. The areas of the these two Gaussians are constrained to be the same. The fitted yield is 14+11.

We finally calculated that 81 16 of A+(2593) decays are to E's from a total number of 93 20 A+ (2593)'s in the mass-difference range between 304 MeV/c2 and 314 MeV/c2. This is consistent with what we have seen in the A+ (2593)-*Au7r7r decay, for which the Ec7r substructure dominates. The result of fr+(A+ (2593)) is presented in Table 4.12 after proper systematic errors are evaluated.


4.5 Search for Other Decays

Since isospin is conserved in strong decays, the A+ -+ A+7r' is forbidden. If any of the two A+7r+7r- states we observed were excited Ec baryons, A7r decay should be not only allowed but more favorable than Ai7r7r decays due to the larger phase space. Aj's are allowed to decay electromagnetically to A+y, and if any Aj's intrinsic width is sufficiently narrow, its decay may be competitive with A+7r7r decays.

To search for these decays, we reconstructed Ai7r0 and AcYy combination using our previously defined candidates of A+, 7r0 and y. Based on the optimization of Monte Carlo signals versus the background from data, a 200 MeV/c r0 momentum cut for A+ir' and a 300 MeV/c photon momentum cut for A+y are used.

Figure 4.12 shows the mass-difference spectrum of M(Afir0) - M(A+), and no signal can be observed. To measure the upper limit of decay ratios, three functions are used to fit the distribution. A Breit-Wigner, with fixed 4.7 MeV/c2 A+(2593) width, convoluted with a Gaussian with fixed 5.7 MeV/c2 Monte Carlo predicted resolution, is used to fit at a fixed mean value of 307 MeV/c2; a single Gaussian







'9


100




75




50
50
C

>25





0.290 0.315 0.340 0.365 0.390
GeV/c2 Figure 4.12: Mass difference of M(A 7r0) - M(A+).









150 . . . .






100






0
C14
V)

-C 50 bJ





0.290 0.315 0.340 0.365 0.390
GeV/c2 Figure 4.13: Mass difference of M(A+y) - M(At).






80


Table 4.5: Fitting results on M(A+7r0)-M(Aj) and M(A'y)--M(A+) distributions.


with 6.7 MeV/c2 Monte Carlo predicted resolution is used to fit at a fixed mean value of 342 MeV/c2; and the background is fitted with a second-order polynomial.

Also, no signal is found at mass-difference spectrum of M(A+'y) - M(A+), as shown in Figure 4.13. We used the exact-same fitting procedures as in the M(A7r0) -Ai(A+) case, except different Gaussian resolutions, which are 7.4 MeV/c2 at mass difference 307 MeV/c2 and 7.9 MeV/c2 at mass difference 342 MeV/c2.

The fitted yields and their projected upper limits are shown in Table 4.5. We conclude that we have observed no evidence of A+T0 or A,-y decays from A+.


4.6 Masses and Widths


4.6.1 Systematic Uncertainties

One major part of the systematic error of mass measurements is the fitting error, mostly from the uncertainty of the background shape or sometimes even the signal shape. To evaluate this error, we use many different fit types and check the variations of the mean value of the signal. For a particle with a considerably wide natural width, such as the Z++, or a particle with an uncertain shape of the signal, such as the A+(2593), the fitting error generally dominates the systematic uncertainty.


Decay Yield Yield Upper Limit (90% C. L.)
A'(2593) - A+7r0 26 28 160
A+(2625)-+ A+70 -8 t 36 165
A+ (2593)-+ AY 96 + 71 381
A+ (2625)-+ Ay -42+ 52 120






81


Since we measure the mass difference between the A7r7r and the A+ instead of measuring the A+ directly, most of the experimental uncertainties from the reconstruction of the A+ cancel. As we checked, 3 MeV/c2 change of the A+ mass shifts the M(At7+7r-) - M(At) by no more than 0.01 MeV/c2. So the systematic uncertainties other than the fitting errors mostly come from the measurement of the momenta and decay angles of the two extra pions. For charged pions, these errors are dominated by the uncertainties in the magnetic field normalization and the energy loss correction which is applied to the tracks traversing the beam pipe and the drift chambers. For 7r's, the errors come from the shower energy measurement by the crystal calorimeters.

To evaluate the systematic errors of mass-difference measurements caused by the independent charged pions with low momentum, we measured the mass difference M(D*+) - M(D0) in decay D*+ -> D07r+ since the mass-difference measuring technique is the same as M(At7r+7r-) - M(At) and the independent pion is soft. Our fitted result is 145.39 0.01 MeV/c2 in excellent agreement with the PDG value, which is 145.397 0.030 MeV/c2. We found that 0.2% momentum change of all charged tracks will shift the M(D*+) - M(DO) by about 0.05 MeV/c2, larger than the error of the PDG average. Therefore we believe 0.2% change in momentum is a reasonable amount to study the momentum scale in mass-different measurement with charged soft pions.

For the systematic errors caused by the measurement of the soft 7r0's, similar to the charged ones, we check the photon energy scale by looking at the mass difference of M(D*O)- M(DO), and our fitted value agrees very well with the PDG value, which is 142.12 0.07 MeV/c2. We think 1% energy change is a reasonable amount used for an energy-scale study since it shifts M(D*o) - M(DO) by about 0.10 MeV/c2.

In the study of AI(D*+) - M(DO) measurement, we find that mass difference is more sensitive to the systematic shifts of the position and angle parameters of






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tracks. However, the charged tracks are measured much more accurately. Our vertex constraint program would shift the track positions and angles by fair amounts. We find that calculating the mass difference by constraining the D' and the pion to be from the event vertex, gives up to 0.02t0.01 MeV/c2 mean-value difference, compared with the mean value of mass difference reconstructed without vertex constraint. This difference reasonably reflects the systematic error from the decay angle measurement.

The systematic error on the width measurement comes from two sources: the fitting error and the mass resolution of the detectors determined by Monte Carlo studies. The fitting error dominates the total error when the natural width of a particle is wide, and it can be evaluated by varying parameterizations of the background and the signal shapes. The detector resolution becomes important when it is close to, or bigger than the natural width, and its correctness can be checked by fitting the signals of other particles with well-known widths and comparing the results with corresponding Monte Carlo signals. As we tested, the CLEO Monte Carlo program does a very good job with tracks with medium-to-high momentum spectra, but for tracks with low-momentum spectra, it tends to overestimate the detector performance and therefore predicts a mass resolution with a lower value than the real resolution. But by the time this research work was performed, we are unable to make corrections, since it is very difficult to detect what the exact reason is and by exactly how much the Monte Carlo is wrong. So we have to be very careful and conservative with our estimates of the uncertainties on narrow-width measurements.






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4.6.2 A+ (2625) Mass and Width Limit

The result presented on the A' (2625) mass difference with the A+, 341.80 0.10 MeV/c2 is our measured mean value by fitting the Air+- signal with a widthfloat single Gaussian. By fitting the A7ror0x signal, we obtained a value of 342.9 t 0.9 MeV/c2. We have also checked the fits to the A+7r+-- signal using a double Gaussian, a bifurcated Gaussian, and a Breit-Wigner convoluted with a Gaussian, with variations of different shapes. All fitted means agree within 0.13 MeV/c2.

In the momentum-scale study, we find that a 0.2% momentum change for all charged tracks shifts M(A+ (2625)) - M(A+) by about 0.22 MeV/c2. We find that the mass difference M(A+ (2625)) - M(A+) shifts for about 0.2 0.1 MeV/c2 if we do not constrain the A+ and the two pions to be from a single vertex compared with constraining them into the main vertex. This proved that the uncertainty of the pion decay angle does not bring large systematic errors. We also compared M(A+7r+7r-) - M(Af) with M(Aur+i -) - M(A+), and their mean values agree within statistical errors.

According to Table 4.1, the fitting error due to the background parameterization with the signal fitted by a single Gaussian is about 0.04 MeV/c2, which is tiny compared with the uncertainty of the soft pion momentum measurement. Considering all these sources of errors, we conservatively estimate that the systematic uncertainty is 0.35 MeV/c2

With the width of 0.7 0.3 MeV/c2 extracted from the Breit-Wigner convoluted with a Gaussian fit, considering that our Monte Carlo predicted resolution should not be larger than the actual one, we calculated the upper limit of the A+(2625) width to be 1.4 MeV/c2 at 90% confidence level.






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Table 4.6: Measurements of the A'(2625) mass and width limit.


Experiments [M(Aj) - M(Aj)](MeV/c2) I (MeV/c2)
E687[29] 340.4 0.6 0.3
CLEO-II[30] 342.2 0.2 0.5 < 1.9
ARGUS[32] 342.1 0.5 0.5 < 3.2
CLEO-II(this) 341.80 0.10 0.35 < 1.4


Table 4.7: Measurements of Aj(2593) mass and width together with the mass resolutions in the corresponding experiments. All quantities are in units of MeV/c2. Note that E687[31] fitted their signal using a single Gaussian and the fitted Gaussian width is consistent with that A'(2593) has a zero intrinsic width.


Experiments Resolution [M(A I) - M(At)](MeV/c2) I (MeV/c2)
CLEO-II[30] 2.0 307.5 0.4 1.0 3.2-1.0
E687[31] 1.8 309.2 0.7 0.3
ARGUS[32] 1.8 309.7 0.9 0.4 2.92.91.
CLEO-II(this) 1.62 308.8 0.4 0.4 4.71.1.


The results of mass difference with the A+ and the upper limit of the width are listed in Table 4.6. A comparison with the previous experiment results is given in the table.


4.6.3 A+(2593) Mass and Width

In Figure 4.1, we fit the A+ (2593)-A4Ar+7r- signal in the same manner as the previous experiments: using a Breit-Wigner function convoluted with a Gaussian. The results of the mass and width are listed in Table 4.7, together with the measurements of previous experiments. Here the systematic errors are mostly fitting errors, evaluated based on Table 4.1.

Although our measurements agree with previous experiments, we doubt the results, and the most obvious reasons comes from the following facts: (1) A+(2593)






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has a nearly 100% dominating decay channel, E,7; (2) the combination of Er+ (or E+T-) has a kinematic limit at the mass difference of about 307 MeV/c2; (3) the fit to the A+(2593) signal in Figure 4.1 is poor. Because of these and some other thoughts which will be stated later, we feel that using a full Breit-Wigner distribution to parameterize the E 7r+ (or Ecxr) decay very close to the kinematic threshold may not be correct. We will describe a new way to parameterize the signal in the next chapter, since the new method uses the Ef+ and Emasses and widths.


4.7 Fragmentation Functions


As stated in Chapter 1, all quarks "fragment" into hadrons. The initially produced pair of hadron and anti-hadron should be expected to have more energy than the subsequent hadrons produced further in the decay chains. Each hadron, as it is produced, carry away a fraction, z, of total energy of the corresponding original quark. A fragmentation function (N, where N is the number of hadron produced from a type of specific physical process) proportional to the probability a hadron being produced in the interval of [z, z + dz).

In e+e- annihilation experiments, measurement of the fragmentation functions of heavy quarks provides information about non-perturbative particle production in a variety of experimental environments. Many forms of functions have been suggested to describe the normalized momentum spectra for heavy quarks. Among those, the functional form given by Peterson et al.[33] is the most widely used. The Peterson function has form
dN 1
dz z[1 - (1/z) - fp/(i - Z)]2

where z = (E + pIj)haron/(E + pQ), and pli is the longitudinal momentum and pQ is the total momentum of the heavy quark. The quantity z is not experimentally accessible, and in CLEO experiments a close approximation is made by using the






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Table 4.8: Efficiencies and productions of Ali's for different x,'s. The statistical errors on efficiencies are negligible.


xP Efficiency(%) Yield Normalized Yield A'7(2593) 0.5-0.6 5.45 34 16 0.13 0.06
0.6-0.7 6.44 74 18 0.25 0.06
0.7-0.8 7.07 91 18 0.27 0.05
0.8-0.9 7.11 71 15 0.21 0.05
0.9-1.0 5.47 35 11 0.14 0.05
A+j(2625) 0.5-0.6 5.63 114 13 0.18 0.02
0.6-0.7 6.47 217 16 0.30 0.02
0.7-0.8 7.08 214 16 0.27 0.02
0.8-0.9 7.78 161 14 0.19 0.02
0.9-1.0 7.48 48 8 0.06 0.01


scaling variable P p/Prnax, as defined for A+ in the last chapter. Ep physically represents the "hardness" of the heavy quark fragmentation. The smaller the value of ep is, the larger the portion of the total momentum the heavy quark carries.

Although the Peterson function agrees pretty well with the fragmentation of D0 and D*+ measured in the experiments [34][351, there is no reason why any charmed particle momentum spectrum should follow an analytical curve of this type, as many particles are the decay results of excited states. However, the measurement of Ep of Peterson function remains useful for comparing the spectra of different particles.

To measure the Peterson function of a particle, we fit the distribution of efficiencycorrected cross section at a different x, range and extract the parameter ep. Table 4.8 shows the yields and Monte Carlo derived efficiencies at different xP ranges. Also listed are the efficiency-corrected yields normalized to xP > 0.5.

Figure 4.14 shows the dN (N is the efficiency-corrected number of Ali's for XP > 0.5) distribution for the A'j(2593) and the A'j(2625) based on the efficiencycorrected yields listed in Table 4.8. Only statistical errors are shown in Table 4.8. Systematic errors are dominated by fitting procedures and are found to be a little






87


0.4 I I I




0.3

9.
x

b0.2

b



0.1




0.0
0.0 0.2 0.4 0.6 0.8 1.0
X,


Figure 4.14: Normalized spectra of scaled momentum for A' samples. The data for the A' (2593) (diamonds) and the A' (2625) (triangles) are fitted to the Peterson function overlaid as the solid and dashed curves, respectively. smaller than the statistical errors. The error bars shown in Figure 4.14 are the total errors. Also shown in the figure are the curves obtained by fitting the distributions by Peterson function. The measurement results are listed in Table 4.9 compared to the previous measurements. The measurements show that A+ fragmentation at 10 GeV/c2 is close to the fragmentation of D*+, which was measured to have Ep = 0.078 0.008[36].






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Table 4.9: Measurements of the fragmentation of A+'s using Peterson functions.


4.8 Decay Ratios and Production Ratios


4.8.1 Systematic Errors on Yields and Efficiencies

To calculate the branching ratios and productions, the yields on the signals and the Monte Carlo derived efficiencies are used. Both bring systematic errors to the result.

The systematic errors on the yield of a signal come from the fitting procedures, including the signal and background parameterizations and the mass resolution determined by the Monte Carlo. As we explained in the last section, for the E*(2593)-At7r+7r-- signal, the systematic error is dominated by the uncertainty of the signal shape, and background parameterization is also a factor since the signal is just at the kinematic threshold. Based on Table 4.1 and other fit results, the fitting errors of the E*(2593)-+A+7+7r~ yield are 15% from the peak parameterization and 8% from the background parameterization. As we tested, varying the Gaussian resolution by a reasonable amount only changes the A+(2593) yield by 2%. We therefore estimate the fitting error on the A+ (2593)-A7r+7- yield to be 17%. For A+ (2625)-A7r+7r-, we have a clean signal at very low background, so the systematic error comes mostly from the Monte Carlo predicted resolution or,


Experiments (P
A, (2593) CLEO-II[30] 0.057 0.023 0.016
ARGUS[32] 0.069:06 0.040
CLEO-II(this) 0.064it:02
A+(2625) ARGUS[28] 0.044 0.018
CLEO-II[30] 0.065 0.016 0.013
CLEO-II (this) 0.108+0:011






89


equivalently, the uncertain natural width of this state. We finally estimate that the fitting error of the A'(2625)-+A+r+7r~ yield is 10%.

As the A+-+A7ro7r0 signals are poor, both statistical and fitting errors are very large. The fitting errors are mostly due to the uncertainty of the mass resolutions and the natural widths of the states. We expect the A+ (2593)-A>r07r0 signal to be nearly a full Breit-Wigner convoluted with a Gaussian, since the kinematic threshold is at 301 MeV/c2. The fitting errors are evaluated by reasonably varying the background parameterizations, the mass resolutions, and the widths of the states. From the results listed in Table 4.3 and some further tests, we estimate the fitting errors on A+j -+A r07r0 signals are 13% for A'(2593) and 127%.

Since we measure the branching fractions by ratios, the systematic errors on the efficiencies of A+ reconstruction will cancel. Based on comprehensive studies by the CLEO collaboration, the systematic errors on efficiencies are 1% on finding one charged track and 5% on finding a r0.


4.8.2 A+7r070, A+7r0, and Ac-y Decays

Since the yield of A+->A+7r+7r- was the best measured for A+, the branching ratios we measured are all given relative to this decay mode.

This is the first time that the decay A+-+A+7r0w70 is reported. Of interest is the branching ratio B(A 7r07r)/B(A+7r+r-). If only isospin symmetry is applied on these states, this ratio should be 1/2.

Based on the discussion in the last subsection, we assign the systematic errors on B(A+7r07r')/B(A7r+7-) to be 26% for the A+ (2593) and +1% for the A+(2625). Table 4.10 gives the result calculated from the yield and the Monte Carlo predicted efficiency of each decay mode.






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Table 4.10: Branching ratios of At7r0 r0 relative to A+7r+7r-.


Particle B(A'7070)/B(A+ 7+7r-)
A+(2593) 2.6 0.6 0.7
A+ (2625) 1.0 0.3ii_


Table 4.11: Limits on branching ratios of Af+->Au7r' and Aj-+A+-y relative to A+ -*A+r+7r-. All values are evaluated at 90% C.L.


Experiments B(A0+7r)/B(A+7+7r~) B(A-y)/B(A+7+7r-)
A+ (2593) CLEO-II[30] < 3.53 < 0.98
CLEO-II(this) < 1.1 < 3.0
A+(2625) CLEO-II[30] < 0.91 < 0.52
CLEO-II(this) < 0.45 < 0.36


The result on the A+(2625) is larger than 0.5 but consistent with it, but the number on the A+(2593) is significantly larger than 0.5. This can be explained by the phase-space suppression. The A'(2593) mostly decays into Ec7r first then goes to the final state A7r7r. Since the mass of the A+ (2593) is just at the threshold to decay into a Ec plus a charged pion, so the decay A+ (2593) -* E+7- and A+ (2593) -* E07r+ will be suppressed. On the other hand, isospin symmetry is not exact, so the 7r0 mass is about 5 MeV/c2 lower than charged ones, so the decay A+(2593) -+ E7r0 is not suppressed by phase space. Thus for the A+ (2593), we expect B(A+ -+ A+7r07r0)/B(Aj -4 A+r+7r~) to be higher than 1/2. We will discuss this more in the next chapter.

According to Table 4.5, taking the systematic errors on A7r+7r- yields into account, we estimated the upper limits of A+7r0 and AcYy decay ratios relative to A+7+7r -.






91


Table 4.12: Branching fractions of substructure E+ in A'-*A+7r+7r- decays. Note the Acj yields are smaller than the fitted results in Figure 4.1 since we measure the Ec yields from 304 MeV/c2 to 314 MeV/c2 of the A+ (2593) peak and from 337 MeV/c2 to 347 MeV/c2 of the A+(2625) peak.


Decay Aij Yield Ec Yield f F
A,(2593) E+7-r 137 22 22 67 7 5 0.45 0.12 0.11
C
E07r+ 137 22 t 22 65 7 5 0.47 0.12 0.11 E_7r0 93 20 22 74 11 10 0.73 0.20 0.20
A+ (2625) E+7r 450 29 9 24 10 7 0.05 0.02 0.02
E 7+ 450 29 9 32 10 7 0.07 0.02 0.02


Table 4.13: Comparison of measurements of branching ratios of E++ and E' substructures in A+i(2593)Ai7r+r- decays from different experiments.


Experiment f __fro _ _
E687[29] > 0.51 90% C.L.
CLEO-II[30] 0.36 0.09 0.09 0.42 0.09 0.09
ARGUS[321 0.37 0.12 0.13 0.29 0.10 0.11 0.66I-g1 0.07
CLEO-II(this) 0.45 0.12 0.11 0.47 0.12 0.11


4.8.3 Ec7r Decays

The A(1405), the spin 1/2 strange baryon, decays 100% to E7r; and the spin 3/2 state A(1520) decays to both EZr and Alr7r. We have observed the similar phenomenon for the A+(2593) and the A+(2625). Measurements of frE = B(Aj -+ Ec7r)/B(A+ -+ A+ r7r) for E+, E+, and E0 are tabulated in Table 4.12. The systematic errors are dominated by the fitting errors on Ec yields on A+j signals and backgrounds.

Our observation is close to the previous CLEO measurements and consistent with the prediction that the A+(2593) and A+(2625) have JP 1/2- and 3/2-, respectively. The A+(2593) can decay through both S-wave EcTr and P-wave nonresonance AZ7r+7r- channels, but the S-wave is preferred. However, angular mo-






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Table 4.14: Comparison of measurements of branching ratios of Ef+ and E' substructures in A' (2625)--+AfTr+7- decays from different experiments.


Experiment f _+ f_ __++
ARGUS[28] 0.46 0.14
E687[31] < 0.36 90% C.L.
CLEO-II[30] < 0.08 90% C.L. < 0.07 90% C.L.
CLEO-II(this) 0.05 0.02 0.02 0.07 t 0.02 0.02


Table 4.15: Measurements of A+ A+7+7r inclusive A, production.


production ratio relative to the total


mentum and parity conservations require A+ (2625)-ZEc7r to be D-wave, so for the A+ (2625), the P-wave non-resonance A+7r7- is preferred and expected to have a smaller width.


4.8.4 A' Production Ratios

Since we do not have good statistics with A+7r07r0 decay channels, we only present the A+ j-A+7+7r- production as a fraction of A+ baryons in the 10 GeV/c2 e+eannihilations. We have only measured the number of At's and Aj's at xp(Aj) > 0.5, so we need to extrapolate the Peterson function to zero momentum. Fortunately, the two A 's are fragmented very hard (only about 20% are fragmented below XP = 0.5,) so the systematic errors from extrapolation are not very large. Based on our estimation, the sources and their values of systematic errors of the A+(2593)


Experiment ((A%-7)
A+ (2593) CLEO[30] 1.44 0.24 0.30
ARGUS[32] 2.1t[ 1.1 CLEO(this) 1.46 +:.23+0.2 A+(2625) ARGUS[28] 4.1 1.0 0.8
CLEO[30] 3.51 0.34 0.28
CLEO(this) 3.47 0.17+04






93

are 15% for the peak parameterization, 8% for the background parameterization, and 10% for the x, = 0 extrapolation. We estimate the total systematic error of the A+(2593) production ratio measurement to be 20%. For the A+(2625), the fitting errors are dominated by the uncertainty of the detector resolution. The total fitting error is estimated to be i1%, and the x, = 0 extrapolation uncertainty is estimated to be 7%. Thus the total systematic error of the A+(2625) production ratio measurement is estimated to be + 2%. Our results are consistent with the previous experiments.




Full Text

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STUDIES OF CHARMED BARYONS DECAYING TO A+(n7r) By JIU ZHENG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1999

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ACKNOWLEDGMENTS Most of all, I would like to thank my adviser, John Yelton. He taught me from scratch how to do physics analysis in CLEO, introduced me to charmed baryon studies, and suggested a research topic which turned into this dissertation. Over five years he has been always very supportive in my work in physics and with many other aspects of my life. I thank Paul Avery, who has taught me much about high energy physics, data analysis, and CLEO software. I gained a large part of my knowledge of elementary particles from his one year introductory course. The magnificent KNLIB he provided has given tremendous help to my analysis. I am greatly indebted to my former college classmate, Song Yang, who influenced me to pursue the study of high energy physics. When he was a research associate at the University of Florida, he gave me much help with Monte Carlo simulations, Unix, C++, and GNU Make. Thanks go to Craig Prescott for answering many of my questions about CLEO software and for engaging in much useful discussion about physics. My life in CLEO would have been much more difficult without him. His longtime maintenance and support of the CLEO software library have helped everybody in CLEO do better analyses. I used his Vee-finding library and primary-vertex-finding routine directly in my analysis. I enjoyed lectures on "the Standard Model" by Pierre Sikivie and on "the Experimental High Energy Physics" by Guenakh Mitselmakher. I also thank Zongan Qui, Sergei Obukhov, and Charles Hooper for their first-year courses. I appreciate ii

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the help provided by my former colleagues, Jorge Rodriguez and Fadi Zeini. The Latex template provided by Youli Kanev and Mike Jones saved me a lot of time on writing this dissertation. I would like to express my gratitude for the entire CLEO collaboration and all staff members in the Cornell Electron Storage Ring. I wish happiness and success to all high energy physicists. The world is a much better place with these people's dedication to answer the big, important questions. Finally, I would like to thank my wife, Hongyan Yan. This work would have been impossible without her love and support. Much credit for this work goes to my mother, Chunyu Xu, my father, Zhiyi, and my father-in-law, Boxun. I have learned many things about life from my little son, David. iii

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To my grandmothers

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TABLE OF CONTENTS ACKNOWLEDGMENTS ii ABSTRACT vii CHAPTERS 1 THEORY OVERVIEW 1 1.1 Quark Model 1 1.2 Heavy-Quark Effective Theory 3 1.2.1 QCD 3 1.2.2 Potential Models 5 1.2.3 Heavy-Quark Chiral Perturbation Theory 7 1.3 Introduction to Charmed Baryons decaying to A+(n7r) 8 1.3.1 Spectroscopy 8 1.3.2 Strong Decays 11 1.4 HQET Predictions on £W and A+ x 12 2 EXPERIMENTAL FACILITIES 17 2.1 CESR 17 2.2 CLEO-II 19 2.2.1 Tracking System 19 2.2.2 Time-of-Flight System 26 2.2.3 Electromagnetic Calorimeter 28 3 A+ RECONSTRUCTION 29 3.1 Introduction 29 3.2 Data and Monte Carlo Sample 29 3.3 Event Selection 31 3.3.1 Track Selection 31 3.3.2 Particle Identification 32 3.3.3 7 and 7r° Finding 33 3.3.4 Event Vertex Finding 35 3.3.5 Vee Finding 35 3.3.6 £ and E Finding 3g 3.4 A+ Selection gg v

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4 STUDIES OF A£ BARYONS 52 4.1 Introduction 52 4.2 Monte Carlo Studies 53 4.3 Signals and Fits 56 4.3.1 A+7T+7T^ 56 4.3.2 A+ttV 61 4.4 Substructures 66 4.4.1 A+, -> E++7Tand A+, -> E°tt + ' ' ' ' 66 4.4.2 A+ ^ E+tt 0 74 4.5 Search for Other Decays 78 4.6 Masses and Widths 80 4.6.1 Systematic Uncertainties 80 4.6.2 A+ (2625) Mass and Width Limit 83 4.6.3 A+i(2593) Mass and Width 84 4.7 Fragmentation Functions 85 4.8 Decay Ratios and Production Ratios 88 4.8.1 Systematic Errors on Yields and Efficiencies 88 4.8.2 A+ttV, A+7T 0 , and A+7 Decays 89 4.8.3 E c 7r Decays 91 4.8.4 A^ Production Ratios 92 5 STUDIES OF E c AND E* BARYONS 94 5.1 Introduction 94 5.2 Signals 95 5.2.1 a+7t± 96 5-2.2 A+Tr 0 101 5.3 Masses 105 5.4 Widths 108 5.5 Fragmentation Functions 110 5.6 Production Ratios 113 5.7 New Measurements of A+ 1 (2593)^A+7r + 7r116 6 SUMMARY AND DISCUSSION 124 REFERENCES 128 BIOGRAPHICAL SKETCH 131 vi

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STUDIES OF CHARMED BARYONS DECAYING TO A+(n7r) By Jiu Zheng May 1999 Chairman: J. Yelton Major Department: Physics This dissertation presents studies of charmed baryons the A^, E c , and £*. The two A+! baryons are the L = 1 excited states of the A+, and they decay to a A+ and two pions; the E c triplet is the spin 1/2 7 = 1 state corresponding to the A+; and E* is the spin 3/2 excitation of the E c . Both E c and E* decay to a A+ and a pion. We performed comprehensive measurements on the masses, widths, fragmentation functions, and the production ratios of these particles from 10 GeV/c 2 e + e~ annihilations. A new decay channel of the A+ x , A+7r°7r°, is first observed and its decay ratio relative to A+7T+7Tis reported. A detailed study of A^ decays through the intermediate E c is performed. The E c intrinsic widths are first measured with consistency with theoretical predictions. The relative production ratios among the three E c 's are measured to be consistent with 1. The first evidence of the existence a new particle, the E*+, is reported. vii

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CHAPTER 1 THEORY OVERVIEW 1.1 Quark Model Tremendous progress has been made in high energy physics since the beginning of this century. We now have a simple picture about the ultimate constituents of matter: All matter is composed of quarks, which carry fractional electric charges, and leptons, such as the electron and neutrino. A quark does not exist individually and strong interactions hold quarks together in hadrons, which are built from two types of quark combination: a baryon consists of three quarks and a meson consists of a quark and an antiquark. Quarks come in six flavors (called d,u,s,c,b, and t), as do leptons (three types of charged and three of neutral). Each quark has spin 1/2 and baryon number 1/3. Table 1.1 shows the additive quantum numbers (other than baryon number) of the three generations of quarks. By convention each quark is assigned positive parity, so each antiquark has negative parity. The masses of quarks vary largely for different Table 1.1: Additive quantum numbers of quarks. Flavor d u s c b t Charge Isospin z-component i 1 ~2 T 2 l "3 0 0 l "3 0 T 3 0 Strangeness 0 0 -1 0 0 0 Charm 0 0 0 +1 0 0 Bottomness 0 0 0 0 -1 0 Topness 0 0 0 0 0 +1 1

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2 flavors,* ranging from a few MeV/c 2 for u and d quarks to about 170 GeV/c 2 for t quark. Since u and d are very light, the isospin SU(2) symmetry is a very good approximation. In the limit that isospin is an exact symmetry, the u and d quarks are considered identical except the charge difference. Analogous to the photon in electromagnetic interactions, a strong coupling happens via a mediating boson, call a gluon. In the theory of quantum chromodynamics (QCD), there are six types of strong charge, called "color," representing an internal degree of freedom. A quark can carry one of the three red, blue, or green colors, and an antiquark can carry one of the corresponding anticolors. The quark-quark force is independent of quark color, so the color symmetry, SU(3), is exact. All baryons are three-quark (qqq) states, and each such state is an SU(3) color singlet, a completely antisymmetric state of the three possible colors. Since quarks are fermions, the state function for any baryon must be antisymmetric under interchange of any two equal-mass quarks (up and down quarks in the limit of isospin symmetry). The state function of a baryon can be written as \qQQ)a = \ c °l° r )A x l s POce, spin, flavor) s , where the subscripts S and A indicate symmetry or antisymmetry under interchange of any two of the equal-mass quarks. For baryons made up of u, d, and s quarks, the three flavors imply and approximate flavor SU(3). This flavor SU(3) symmetry requires that a corresponding group of baryons belong to the multiplets on the right side of 3 ® 3 o 3 = io s e 8 M e 8 M e 1.4, *The values of quark masses depend on precisely how they are denned. The quark masses we referred to here follow the meanings defined by the Particle Data Group [1], which are different from the constituent quark masses.

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3 where the subscript M indicates mixed-symmetry states under interchange of any two quarks. Taking spin symmetry, SU(2), into account, the two 8' M s will end up with one octet of baryon states of \spin, flavor) s . This octet is shown as the bottom layer of Figure 1.1(a) In the ground state of the multiplet, the SU(3) flavor singlet 1 is forbidden by Fermi statistics. The decuplet formed by 10 5 , shown as the bottom layer in Figure 1.1(b), contains the states with the three quark spins aligned to the same direction (spin J = 3/2). If we add the c quark to the three light quarks, the flavor symmetry is extended to SU(4). The SU(4) multiples are shown in Figure 1.1(a) and Figure 1.1(b). All the particles in a given multiplet have the same spin and parity. Since the mass of the c quark is large, this SU(4) symmetry is very badly broken. 1.2 Heavy-Quark Effective Theory 1.2.1 QCD In QCD, the Lagrangian describing the interactions of quarks and gluons is Lqcd = --fijF^+z^l^D,)^ £m^>*. (1.1) 9 q = %K d v Al + g s f ab cAlAi, a 1 where g s is the QCD coupling constant (a s = g*/4n), and the f abc are the structure constants of the SU(3) algebra. The (j) q (x) are the 4-component Dirac spinors associated with each quark field of color i and flavor q, and the A*(x) are the Yang-Mills gluon fields.

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Figure 1.1: SU(4) multiplet of baryons made of u, d, s, and c quarks shown in (I Z ,S,C) coordinates, (a) The 20-plet with an SU(3) decuplet. (b) The 20-plet with an SU(3) octet.

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5 QCD is believed to be the fundamental theory of strong interactions. But to date, there are no practical means to do full QCD calculations of hadron masses and their decay widths, and a variety of different approximate methods have been introduced. Potential models have been well recognized to be the most useful in understanding the mass spectrum and the decay patterns of heavy-flavor hadrons. The correlation between flavor and spin wave functions is outside the realm of QCD. Some assumptions can be made using the empirical evidence of the constituent quark model. Heavy-hadron perturbation theory can be used to predict the decay widths. 1.2.2 Potential Models Although the details of modern potential models have evolved greatly since the discovery of J /(f), the essential features remain unchanged. The potential between two quarks is often taken to be of the form V s = --— + kr, 3 r where r is the inter-quark separation, and a s ~ 1, about two orders larger than a, represents the magnitude of the strong coupling. The factor 4/3 holds for the interaction between a quark and an antiquark. It is 2/3 for the interaction between two quarks. The first term dominating at small distance r arises from a single gluon exchange, and the linear term is associated with the confinement of quarks and gluons inside hadrons at large r. Because of the linear term, attempts to free a quark from a hadron simply result in the production of new qq quark-antiquark pairs. The annihilation process e + e" -> hadrons is viewed in terms of the process e + e~ -> qq followed by "fragmentation" of the quark and antiquark into hadrons. One important feature of potential models is that, except for mass dependencies, the inter-quark potential is independent of quark flavor.

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6 Potential models cannot be formally derived from QCD, but they can be interpreted by it. In QCD, the short-distance behavior is dominated by one gluon exchange described in the lowest-order perturbation theory. The linear behavior at large r can be seen by considering that a qq pair are attracted to each other and a color flux tube forms between them. Lattice calculations suggest that the tension per unit length in this flux tube is a constant[2, 3], and therefore the energy stored in the tube is proportional to the separation of the charges. Finally, couplings described in QCD are flavor independent. The most well-known and successful potential model is described Isgur, et al. [4, 5, 6]. Early models[5, 6] are non-relativistic and later they are improved by adding some relativistic terms[4]. The Hamiltonian of a baryon is, H = EK + |H + + hi bfI (i.2) i=l * m i i
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7 spin-orbit coupling cancel almost exactly. Since this model does not perform a full relativistic treatment, it is called a "relativized" quark potential model. Compared with non-relativistic models, it has slightly different values of a and b. In the limit of m Q -> oo, where Q indicates the heavy quark, the Hamiltonian is simplified and a new good quantum number j the total angular momentum of the light degrees of freedom, is introduced, j , is the direct analogy with the total angular momentum of the electron in a hydrogen atom. 1.2.3 Heavy-Quark Chiral Perturbation Theory The quark contribution to the QCD Lagrangian in equation 1.1 can be considered to have two parts. The first comes from the light degrees of freedom, and the second part is from heavy quarks. Each of the two parts has distinct symmetry. The light-quark part of the Lagrangian has a flavor SU(3) l xSU(3)h chiral symmetry in the limit that the light-quark masses are set to zero. SU(3) L xSU(3) fi is only an approximate symmetry since the quark masses explicitly break it. This chiral symmetry is spontaneously broken and leads to eight massless Goldstone bosons, the 7r's, AT's, and 77. Their couplings to hadrons are determined by PCAC (partial conservation of axial-vector current) and current algebra, or, alternatively, by the nonlinear chiral Lagrangians. For the heavy-quark part, in the limit of infinite quark masses, the dynamics of a heavy quark in QCD depends on its velocity and is independent of its mass and spin. As a consequence, a new flavor and spin symmetry appear for hadrons containing one heavy quark. This symmetry is called heavy-quark symmetry. Many models based on different approaches have been proposed by theorists from [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. This new symmetry implies that the excitation spectrum and the transition form factors in weak decays of heavy hadrons are independent of the

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8 heavy-quark species and heavy-quark spins. This is similar to a hydrogen-like atom in QED having an excitation spectrum and transition matrix elements independent of the mass and spin of the nucleus. Since heavy hadrons contain both heavy and light quarks, both the chiral symmetry of the light quarks and heavy-quark symmetry affect the low-energy dynamics of heavy hadrons interacting with the Goldstone bosons. Experimentally, strong decays such as E c -» A+7r involving soft pions give such examples. 1.3 Introduction to Charmed Baryons decaying to A.+ (nn) 1.3.1 Spectroscopy The charmed baryons which are covered in this work are those containing a c quark and two u or d quarks. The two light quarks are often referred to as a diquark. In the m c -> oo limit, the total angular momentum of the light constituents, ~fi = + ~t, become a good quantum number. Here is the total spin of the two light quarks and ~t is the orbital angular momentum between the c quark and the two light quarks. In potential models, j l has an analogy with the total angular momentum of an electron in a hydrogen atom. Therefore, the properties of a charmed baryon are mostly dictated by its light-quark contents. In HQET, the final angular momentum of the baryon is given as where ^ c is the spin of the c quark.* *For L = 0, we simply have 7 = 5^, + ^ c . But when L is non-zero, the angular momenta can be coupled as either 7 = (S c + S,) + £ or 7 = ~S C + (3, + Although the final physics

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9 Table 1.2: The s-wave (both L and L, are 0) and p-wave (either L or L t is 1) charmed baryons and their quantum numbers: isospin (/), orbital angular momentum between the diquark and the c quark (L), orbital angular momentum between the two light quarks (L/), total spin of the diquark (5/), total angular momentum of the light degree of freedom (j,), and spin-parity of the baryon (J p ). 5/ and j t are good quantum numbers in the limit of m c — > oo. State I L u Si ./'' A c + 0 0 0 0 0 1+ 2 £ c 1 0 0 1 1 1+ 3+ 2 ' 2 A c i 0 1 0 0 1 132 > 2 S C 0 1 1 0 1 0 1 2 £ C 1 1 1 0 1 1 132 ' 2 2 C 2 1 1 0 1 2 352 ' 2 A' c0 0 0 1 1 0 12 Ki 0 0 1 1 1 132 ' 2 0 0 1 1 2 352 ' 2 1 0 1 0 1 132 ' 2 The properties of all L = 0 (s-wave) and L = 1 (p-wave) baryons of cim, cud, and cdef states are listed in Table 1.2. The lowest-lying L = 0 state is the A+, a cud state in which the ud diquark has isospin of / = 0. The state is antisymmetric under the exchange of the u and d quarks. Since it is required that the total \spin, flavor) be symmetric, the spin state has to be antisymmetric. The the ud diquark must be in a Si = 0 state. Combining Si with the spin of the c quark gives a total spin of J = 1/2. By convention, the A+, like all spatial ground state baryons, has positive parity. For E c states, which have / = 1, the diquark must have 5/ = 1 to satisfy the requirement of \spin, flavor) being symmetric. Adding S, = 1 with the spin of the does not depend on the order of coupling, the latter choice leads to a larger amount of algebra in the calculations of most of the HQET models. The choice of ~f = !) c + j , coupling also helps us derive the physical states more easily.

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10 c quark results a doublet having J p = 1/2+ (E c ) and J p = 3/2+ (E*). A+, E c , and E* are called s-wave particles since there is no orbital angular momentum involved. It is worthing mentioning that we have the similar L = 0 states in the strange baryon sector, A, E, and E*. An important fact is that M(E C *) M(E C ) m s M(E*) M(E) ~ m c ' for the hyperfine splittings. Based on HQET, a hyperfine splitting arises from the color magnetic moment of the heavy quark. Since m s /m c ~ 1/3, the M (E*)-M(E C ) is expected to be about one-third of M(E*) M(E). Now Let us consider the lowest-lying L = 1 (p-wave) particles. In the / = 0 case, there must be S = 0 for the same reason as for the A+ baryon, so j t = 1. The c quark brings hyperfine splitting to give two baryon states of J p = l/2~ and J p = 3/2", where the negative parity comes from the one unit of the orbital angular momentum. This doublet is named A cl . Same as E c , for / = 1, we have S = 1. This gives j, = 0, 1, 2. Each of these is split by its hyperfine interaction with the c quark. This type of excitation ends up with five baryons: the E c0 singlet, the E cl doublet, and the E c2 doublet. Another type of pwave states come from one unit of the orbital angular momentum between the two light quarks, L t = 1. This implies that the / = 0 ud diquark must have 5 = 1. This produces j t = 0, 1,2. Then the hyperfine splittings give five baryon states: the singlet, the A' cl doublet, and the A' c2 doublet. Finally, it can be easily derived that U = 1 and 1 = 1 require 5 = 0. Then the hyperfine splitting gives a doublet of E' cl baryons. Note that the degeneracy of the L = 1 (L t = 1) and L t = 1 (L = 1) switches with the change from / = 0 to / = 1.

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11 1.3.2 Strong Decays All the charmed baryons we described in the last section will decay to the A+, since it is the lowest state of it, d, c compositions. The purpose of these research work is to get better understanding on how the baryons and even p-wave charmed baryons decay to A+. To date, only the E c triplet, two states of the E* triplet, and the A c i doublet have been found, and only strong decays through one or two pions have been observed. Based on the mass predictions by the relativized potential model[4], other p-wave baryons may decay strongly to the final states containing a A+ and one, two, or three pions, but this work failed see any more p-wave states higher than the A cl . In general, the higher states which have the same decay modes are expected to be wide and difficult to observe. So this dissertation only reports the studies of the E^ and A cl baryons. This subsection gives a brief review of the strong decays of these baryons. The selection rules of these decay can be easily derived from conservation of parity and angular momentum. For a strong decay A -> BC, where the spinparities of these particles are denoted by J P A A , J^ B , and jfP, and a possible orbital angular momentum between B and C is denoted by L BC , it is required that L must satisfy A = L BC + ~3 B + ~~?Ci and Pa = P b Pc{-1) Lbc in order to decay with a partial wave corresponding to L B cIn addition, isospin has to be conserved in all strong decays.

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12 Table 1.3: Allowed partial waves for strong decays of the E^ and A c i baryons. The A+7T7T mode listed in the table only represents the non-resonance decay mode. Particle Decav Mode Allowed Partial Wave s c A+7T P E* A+w P Alu/2) A+7T7T P A cl (l/2) E C 7T S A c i(3/2) A+7T7T P A cl (3/2) E C 7T D Table 1.3 lists the all the possible decay channels for strong decays of the and A cl baryons. The E^ baryons do not have the A+7T7T decay because there is no phase space. They should entirely decay through A+7T. The A c i baryons do not have the A+7r decay because of isospin conservation. Based on the table, we should expect that the Swave E c 7r would dominate the A c i(l/2) decay. The A cl (3/2) can only have D-wave E c 7r decay because of the conservation of total angular momentum; the A cl (3/2)-»E*7r decay would be S-wave, but is kinematically forbidden. Thus we should expect that P-wave non-resonance A+7T7T decay dominates the A cl (3/2) decay. 1.4 HQET Predictions on £<*) and A+ x Many quark models have the ability to make quantitative predictions on heavybaryon masses, and almost all of such models use the "constituent quark masses" which are derived from well-known hadron masses. Predictions vary from model to model, and they all fall in roughly the same range. Among all the models, the quark potential model developed by Isgur et al.[4, 6] is the most complete, and it covers all the baryons from the proton to bottom baryons.

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13 Table 1.4: The constituent quark mass assumptions by the potential models. All numbers are in units of MeV/c 2 . Quark Non-relativistic Model Relativized Model u 350 220 d 350 220 s 550 419 c 1500 1628 b 5000 4977 Table 1.5: Some charmed baryon mass predictions by the potential models in comparison with average values of experiments. All numbers are in units of MeV/c 2 . All uncertainties of the experiments measured numbers are less than 3 MeV/c 2 . Quark Non-relativistic Model Relativized Model Experiment 2260 2265 2285 s c 2440 2440 2453 K 2510 2495 2518 A c + i(l/2) 2510 2630 2594 A+(3/2) 2590 2640 2627 An important part of the potential models is to specify the constituent masses of quarks. Typical values used in both non-relativistic models and relativized models are listed in Table 1.4. Although they use different mass assumptions, both models work extremely well for light baryons and strange baryons, and their predictions on charmed baryons are also close. Table 1.5 lists some of the predictions[4, 6] compared with the average experimental values[l]. Potential model also predicted the masses of other p-wave charmed baryons. The masses of E c0 (the next state higher than A ci ) and E cl doublet are predicted to lie around 2770 MeV/c 2 , within 10 MeV/c 2 . Other nine states are also close to each other in masses and range from 2780 MeV/c 2 to 2900 MeV/c 2 . Based on these predictions, unless some of these states have very narrow width, it would be

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14 difficult to see them. In our work, we looked at these mass ranges for A+7r ± and A+7r + 7r" decays, and did not see any obvious signals. The potential models can make calculations on decay widths but do not work very well. Their predictions are very rough and agree with experimental values only in their order of magnitude. The most-recognized theoretical model which can predict heavy-hadron widths was developed by Yan et al.[16], who used the nonlinear chiral quark model[17] to calculate heavy-quark coupling to the Goldstone bosons. In a charmed baryon, the diquark with sf' = 1 + can be represented by an axialvector field and the diquark with sf' = 0 + can be represented by a Lorentz scalar field 0. The decays ~^ ^ +7r anc * ^ ~^ ^ +7r can b e described by two independent coupling constants 9\ and g 2 , respectively. For the decay £ c -»A+7r, the decay rate is determined by g 2 and masses of the £ c , A+, and tt. Their mode predicts 2 92 = -gfl 'A, where g A is the coupling constant in the single-quark transition u -> d. g A is generally assumed to have a value of 1, but the experimental extracted value is 0.75[17]. g 2 values are not very different from other theoretical predictions[18, 19, 20]. Their Lagrangian gives the following decay width: where f w = 93 MeV/c 2 is the pion decay constant and p v is the pion momentum in the center of mass frame, equation 1.3 predicts the total width of E° since E c decays 100% to A+tt. equation 1.4, however, is invalid since the decay E*->E c tt is

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15 kinematically forbidden. If we neglect the radiative decay width associated with the decay E*— >E C 7,* the total width of E* is given by g 2 = 0.612 (with g A = 0.75) will lead to T(E C ) = 2.45 MeV/c 2 , = 17.6 MeV/c 2 , if M s . M A + = 233.5 MeV/c 2 . Equations 1.3 and 1.5 show that the E c width is directly related to the E* width, which has been reported by CLEO collaboration [21]. This work includes the first attempt to measure that E c width. If these widths can be measured accurately, g 2 can be derived from equation 1.3 or equation 1.4 and then further predicts the widths of other particles, for example, H*. Recently Pirjol and Yan[22] included all possible strong-interaction couplings (S'-wave, P-wave, and D-wave) among and between s-wave and p-wave baryons in the chiral Lagrangian. This model contains 45 independent coupling constants up to and including D-wave interactions. Besides gi and g 2 , coupling constants h 2 , /i 3 , hi, ... are involved, which correspond to the p-wave baryons. In this theory, they derived model-independent sum rules which contain these couplings and relate them to properties of the lowest-lying baryons. However, couplings h 2 and h$, which correspond to lowest p-wave baryons, cannot be directly predicted from the constituent quark model. Using published masses[l] M(A+ 1 (2593) A+) = *A radiative decay can happen when the strong decay is largely suppressed. Since the widths of scst->E c 7r decays have been measured to be around 16 MeV/c 2 , there should be almost no radiative decay.

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16 308.6 MeV/c 2 and M(A+!(2625) A+) = 341.5 MeV/c 2 together with g 2 = 0.57,* and neglecting radiative modes A^j — A+7, they calculated r(A+(2593)) = 11.9/i 2 + 13.8^ 0.042h 2 h 8 (MeV/c 2 ), r(A+(2625)) = 0.52/1 2 + (0.15 x 10 6 )/i 2 5.2h 2 h 8 (MeV/c 2 ). With r(A+!(2593)) and r(A+j(2625)), the values of h 2 and h 8 can be obtained, and they can be used to further estimate the width of other particles. Based on the published values of r(A+!(2593)) and r(A+ 1 (2625))[l], it can be estimated that h2 = 0.57±° 0 %, h s < 3.5 x 10~ 3 (MeV/c 2 )" 1 . They further estimated that E c0 and E cl have widths larger than 100 MeV/c 2 , If these estimates are correct, it will be very diffucult to observe signals of next-level higher state baryons. •This value is the average value obtained from applying published masses[21] M(S* ++ A+) = 234.5 MeV/c 2 and M(S*° A+) = 232.6 MeV/c 2 to equation 1.5.

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CHAPTER 2 EXPERIMENTAL FACILITIES 2.1 CESR The Cornell Electron Storage Ring (CESR) is an electron-positron collider with a circumference of 768 meters located on the campus of Cornell University, Ithaca, NY. It can produce collisions between electrons and positrons with center-of-mass energies between 9 and 12 GeV/c 2 . It serves both CLEO for the study of particle physics, and the Cornell High Energy Synchrotron Source (CHESS) for a variety of biological and surface physics studies. A diagram of CESR's main components is shown in Figure 2.1. This accelerator consists of three major parts: (1) the linear accelerator (LINAC), (2) the synchrotron, and (3) the storage ring. Electrons are accelerated to 150 MeV/c 2 by the 150-foot LINAC. Positrons are created by 50 MeV/c 2 electrons colliding with a thin tungsten target part-way through the LINAC. The electrons and positrons are then boosted to the operating energy of about 5 GeV/c 2 by the synchrotron and transferred into the storage ring, where they can be maintained in the storage ring for about 1 hour in order to achieve the highest integrated luminosity. Electrons and positrons travel in opposite directions around the storage ring in evenly spaced bunches (currently there are 9) at 390,000 revolutions per second. Electrostatic separators hold the electron beam and the positron beam slightly apart from each other, and two beams only collide in one place — the center of the CLEOII detector. 17

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18 O Positron Bunch Clockwise # Electron Bunch Counter Clockwise Figure 2.1: CESR layout. The CESR lies in a tunnel 50 feet underground. CLEO-II and the LINAC reside in Wilson Lab.

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19 2.2 CLEO-II CLEO-II is a multipurpose high energy physics detector incorporating excellent charged and neutral particle detection and measurement used to analyze electronpositron collision events generated by CESR. It is operated by the CLEO collaboration of over 200 physicists from many institutions, including the University of Florida. Side and end views of the detector are shown in Figure 2.2 and Figure 2.3, respectively. The major components (going outward from the beam pipe) are the central detector (CD) which forms the tracking system, the time of flight (TOF) system, the electromagnetic calorimeter (CC), the 1.5-Tesla superconducting magnet, and muon chambers. The central detector comprises the Precision Tracking Layer (PTL), the Vertex Detector (VD), and the Drift Chamber (DR). CLEO-II is also equipped with timing, trigger, and data acquisition systems. Brief description of the CD, TOF, and CC are given in the following since they are the most important in this analysis. 2.2.1 Tracking System Charged particle momentum is measured by three cylindrical, coaxial wire chambers sharing a common axis in the direction of the beams. Figure 2.4 shows the structure of PTL and VD. The PTL is a cell-strawtubedrift-chamber which extends within 1 cm of the 3.5 cm beam pipe. The device consists of 6 layers of mylar tubes with 64 axial wires per layer. It is used to make precise measurement of the transverse position of the particle near the interaction point, with a resolution of 90 //m; and it does not provide longitudinal information. The VD covers the radial region from 7.5 to 17.5 cm. It has 10 layers of hexagonal cells as shown in Fig. 2.4. arranged in 10 layers. The VD provides a tracking resolution of 150 /zm in r (j> and 0.75 mm in z.

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Figure 2.2: Side view of the CLEO-II Detector.

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21 Muon Chambers Magnetic Coil Barrel Crystals Time of Flight Beam Pipe PTLA and VD Figure 2.3: End view of the CLEO-II detector.

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22 \ * \ | \ \ \ \ J 0.0 cm + Interaction Point Figure 2.4: The VD/PTL wires.

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• Field Wires o Stereo Sense Wires •Axial Sense Wires DR inner Cathodes DR Inner Shell VD Outer Shell Figure 2.5: The DR wires.

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24 Transverse and longitudinal momentum are best measured by DR, shown in Figure 2.5. This 51-layer outer drift chamber extends from 17.5 cm to 95 cm, including 12,240 sense wires and 36,240 wires. One sense wire and three field wires make a rectangular cell structure. There are 40 axial (parallel to the beam line) layers and 11 stereo (not parallel to the beam line) layers. Axial layers measure transverse momentum, the radial distance of the closest approach to the beam line, and the azimuthal direction of tracks. The stereo layers and 2 cathode layers measure the polar angle and the longitudinal position of the intersection of the track with the beam axis. Sequential layers are offset in azimuth in order to resolve left-right ambiguity in drift distance. An r (j) position resolution of 110 /im for the axial wires and a z position resolution of about 3 cm can be obtained with this chamber. Particles can be identified from the specific ionization energy loss (dE/dx) in the DR. The characteristic bands of dE/dx quantity as a function of momentum for different species of particles are shown in Figure 2.6. Protons can be well separated from other particles at momenta below 1 MeV/c, and separation between pions and kaons is possible only below 400 MeV/c. Track-reconstruction programs are used to find a charged-particle track in an event. First, the pattern of hits, which are the records of the wirescaused by the ionized gas molecules, are recognized; then these hits are fitted to obtain the trajectory of the original particle. The data from all three chambers are combined to measure the momentum vector of charged particles. Two major factors limit the momentum resolution — multiple scattering and the position resolution of the track. Multiple scattering dominates the resolution at low momentum, and the position resolution dominates at high momentum, where the track curvature is small.

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Figure 2.6: dE/dx plotted against momentum for different particles.

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26 The CLEO-II charged-track momentum resolution has been measured to be 8p/p = yo.005 2 + (0.0015) V where the momentum p is in GeV/c. The first term represents the contribution from multiple scattering, and the second term is the contribution from the curvature measurement error. The two terms give equal contributions at a momentum of 3.3 GeV/c. Charged particles with a transverse momentum greater than 225 MeV/c and a polar angle less than 45° will reach the outer radius of the DR and pass through the TOF counters and crystal calorimeter. These tracks are the best measured in the CLEO-II detector. 2.2.2 Time-of-Flight System Besides dE/dx measurement in DR, the TOF device is also an important tool for particle identification. The TOF system has two major parts: a barrel system covering polar angles from 36° to 144°, and an endcap system covering polar angles from 15° to 36° on one side and 144° to 165° on the other side. The barrel system, which is located immediately outside the DR, consists of 64 plastic rectangular scintillation counters, and an endcap system consists of the same but wedge-shaped counters. The scintillators are 5 cm thick and 2.5 m long. Lucite light pipes are attached at each end of the scintillators and connected to photomultiplier tubes. It takes a 500 MeV/c pion about 3.5 ns to travel from the interaction region to the barrel TOF counters, while it takes a kaon about 4.5 ns. The time resolution for pions in hadronic events is about 150 ps. Figure 2.7 plots 1/0 {(5 = v/c) against momentum. As we can see in the plot, the distinction in the bands separates K-n

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27

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28 up to momenta of about 1.1 GeV/c, and protons can be separated up to momenta of about 1.5 GeV/c 2 . Like the energy loss information, particles can not be well identified by TOF at high momentum. 2.2.3 Electromagnetic Calorimeter The Csl crystal calorimeter is used to detect photons and to measure the energies of tracks. It is composed of 7800 thallium-doped cesium iodide scintillating crystals, 6144 in the barrel region and 828 in each endcap, covering 95% of the solid angle. Each crystal is 30 cm long and 5x5 cm 2 in cross section. When a photon or a charged particle interacts with the atoms in the crystal, an electromagnetic "shower" is emitted by crystals, and it is recorded by 4 Si photodiodes at the back of each crystal. The device allows detection of photons with energy of 30 MeV/c 2 to 5.3 GeV/c 2 with excellent resolution. Photon energy resolution in the barrel (endcap) is 1.5% (2.6%) at 5 GeV/c 2 , and 3.8% (5.0%) at 100 MeV/c 2 . The angular resolution in azimuth is 3 mrad (9 mrad) at 5 GeV/c 2 and 11 mrad (19 mrad) at 100 MeV/c 2 . A typical tt° (from the decay ) finding efficiency is about 50%, and the width of the reconstructed 7r° peak is roughly 5-10 MeV/c 2 .

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CHAPTER 3 A+ RECONSTRUCTION 3.1 Introduction In order to study the charmed baryons which decay to A+'s, we first need to obtain A+ candidates, then add additional pions (one or two in our study) to reconstruct heavier charmed baryons. Fifteen hadron decay modes were used to reconstruct A+ candidates. They are pl<-7r+, pR-tt+tt 0 , P K°, pKVtt 0 , pKV, Att + , Att+tt+tt", Att+tt 0 , AK + K°, E+7T+7T-, E + 7T°, E+K+K-, E°tt + , ~-R+tt+, and H°K + . All these decay modes have good signal-to-noise ratios and reasonable statistics. The decay pK _ 7r + has a very large branching fraction and contributes almost half of all A+ candidates. It important to check the consistency of measurements by comparing the results obtained by using the pK~7r + mode with those obtained from other modes. 3.2 Data and Monte Carlo Sample CLEO data are taken on and off the T(45) resonance. The beam energy is 5.187 to 5.280 GeV/c 2 for off-resonance and 5.285 to 5.295 GeV/c 2 for on-resonance. We performed our analysis using both on-resonance and off-resonance events in datasets 4S1-4SG,* corresponding to a luminosity of 4.8 fb~\ All Monte Carlo events generated were with the A+ mass 2286.7 MeV/c 2 , which is our measured mean value over all the 15 decay modes. In order to optimize •Each time CESR or CLEO is updated, the data are processed differently, and they become a new dataset. Conventionally, CLEO datasets are named 4S1, 4S2, 4S9 4SA 4SB and so on. "4S" indicates the state T(45). 29

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30 Table 3.1: Monte Carlo (MC) generated branching fractions for and E<* } studies. UtiLay IIlOQc Average D/o^prv. ix ) MC generated branching ratio i i n i no pK"7r + 7r° n fi7+n f)44-0 1 1 U.UI XU.U4XU. X X U. 1UO pis. U.4o±U.Uz±U.U4 A M — O 0.073 pK 7T + 7T 0.52±0.04±0.05 0.082 0.66±0.05±0.07 0.104 Att + 0.18±0.03 0.028 A7r + 7r + 7r~ 0.66±0.10 0.104 i 1 A A7T + 7r 0 0.73±0.09±0.16 0.115 AJtS. IS. C\ 1 O 1 A no l A AO U.12±0.02±0.02 0.019 S + 7T + 7r 0.68±0.09 0.107 E+7T 0 0.20±0.03 0.032 E+K+K" 0.07±0.01±0.01 0.011 E°7T + 0.20±0.04 0.032 E-K+7T+ 0.10±0.02 0.016 E°K+ 0.08±0.01±0.01 0.013 All 1 the cuts* used to reconstruct each decay mode, 15 individual types of events are generated by sufficient amounts (more than 100,000 events for each mode). In our later study on the A+, or the E^ decaying to the A+, we need the Monte Carlo to provide the correct over-all efficiencies. Thus the decay ratios of A+ decay modes were generated as shown in Table 3.1. In the table, the average relative branching ratios for pR-tt+tt 0 , pK°, pK°7r + 7i-, and pKV are the values recently measured by CLEO[23]. For other modes we used the PDG average values[l]. *A cut is an action to remove a certain fraction of the events which contribute mostly to the background. An optimized cut on a measured physical quantity is the one which gives the best signal-to-noise ratio after it is applied.

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31 3.3 Event Selection 3.3.1 Track Selection When a charged particle travels through the tracking chambers, a set of hits, caused by the passage of the track, is generated. The tracking program will fit each set of hits forming a "track," which is a curve representing a possible particle causing the hits. In CLEO, this task is accomplished by the track-finding and fitting program, DUET. Each track is described by the following five track parameters: (1) CUCD: curvature of the track; (2) FICD: 0 of the direction of the track at point of closest approach to the center of the CLEO-II detector; (3) DACD: impact parameter of track with respect to the center of the detector; (4) CTCD: cotangent of the polar angle, 9 (i.e. CTCD = 0 for tracks in the r 0 plane and infinite for tracks pointing down the beam pipe;) (5) ZOCD: z coordinate at point of closest approach to the center of the detector. All other information about the track can be calculated from these five parameters. Before 1996, the track fitter in the CLEO DUET processor ignored the energy loss of a track in materials and included multiple scattering approximately. In 1996, the CLEO collaboration reprocessed the data from 4S1 to 4SG, and the new data are called the recompressed data. For the recompressed data, the old track fitter is replaced by a Kalman Filter. The new Kalman fitter optimally treats both multiple scattering and energy loss, so it gives improved error matrices of track parameters for all tracks and better-measured track parameters for low-momentum tracks. It also fits each track separately for each particle hypothesis. To select a track as a candidate for a pion, a kaon, or a proton, which come from the r 0 range of e+e~ interaction points, we first require it to have not only r 0

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32 also z information. We reject all tracks which are identified inward going. To ensure these tracks are close to the interaction point, we used the following "track quality" cuts: where DBCD is the radial distance of the point of closest approach to the beam line, P is the momentum of the charged track; and Note that the DBCD cut changes from 5 mm at 0 momentum to 1.2 mm at 1 GeV/c and then becomes flat from 1.2 mm. This is because the low-momentum tracks are more poorly measured, but we still want to keep those having fairly good quality. Such selected tracks are used as the charged track candidates which are directly decayed from A+'s. The A+ has a mean lifetime of about 2 x 10" 13 s, so its flight distance in the CLEO detector is within the range of interaction points and is negligible in the invariant mass reconstruction. 3.3.2 Particle Identification As we discussed in the last chapter, two types of detectors are used for the identification of the charged tracks: the time-of-flight counters and the drift chamber for the dE/dx measurement. The information from each device, if present, is quoted as the number of standard deviations of the measurement from the expected value as a given particle hypothesis. For each charged track, we combine the TOF and the dE/dx information to define a joint |DBCD| < < 5 3.8|P| (mm) if \P\ < 1, 1.2 mm if|P|> 1, Z0CD| < 5 cm. (dE/dx) meas (dE/dx) exp ] 2 \{TOF) meas (TOF) exp ° dE/dx Otqf

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where i stands for pion, kaon, and proton hypothesis. The x 2 ranges from zero to infinity and it is not very convenient to use when we perform a track identification cut. So, a equivalent parameter, the \ 2 probability, PROB, is calculated for each hypothesis. PRQB ranges from zero to one.* For data analysis, it has the advantage of being flat in the zero to one range for particles which are the right species and peaking at zero for particles which are the wrong species. One particle identification information will be used if the other device does not have the measurement. If neither TOF nor dE/dx information is present, we assume the track is a pion and assign it a small PR0B(7r) value. In this work, we are more concerned about separating protons, kaons and pions from each other, so a normalized probability, called "PROB level," is used. To strongly identify a proton or a kaon, we make a cut on PRLEV = PR0B W PROB(p) + PROB(A') + PROB(tt) or, PROB(A) KALEV = PROB(p) + PROB(A) + PROB(tt) ' We do not use a PROB level cut for pions, since we take all the tracks selected as pion candidates. 3.3.3 7 and ir° Finding Although the Csl electromagnetic calorimeters can measure the photon energy and angle, they also interact with hadrons. An electromagnetic shower generally has different lateral development than a hadronic shower. This provides us a way *Note it does not really represent the probability of the track to be a specific particle hypothesis.

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34 to distinguish them from each other. The quantity E9/E25 is measured as Energy of 9 central crystals E9/E25 = Energy of 25 central crystals Here the 9 crystals in the numerator are those in a 3 x 3 array, with the most energetic crystal at the center. The 25 crystals in the denominator are those in a 5x5 array. Since electromagnetic showers tend to be more narrowly contained than hadronic showers, they mostly have E9/E25 near 1. The most widely used cut on E9/E25 quantity in CLEO is to keep 99% photons* and get rid of most of the hadronic showers. A E9/E25 cut also gets rid of two photons which are close together. Also, as the high energy showers near to each other often deposit energy to the same crystals, we can use a program to "unfold" the nearby shower clusters. The unfolding routine works well to identify high energy photons but become less efficient when photon energy is low. When we select a photon in this analysis, we mostly use unfolded E9/E25 at 99% (this cut is called 99% E9E25U), and sometimes directly use E9/E25 at 99% (not unfolded, called 99% E90E25) when we are certain that the photon energy spectrum is low. 7r°'s are formed by taking two photon combinations and calculating the di-photon invariant mass. The di-photon combination must have at least one photon in the barrel region of the crystal calorimeters. Unless otherwise stated, we always selected 7r° candidates as just described. In addition, we require the mass of each candidate to be within 2.5 o M 0 of the known 7T° mass, which is 134.976 MeV/c 2 . However, to suppress combinational background, we will place cuts on 7r° momenta in different situations. "This cut value is actually obtained by a program which returns E9/E25 cuts for 1% efficiency loss in a given region of the detector. The 1% is nominal only from MC, and it is a loss in an event with no other showers. Actual efficiency losses are substantially more, e.g., 5-10% efficiency loss for photons in hadronic events from a 1% cut. Harsh cuts, like 5% or 10%, lose too many photon candidates, so they are not often used.

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35 3.3.4 Event Vertex Finding Finding the event vertex, which is the e + e~ interaction point, can be very useful to improve the mass resolution of a reconstructed particle. Most of the charged tracks come from the event vertex or vertices extremely close to the event vertex, so we can obtain the event vertex with errors by performing a vertex fit using charged tracks. However, some tracks are not from anywhere close to the event vertex, and some tracks are not measured correctly. Using these tracks will increase the uncertainty of the event vertex. Therefore, to find the event vertex, we start with the two tracks which are the most consistent with the beam position and also not close to back to back, form a vertex, then add more tracks one by one in the order of their consistencies with the current found vertex, until further adding any track would make a poorer vertex fit. If the error of the final found vertex is not small enough to confine itself within the spread of the beam position, or if we do not have more than one charged track, the beam position will be used as the event vertex. 3.3.5 Vee Finding A large fraction of A+'s decay to tf°'s or A's. In CLEO, the K° is reconstructed by the decay K s ->• 7r + 7i-* and the A is reconstructed by its decay to jm~ . K s 's and A's mostly fly a few centimeters away before they decay. The K s has cr = 2.7 cm and the A has cr = 7.9 cm. Since in each case the shape of the two daughters' paths looks like the letter V, they are generally called Vees. The vertex of a Vee formed by the two charged tracks is called a secondary vertex, in distinction to the primary vertex, the event vertex. To find Vee candidates, we first list the tracks which satisfy — DBCD/DDBCD > 3— (DDBCD is the estimated uncertainty of DBCD) to exclude the tracks coming from the *K° appears in the states of K s (50%) or K L (50%). CLEO detector cannot detect the K L since it travels many meters long (cr = 15.5 m).

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primary vertex. The tracks in the list, called the secondary tracks, are all possible daughters of Vees. Then we take every pair of tracks from the list and fit them to form a vertex. We discard the pair if the fit is very poor (x 2 < 0.001) or if the significance of the three-dimensional flight distance is smaller than 3a. We require the total number of hits inside the found vertex for both daughters to be smaller than 2. Also, the reconstructed mass of a Vee should be within 3 a M of the known K s or A mass. Note that the Kalman Filter only calculates the track parameters of the secondary tracks from the origin. We corrected these track parameters at the secondary vertex, then further recalculated the momentum and the position of the Vees. Details of the CLEO secondary vertex finding program are described by Prescott[24]. In this analysis, we made a few more cuts on Vee candidates to make the signal clearer with a tiny sacrifice of losing events: a Vee is required to come from the range of the beam position; the separation in z of the two daughters at the r intersection should not be large (the significance is required to be smaller than 5); for a K s candidate, each daughter must satisfy PROB(tt) > 0.001; for a A candidate, the daughter which carries most of the momentum in the decay in the laboratory frame (according to special relativity, this almost guarantees that it is the proton if its parent is really a A) must satisfy PR0B(p) > 0.001. 3.3.6 £ and H Finding The decays of the four £ and 3 are shown in Figure 3.1. Because these particles are supposed to be the decay products from the A+, which has very short lifetime, it is very reasonable to assume that they all come from the event vertex. £+ candidates are reconstructed through the decay £+ -> p7r°. The tt 0 selection is described in Section 3.3.3. All charged tracks are taken as proton candidates.

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37 Figure 3.1: Decay paths of (a) E+ -> p7r° and tt° 77, (b) E° -» A7 and A ->. p^-, (c)E -> Att" and A -» p*, and (d) S° -» A7r°, A -> p7r~, and tt 0 -> 77. In each figure, the solid curves indicate paths of charged particles; the dashed lines indicate paths of photons; and the dotted lines indicate paths of neutral hyperons. All £ and S are assumed to be created at the event vertex, which is shown as •. The £+, -~» s °> and A tr avel for a distance before decay. The E° and 7r° decay immediately after being created.

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38 A particle identification cut PRLEV > 0.5 is used. After adding the 4-momenta of the proton and the 7r°, the flight distance of E + can be calculated by constraining the E+ coming from the event vertex, and, further, the E + decay vertex can be obtained. Since the E+ has a long lifetime (cr = 2.4 cm), we require the transverse flight distance of the E + to be bigger than 5 mm and DBCD of the proton to be bigger than 0.5 mm. In addition, to reduce the combinational background, we make a momentum cut of 300 MeV/c 2 for the tt° and 500 MeV/c 2 for the proton. We require the mass of each E + candidate to be 20 MeV/c 2 within the known E + mass, 1189.4 MeV/c 2 . E° candidates are reconstructed through the decay E° -> A7, where selections of the A and 7 are described in the previous sections. A 50 MeV/c 2 photon energy cut is used to reduced the background. We require the mass of each E° candidate to be 20 MeV/c 2 within the known E° mass, 1192.6 MeV/c 2 . E~ candidates are reconstructed through the decay H~ Air~. All negativecharge tracks are used to be the n~ candidates. The E~ has cr = 4.9 cm so its decay vertex should be distinctly displaced from the event vertex. The initial guess of the H~ vertex is at the intersection of the projected A path and the jt track. The combination is discarded if the vertex cannot be reasonably formed or the combined direction does not point back to the event vertex. The invariant mass of Ayr is required to be within 6 MeV/c 2 of the known H" mass, which is 1197.4 MeV/c 2 . Then the track parameters of the A and the n~ are recalculated at the new vertex by constraining the An~ invariant mass to be 1197.4 MeV/c 2 . The H~ momentum and vertex are further obtained more accurately. The E~ flight distance is required to be larger than 5 mm, and its r 0 radial distance is required to be larger than 1 mm. H° candidates are reconstructed by a E° -» Att°. We initially build the H° vertex, then combine the tt° angle with the projected A path. The combined direction is

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39 required to point back to the event vertex. We correct the 77° 4-momentum by constraining it to come from the E° vertex. Then the H° 4-momentum is recalculated. The reconstructed ~° mass is required to be within 8 MeV/c 2 of the known H° mass, which is 1315 MeV/c 2 . The r <\> radial distance of the H° vertex from the event vertex has to be larger than 5 mm. A 100 MeV/c 2 ir° momentum cut is used. 3.4 A+ Selection A A+ is reconstructed by calculating its 4-momentum and decay vertex from the momentum, mass assumption, and vertex information of its direct daughters. The A+ signal can be measured by fitting its reconstructed mass spectrum using Mn_Fit.[25]* Mn_Fit is an interactive plotting and fitting package that uses MINUIT[26] to fit histograms or data read in from a file and to display the fitting results. It is widely used by high energy experimental groups to perform data analysis. Although the purpose of reconstructing the A+ baryons is to observe the A+ x and the E c which decay to the A+, our A+ candidates are not selected by direct optimizing the A+ or E« signals. The A+ or E c signals should not be biased by A+ selection. In general, for each A+ decay mode we try to use cuts to get the best signal-to-background ratio at x p > 0.5. x p is the A+ momentum normalized to the maximum possible A+ momentum, defined as Xp — where E is the energy of the e + (e~) beam of CESR. Note that x p > 0.5 is only used to optimize the A+ selection cuts, and not for A+ selection. The momentum *In this dissertation, all histograms, fitted curves and direct statistical results are obtained from Mn-Fit.

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40 spectra of charmed hadrons from the e + e~~ annihilation have been shown to be hard compared to the combinational background. Therefore a cut on x v is a very good way to improve the signal-to-background ratio. For most of the decay modes, the x p > 0.5 cut makes the signal be roughly same large as the background. Later, when we look at or signals, we make x p cuts on these heavier baryons, and there will be no cut on the x p of the A+. Since a A+ travels at a distance of the order of 100 /im before it decays, its vertex can be slightly displaced from the event vertex. We find that constraining all direct A+ daughters (except 7r°'s which do not have position information) to come from an unknown vertex significantly improves the mass resolution of the A+. Thus for each of the 15 decay modes, the A+ candidate is built at its vertex. For the decay modes containing a proton, strong particle identification cuts are needed. Since the proton momentum spectrum are different for different decay modes (generally higher for two-body decays and lower for three-body and fourbody decays), the cut value on PRLEV does not correspond to the same efficiency for the different modes of background rejection. The numbers we used — 0.3 for pK°, 0.6 for pK-7r+, and 0.8 for pK-yr+Tr 0 , pKVtt 0 , and pKV— have roughly the same efficiencies. For the two modes containing a proton and a K~, the identification cuts are relatively softer since the proton is already strongly identified. Since the signals of E+K+K", E-K+7T+, and ~°K + are already very clean, very soft PWB(K) cuts are used to keep the highest efficiencies. To suppress combinational background, Monte Carlo optimized momentum cuts on charged tracks or 7r°'s are used. For charged particles, we generally cut at high values for two-body decays and lower values for multi-body decays. All decay modes containing a tt 0 have very high backgrounds, so we always need restrictive cuts on 7r° momenta.

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41 Table 3.2: Particle Identification and Momentum cuts used in the 15 decay modes for the A+ selection. The values of physical parameters in the table are required to be larger than the corresponding numbers listed. The momenta P K ±, P n ±, and P n o are in units of MeV/c. Decay PRLEV KALEV PROB(K) 1 /i u pK-7r+ 0.6 0.2 100 pK-TT+TT 0 0.8 0.5 200 500 pK° 0 3 piv 7T 7T U.o 500 pKV 0.8 500 Att+ 300 A7r + 7r + 7r~ 200 Att+tt 0 300 500 AK+K° 0.3 E + 7T + 7r _ 100 E+7T 0 300 E+K+K" 0.02 100 E°7r + 400 E-K+7T+ 0.01 100 0.01 300 The cuts used to reconstruct A+'s for each decay mode are listed in Table 3.2. Note that the vertex constraint routines are common for all modes. The selection criteria of all immediate A+ daughters have been described in previous sections. Figures 3.2 to 3.16 show the reconstructed mass of A+ for the 15 idividual decay modes, and Figure 3.17 shows the sum over all modes. For the purpose of display a x p > 0.5 cut is applied to the A+ momentum. The measurements on all 15 modes and their summation are tabulated in Table 3.3. All parameters are obtained by fitting the signal with a single Gaussian. The Gaussian width of each decay mode reflects the detector resolution of the A+ mass. The table shows that the fitted widths agree very well with those of the Monte Carlo, except some modes with a tt° and "All." For the modes with a tt°, we found that the widths are all wide and the signals could not be fitted well by a single Gaussian.

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5000 4000 ^ 3000 d \ 2000 in c 0) > 1000 ~1 I I 1 1 1 1 1 1 r-i 1 rJ 1 1 1 I I I I I 2.10 2.20 2.30 GeV/c J 2.40 Figure 3.2: Invariant mass of pK~7r" 2.50 > in o 400 300 200 100 "i i i — | — i — i — i — | — i — i — i — [0 ' — ' — 1 — 1 — I — 1 — i — i — I — i i I— i— i— _i 2-10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.3: Invariant mass of pK n^Tr 0 .

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43 600 I 1 1 1 1 1 1 1 1 i i 1 1 1 1 r 0 ' — 1 — 1 — 1 — I — i — 1 — ' — I — i — i i I ' 2.10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.4: Invariant mass ofpK°. 400 | — i — i — i — | — , — i — i — r 2-10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.5: Invariant mass of pK°7r 0 7r°.

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44 1 60 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 0 I 1 1 1 1 1 1 1 1 i i i 1 2.10 2.20 2.30 2.40 2.50 GeV/c J Figure 3.6: Invariant mass of pK°7r°. 2-10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.7: Invariant mass of An + .

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45 2-10 2.20 2.30 2.40 2.50 GeV/c J Figure 3.9: Invariant mass of A7r + 7r°.

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2-10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.11: Invariant mass of E+7r + 7r~.

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240 I — i — i — i — | — i — i — i — | — i — i — i — |40 0 ' — 1 — 1 — 1 — I — i — i — i I i i i I i i 2.10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.14: Invariant mass of E°7r + . 2.10 2.20 2.30 2.40 2.50 GeV/c 2 Figure 3.15: Invariant mass of H~K + 7r + .

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49 2.50 Figure 3.16: Invariant mass of E°K+. 6000 o \ > 4000 m d \ W #-' c UJ 2000 "i i i 1 1 1 r i i» uu * | "V" ' JP v tf . <>«ruj 0 2.10 -i — i i_ —i — i — i — I 'ill 2.20 2.40 2.50 2.30 GeV/c 2 Figure 3.17: Invariant mass of A+ candidates reconstructed by 15 decay modes. Although the distribution overlaid by 15 different Gaussians is not exactly in a Gaussian shape, we fit it by a single Gaussian to roughly check the central mass value and the signal-to-background ratio.

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50 Table 3.3: Masses, Monte Carlo widths (a M (MC)), Fitted widths (a M (Fit)) together with the number of A+'s found with x p > 0.5. The mass for all modes is the errorweighted mean value over all modes and the same value is obtained when we fit Figure 3.17. The signal the background shown in the table are the fitted areas within 1.6cr M (Fit) around 2286.7 MeV/c 2 . Masses and widths are in units of MeV/c 2 . Only statistical errors are shown. The statistical errors on Monte Carlo width are all 0 01 MeV/c 2 . Decay Mode Mass a M (MC) a M (Fit) Signal Background pK-7r + 2286.7±0.1 5.20 5.26±0.11 9650 11660 pK-7r + 7r 0 pK TY + TC~ p kV 2286.4±0.6 8.11 9.04±0.62 1252 1928 2287.1±0.2 6.51 6.33±0.23 1716 1019 2287.1±0.3 3.98 4.07±0.30 568 690 2285.2±0.6 8.61 7.63±0.63 514 490 Att+ 2287.8±0.3 7.03 7.15±0.31 1368 658 A7r + 7r + 7r _ 2287.0±0.2 5.28 5.37±0.21 1916 1812 Att+tt 0 AK+K° 2285.0±0.4 10.38 11.18±0.56 2007 1864 2286.5±0.4 2.91 2.51±0.32 70 25 E + 7T + 7T~ 2287.6±0.3 7.41 6.96±0.38 947 696 E+7T 0 2284.0±1.7 10.32 9.80±0.23 95 101 E+K+K2287.0±0.4 2.61 2.54±0.31 65 18 E°7T + 2286.5±0.6 7.54 7.79±0.59 707 896 H-K+7T+ 2286.7±0.1 3.50 3.27±0.25 317 171 H°K+ 2286.9±0.5 6.73 6.10±0.51 221 173 All 2286.7±0.1 20675 22160 If we fit them by a double-Gaussian, the data and the Monte Carlo are in better agreement (about half way closer). Thus we can conclude that the Monte Carlo can predict the mass resolution of the A+ very well. Note that our measured mean value of A+ mass, 2286.7 MeV/c 2 , is slightly larger than the PDG mean value 2284.9±0.6 MeV/c 2 , which is partially determined by the result of CLEO-I.5[27]. CLEO-II has measured many more decay modes with much better mass resolutions and tiny statistical errors, and has constantly shown a higher value. So in this work, we decided to use the CLEO-II value as the "known" A+ mass. As we will show in later chapters, as we look at A + , or £(*)

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51 mass by mass differences with A+, the error on A+ mass contributes little to the systematic errors of our measurements. The purpose of this work does not include the A+ mass measurement. It should be a separate research work which will require a comprehensive study of the systematic uncertainties of the mass scale.

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CHAPTER 4 STUDIES OF A+ BARYONS 4.1 Introduction Two particles have been found decaying to A + and two charged pions. They have been named A+(2625) and A + (2593) by the Particle Data Group[l]. The first observation of the A+(2625) was made by the ARGUS Collaboration[28]. The E687[29] and CLEO[30] Collaborations subsequently confirmed this charmed state. CLEO also reported the first observation of A+ (2593), and E687[31] and ARGUS[32] published the confirmation of these states. Since hese particles were seen only in A+7T+7Tmodes but not in A+tt° mode, they are believed to be the excited A + baryons rather than higher states of E c baryons, which decay through both A+?r and A+7T+7Tchannels but should prefer A+?r modes. Proposed by the previous experiments and strongly confirmed in this work, the two states are a fine structure doublet of the excited A+ baryons in which the light diquark ud has an orbital angular momentum L = 1 with respect to the c quark, Therefore, even though they were called A*+ in previous experimental publications just referred above, we prefer to call them the A+(2593) and A+(2625),* where subscript 1 refers to the total spin of the light degrees of freedom. The A+j(2593) decays largely, and perhaps entirely, into £ c tt. As explained in Chapter 1, this is the expected dominant decay channel. The quark model predicts that E c has J p = 1/2+ so almost certainly the A+^2593) has J p = 1/2". The *They are called A+(l/2) and A+ (3/2) in Chapter 1 in order to conviently distinguish the spin difference But the general convention to name a excited state particle is to used the particle name followed by its first observed mass. 52

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53 J p of the A+j(2625) is expected to be 3/2". The A+i(2593) and the A+^2625) are presumably the charm counterparts of the strange particles the A(1405) and the A(1520). Since the last publication of these states in 1995, the CLEO-II detector has collected 60% more data, and the recompress made in 1996 significantly improved the resolution of low-momentum tracks, which is very important in order to observe A*i->A+7r + 7rdecays. We think it is time to confirm or update our previous results and look for a new decay channel, A+7r°7r°. In this chapter, we first describe Monte Carlo simulation of A+ x decays. This is followed by the observations of A+tt+tT and A+ttV signals. Then we present our measurements on E c 7r decay substructures and the search for the decays of A+7r° and A+7. In later sections, we report the results on masses, widths, fragmentation functions, branching ratios, production ratios, together with a detailed discussion on estimating systematic errors. We also compare our results with theoretical predictions. 4.2 Monte Carlo Studies In order to determine the detector resolution of signals and estimate the reconstruction efficiencies, large amounts (more than 100,000 events for each decay mode) of Monte Carlo events were generated. Therefore, statistical errors on all quantities directly derived from Monte Carlo can always be neglected in the numerical calculations. The A+ x (2593) events are first generated with a mass of 2593.9 MeV/c 2 and zero width to obtain the mass resolution of the detector. After a preliminary measurement of the natural width using the real data, more A+i(2593) events with the measured natural widths were generated. We found that our invariant mass recon-

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54 struction program can extract the Monte Carlo generated natural width very well, and efficiencies calculated from 0 width events and events with a finite width are very close. The A+ 1 (2625) events are generated with a mass of 2626.6 MeV/c 2 and zero width. To study the substructure of decays, we generated samples with both E c 7r and non-resonance decay modes. The non-resonance modes are simply the decays A+^A+tttt and A+^A+ttV. The E c tt modes are (1) the mixed 50% A+^E^+ttand 50% A+->E°7r+, with E++->A+7r + and E^A+tt", and (2) the A+-+ E+tt 0 with E+->A+7T°. TheA+!-^E c 7r and A+^A+tttt modes are used for the A;!i(2593) and the A+ x (2625), respectively, to evaluate the corresponding efficiencies and resolutions, as the data show us that these are the dominating decay modes. Determination of the detector resolution by the Monte Carlo is very crucial for extracting the intrinsic width of a particle when its intrinsic width is close or smaller than the resolution. As stated in the last chapter, we have checked for all 16 A+ decay modes, and the Monte Carlo predicted widths are all in good agreement with the fitted widths of the data signal. However, the charged daughters of A+'s are all at quite high momentum ranges, but the two independent pions in A+ x -> A+7T7T decays are both soft. It is possible that the CLEO-II official Monte Carlo program overestimates the performance of the detectors on measurements of low-momentumtrack parameters. This can make the Monte Carlo predicted resolutions smaller than actual resolutions of A^-^ A+nn signals. Measuring the signal of the D* + , which has F < 0.13 MeV/c 2 at 90% confidence level[l], can be used to check the accuracy of the resolution of the low-momentum pions by the Monte Carlo. To do this, we looked at the mass difference M(D* + ) M(D°) of decay D*+ -> D°tt+ (and D° -> K~ir+) in which the momentum spectrum of the independent pion is close to those of the two independent pions from A+,

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55 decays. The fitted width of the signal of M(D* + ) M(D°) distribution is (0.550 ± 0.001) MeV/c 2 for the Monte Carlo, but about 0.63 MeV/c 2 for the real data in the worst case,* about 15% larger. We think the actual detector resolution is in the 0 15% range larger than the Monte Carlo predicted one. The D* + width is largely affected by the angular resolution of the soft pion. This is not the case for widths based on our study of comparing the Monte Carlo widths with the data at different decay angle. So the amount of the disagreement between real data and the Monte Carlo for D* + may not reflect the same amount of the disagreement for Ati widths. But it appears that the Monte Carlo prediction of the resolution is too optimistic. This was not noticeable in the previous research in CLEO since the mass resolution itself was poor. For the CLEO-II recompressed data, this effect should be seriously considered as a big source of systematic uncertainties for particles whose natural widths and mass resolutions are small. Some studies are performed to check the correctness of Monte Carlo determined efficiencies of particle reconstruction. We calculated the decay ratios of each A+ decay mode relative to P K-tt + based on the actual yields from the data and Monte Carlo predicted efficiencies, and they all agree within 10% with the Monte Carlo generated ratios. As we measure all production and branching fractions by ratio relative to A+, the effect of the error of A+ reconstruction efficiency mostly cancels in the ratio. For the real data, the M(D*+) M(D°) spectrum is difficult to fit due to the uncertain background shape near the peak, which is very close to the kinematic threshold. When we fitted the signal at a different pion momentum range, we found that fitted width is closer to the Monte Carlo predicted resolution at higher momentum pions. By using different fitting procedures to fit signals at different pion momentum ranges, 0.63 MeV/c 2 is the largest fitted width. We believe that 15% is a conservative estimate of how much the Monte Carlo miscalculates the mass-difference resolution.

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56 4.3 Signals and Fits To observe signals, we combine each A+ candidate with two pions (ir + n~ or 7r°7r°), reconstruct the invariant mass with the A+, then fit the spectrum of the mass difference M(A+7T7t) M(A+). A+ selection criteria are described in the last chapter, and the reconstructed masses of A+ candidates are required to be within l.6a M of 2.2867 MeV/c 2 , our fitted mean value of the A+mass. As A+j decays are strong decays, their lifetimes are very short. We can assume that they decay at the interaction point of e + e~ annihilation. The event vertex finding procedure is described in Chapter 3. When we reconstruct the invariant mass of each A+7T7t combination, we constrain the three particles to be from the event vertex. We find that using vertex constraint improves the resolution of the A+ 1 (2625) by more than 10% for the A+7r + 7i-case. In order to see very clean signals,* we require x p > 0.7 for each A+irn combination. x p is defined as yfELm Ml + ' where p A + is the total momentum of the A+tttt combination, E beam is the beam energy of the e + (e~), and M A+ is the mass of the A£. 4.3.1 A+7T+7Tc Shown in Figure 4.1 is the mass-difference spectrum of A+tt+tt" combinations. The large peak at 342 MeV/c 2 is due to the decay A c + !(2625) ^A+tt+tt", and the smaller peak at approximately 309 MeV/c 2 is from A+ 1 (2593)^A+7r + 7 r-. To fit the the mass-difference distribution, we used a second-order Chebyshev polynomial to fit the background and two signal functions to fit the peaks. Each *As we can see in later sections, having low background is very important to measure the E.tt substructure.

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57 Figure 4.1: Mass difference M(A+7r + 7r-) Af(A+)

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58 signal function is a Breit-Wigner function with a floating width convoluted with a single Gaussian function with a fixed width. The Breit-Wigner widths reflect the intrinsic widths of the particles; while the Gaussian widths, which are 1.28 MeV/c 2 for the A+(2593) and 1.62 MeV/c 2 for the A+^2625) determined from the Monte Carlo studies, are used to parameterize the detector resolutions. In order to prove that signals in Figure 4.1 are not artifacts of special selection criteria, we checked the backgrounds from two sources: one is the combination of a fake A+ candidate taken A+ sidebands and 7r + 7r~, the other is the combination of a A+ with two same-sign pions (7r ± 7r ± ). As Figure 4.2 shows, these mass-difference distributions are smooth and similar to the A+7T+7Tbackground. These plots can be fitted very well using the fixed background parameterization as used in Figure 4.1. As shown in Figure 4.1, it is obvious that the A+^2593) peak is not fitted well by a Breit-Wigner convoluted with a Gaussian. Fitting uncertainties on both the mass and the width are big. We will discuss this further in the next chapter after presenting the S c mass measurements.* The extracted Breit-Wigner width of the A+j(2625) with a 1.62 MeV/c 2 Gaussian resolution is 0.7±0.3 MeV/c 2 , close to zero. But the question is, have we measured a finite width of the A+^2625)? As we mentioned in the last section, for CLEO-II the actual detector resolution may be as much as 15% larger than the Monte Carlo predicted value. If we fit the A ^i(2625) with a single Gaussian with a floating width, the fitted width is 1.76±0.12 MeV/c 2 , less than 10% larger than the Monte Carlo predicted value. So taking statistical errors into account, we cannot conclude that we have observed a finite natural width of the A+(26 25). Therefore, in the following study, we calculated the *We also remeasured the A+(2593) signal by a new technique. This second method is only possible after a measurement of E c width and mass. The measurements give different mass and width values.

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59 30 20 10 0 20 10 0 20 10 0 1 1 1 1 — 1 1 i i i i i — i — i — i — | — i — i — i — i — A c + 7t~7y" : i i i i | i i i i 1 i i i i : A c + 7T + rr + \ h : -r ii i i | i i i i 1 i i i i " A c + Sidebands 1 — i — i — i — i — i — i — i i i i— i " 0.290 0.315 0.340 0.365 0.390 GeV/c 2 Figure 4.2: The top plot shows the mass difference M{K + tt~ti-) M(A+) and the middle plot shows M (A+7r+7r+)-M(A+), and A c +'s candidates are taken with masses with 1.6 a M ^ from 2.2867 MeV/c 2 . The bottom plot shows M(A+7r+7r-) M("A+ side"), where a "A c + side" is from A+ sidebands which are taken from 3 4 to 5 0 (Jm s+ away from 2.2867 MeV/c 2 .

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60 production rate of the A+^2625) by using the yield of the signal fitted by a single Gaussian, which is roughly 10% smaller than the yield obtained from the fit using a Breit-Wigner convoluted with a Gaussian. Corresponding systematic uncertainties were added in the final results of branching ratios and production ratios. Table 4.1 shows the yields, mass differences, and widths obtained by using different fits to Figure 4.1. Fit Type 1 uses a Breit-Wigner convoluted with a Gaussian for the A+^2593) peak and a single Gaussian for the A+j(2625) peak. Type 2 fits the region right to 294 MeV/c 2 , excluding two entries from the plot. Type 3 uses a third-order polynomial to fit the background instead of the second-order one. Higher-order polynomials were also used, and the results are very similar. Types 4, 5, and 6 only fit the A+^2593) peak. Type 4 excludes the region from 325 MeV/c 2 to 360 MeV/c 2 ; Type 5 excludes from 335 MeV/c 2 to 350 MeV/c 2 ; Type 6 only fits the region from 290 MeV/c 2 to 325 MeV/c 2 . Types 7 and 8 only fit the A+(2625) peak. Type 7 fits only from 335 MeV/c 2 to 390 MeV/c 2 and Type 8 excludes from 300 MeV/c 2 to 325 MeV/c 2 . Type 9 uses a Breit-Wigner convoluted with a Gaussian to fit the A+ (2625) peak instead of a single Gaussian. The errors from Type 2 to Type 8 are not shown since they are roughly the same as in Type 1. We have performed more variations of fits other than listed in Table 4.1. Variations of the results are all within the range Table 4.1 shows. Different values of x p and cut around the A+ mass may vary the results of the mass and the width. As we checked, the variation of the widths on both particles and the mass difference of the A+(2625) is less than the one shown in Table 4.1, but the mass of the A+(2593) varies from 308.2 MeV/c 2 to 309.1 MeV/c 2 .

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61 Table 4.1: The measured yield, mass, and extracted width of A^-^A+tf+jr by various fits. Fit Tvnp ail Jv ^/c YiplH I lclU iviass^ivie v c I Widtn(MeV/c ) A+ ( 25931 1 1 i qi +31 iyl -28 dUo.o ± U.4 A -7+1.3 9 £t 904 QOQ 1 oUo. 5.2 Q O 1 ( D oUo.D 4.2 zuy oUo.y 5.3 5 194 308.7 4.9 6 181 308.7 4.4 A c + i(2625) 1 431 ± 23 341.80 ±0.10 2 428 341.78 3 428 341.81 4 433 341.84 7 429 341.77 8 431 341.86 9 475l 2 2 8 9 341.84 ±0.11 0.7 ±0.3 4.3.2 A+ttV To search for A+ -)• A+7r°7r° signals, we combined each A+ candidate with two 7r°'s and measured the mass difference with A c +. tt 0 selection criteria are described in the last chapter. However, to suppress large background we need an additional cut on tt 0 momentum. We chose the cut based on the optimization of the Monte Carlo signal versus the background from the data. As Table 4.2 shows, the Monte Carlo predicts that 150 MeV/c gives best signal to background ratio for different momentum cuts. By fitting the signals in the M(A+7r°7r°) M(A C +) spectrum of the data using different P(n°) cuts, we have found the results are consistent with the Monte Carlo efficiencies. The spectrum and its fit of the mass difference of A c +7r°7r° combinations are shown in Figure 4.3. As we expected, two A+ signals present at 309 MeV/c 2 and 342 MeV/c 2 . Unlike the A+tt+tt" case in which we see a much larger A+(2625) signal than A+ 1 (2593)'s, the two signals are roughly the same size. The A c + X (2593)

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G2 Table 4.2: Signal versus background of A+7r°7r° combinations for different 7r° momentum cuts. Si and S 2 in the table are the fitted areas of the A+^2593) and the A+^2625), respectively, decaying into A+7r°7r° from Monte Carlo studies; while B is the background from plotting A+7r°7r° combinations of real data. P{ir°) (GeV/c 2 ) Si s 2 B S 2 /y/B 0.50 747 661 6480 9.3 8.2 0.10 697 575 4380 10.5 8.7 0.15 518 424 2290 10.8 8.9 0.20 279 277 1078 8.5 7.2 0.25 69 109 414 3.4 5.4 signal is three times as large as our estimation from Monte Carlo efficiencies and isospin symmetry. We will provide an explanation in the next chapter. To fit the plot, we have used the same functions as in the A+7T7T mass-difference spectrum. Also shown in the plot as a histogram is the mass-difference spectrum obtained by using A+ sidebands instead of A+ candidates. Sidebands are picked from 3.4 to 5.0 o M/ ^ + on both side of A+ mass. No evidence of peaks can be seen* in this A+ sideband mass-difference distribution and its shape is consistent with the M(A+7r°7r°) M(A+) background. We have fitted Figure 4.3 in many different ways. Table 4.3 shows the results from some different fitting procedures. Fit Type 1 uses a Breit-Wigner convoluted with a Gaussian with a fixed width of 2.4 MeV/c 2 to fit the A+ 1 (2593) signal and a single Gaussian with a fixed width of 2.9 MeV/c 2 to fit the A+(2625) signal. Both Gaussian widths are determined by Monte Carlo studies. Type 2 fixes the width of the A+ x (2593) signal using the measured value from the A+tttt decay, with the Gaussian width floated. Types 3 and 4 only fit the A+^2593) signal. Type 3 fits the region from 290 MeV/c 2 to 320 MeV/c 2 , and Type 4 excludes the region from 230 MeV/c 2 to 355 MeV/c 2 . Type 6 -Q^tTwMVI fiXed maSS6S WidthS ' WG find yidds ° f 23 ± 14 at 307 MeV / c2 and

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63 o > CD CM CO -+-• c CD > 120 100 80 60 40 20 "i i i 1 1 1 1 1 r 4 V A V 1 i 1 1 1 1 1 1 1 r 0 ' 1 1 1 1 ' 1 ' ' 1 1 i i ' I | | | i 0.290 0.315 0.340 GeV/c 2 0.365 0.390 Figure 4.3: Mass difference M(A+7r°7r 0 ) M(A+) together with the rescaled histogram which is the mass difference M(A+7r°7r°) M("A+ side"), where "A+ side" is the same as the one in Figure 4.2.

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04 Table 4.3: The yield, mass difference(A(A/)), Breit-Wigner width(r), and Gaussian width(cr) of signal events from various fits to \^ -> A+7r°7r°. The numbers labeled by * are fixed values in the fit. rit lype \ leld A(M)(MeV/cr) r(MeV/c 2 ) a(MeV/c 2 ) A£(2593) 1 99+^ — ZD 306.3 ± 0.7 2 9 + on ^•• 3 — 2.0 2.4* 2 113+H 306.4 ± 0.7 4.7* 2 3 +11 2.4* 3 129^ 306.6 ± 0.8 5.8±1;I 4 109ta! 306.2 ± 0.7 q 0+2.8 2.4* 5 102^ 306.2 ±0.7 o -, +2.7 0\1_ 21 2.4* A c + x(2625) 1 105 ±22 342.9 ±0.9 2.9* 5 342.2 ± 1.1 4.61};? 6 132 ±27 342.7 + ?;jj 1.5* 2.9* 7 106 ± 24 343.0 ± 0.9 2.9* 8 107 ±23 342.8 ±0.9 2.9* and further only fit the A^i(2625) signal. Type 6 fits the signal with a Breit-Wigner with a fixed width of 1.5 MeV/c 2 convoluted with a Gaussian with a fixed with of 2.9 MeV/c 2 .* Type 7 fits the region to the right of 320 MeV/c 2 , and Type 8 excludes the region from 300 MeV/c 2 to 315 MeV/c 2 . Many other variations of fits like these are also performed. We find that using higher-order polynomials to fit the background gives almost the same results. Also, results are consistent with the ones in Table 4.3 if we fit only one peak by excluding the region of the other peak in the plot. These fitting results show very strong evidence that the decay mode A+ x ->• A+ttV does exist for both the A+(2593) and the A+(2625). The next point of interest is to calculate the branching ratio B(A^ ->• A+7r°7r°)/S(A+ 1 -> A+tt+tt-). To do this we need to estimate the errors on the yields of A+ttV signals. We not only have large statistical errors because of the poor signal, but also large systematic errors, mostly due to the uncertainties of the resolutions and the natural *The reason we do this fit is that we do not trust the result on fit Type 5 since the width is too much wjder than the Monte Carlo predicted resolution. Here we use this fit trying to estimate the upper limit of the yield

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65 Table 4.4: Comparison of productions of A+7r°7r° for different momentum cuts. The A^(2593) yields are from the fits using a Breit-Wigner function with T = 4.7 MeV/c 2 convoluted with a Gaussian with fixed width from Monte Carlo studies. The A+j(2625) yields are from fits using a single Gaussian with fixed width from the Monte Carlo. The statistical errors on efficiencies are tiny. P,o(GeV) Yield Efficiency(%) Yield/Efficiency(xl00) A+(2593) 0.05 133 ± 30 2.35 57 ±13 0.10 145 ± 28 2.19 66 ± 13 0.15 115 ±20 1.63 70 ± 12 0.20 59 ± 13 0.88 67 ± 15 0.25 11 ±9 0.22 50 ±41 A c + i(2625) 0.05 107 ±34 2.46 43 ± 14 0.10 95 ±30 2.31 41 ± 13 0.15 105 ± 22 1.78 59 ± 12 0.20 65 ± 17 0.95 68 ± 18 0.25 38 ± 11 0.37 103 ± 30 width of the particle. Thus we have fitted the signals by varying the resolution by ±20% of the Monte Carlo predicted values, varying the width of the A;!i(2593) from 2 MeV/c 2 to 7 MeV/c 2 , and varying the width of the A+j(2625) from 0 to 1.5 MeV/c 2 . We then estimate that the fitting uncertainties of the yields are +g for the A+(2593) and tU for the A+(2625). Since a 150 MeV/c momentum cut on both independent 7r°'s is a very hard cut, a consistency check has been made by comparing the efficiency-corrected productions for different tt° momentum cuts. As shown in Table 4.4, for the A+j(2593) decay, the Monte Carlo and the data agree very well, but for the A+(2625), we see some disgreement. Thus we need to intoduce a corresponding systematic error when we calculate the decay ratios.

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66 4.4 Substructures Studying A^-^A+tttt decay substructures through intermediate E c 's is very useful to identify J p of the A^'s and gain more understanding of these two states. In this section, we describe the measurements on the number of A+j's which decay to Ec's. The ratio is defined to be h c = B(A+ -> E c tt)/£(A+ -> A+tttt). 4.4.1 A+ -» S++7Tand A+ -» E°tt+ Figure 4.4 plots the mass difference M(A+ti-) M(A+) against M(A+tt+) M(A+) for the same A+tt+tt combinations in Figure 4.1. By looking directly at the figure, it is easy to tell that there are two very prominent clusters which correspond to the decays through intermediate E ++ and E°at the two ends of the diagonal band of A+ 1 (2593)'s in which all entries are shown as inverted triangles; in the diagonal band of A+ 1 (2625)'s in which all entries are shown as triangles, no obvious clusters can be seen. Therefore, by simply inspecting this scatter plot, we can tell that the E c tt mode dominates the A+(2593) decay, and the non-resonant A+tttt mode dominates the A+^2625) decay. To determine the fraction / E ++ and / E o of the A+(2593), we first measured the A+(2593) yield as a function of A+TT+ submass. Figure 4.5 shows the mass enhancement of E? and E c + + from A+tt+tt" combinations with the mass difference M(A + tt + tt-) M(A+) between 304 MeV/c 2 and 314 MeV/c 2 . We fit each plot in Figure 4.5 with a bifurcated Gaussian* (left) and a single Gaussian (right) together with the same background function. The same combinations in the two plots are constrainted to have the same area. *A bifurcated Gaussian is A Gaussian with different slopes on either side of the mean.

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G7 Figure 4.4: Scatter plot of the mass difference M(A+7i-)-Af (A+) vs. the mass difference M (A+7T+) M (A+). Shown in the plot are (1) the vertical band at A+tt+ mass difference of about 168 MeV/c 2 , corresponding to E++ -> A+7T+; (2) the horizontal band at A+tt mass difference of about 168 MeV/c 2 , corresponding to E° -> A+tt^(3) the diagonal band extending from (0.14, 0.20) to (0.20, 0.14), corresponding to combinations from the A+(2625) signal region in Figure 4.1 (triangles); and (4) the diagonal band extending from (0.14, 0.168) to (0.168, 0.14), corresponding to combinations from the A+(2593) signal region in 4.1 (inverted triangles), within which there are two lobes at the kinematic limits: (a) the enhancement in the £++ band just above the threshold for A+7T+, and (b) the enhancement in the S° band just above the threshold for A + 7r~.

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68 0.145 0.155 GeV/c 2 0.165 0.175 Figure 4.5: Events and fits of £°'s and E++'s with the mass difference of M (A+tt+tt ) M (A+) between 304 MeV/c 2 and 314 MeV/c 2 (the A+(2593) signal). Plot (a) shows the mass difference M{^~) Af (A+). The right peak centered at 167 MeV/c 2 is the £° signal; and the left peak is the reflection of the £++ signal on the A;?! (2593) band. Plot (b) shows the mass difference M(A+?r + ) M (A + ) The right peak centered at 167 MeV/c 2 is the £++ signal; and the'left peak is the reflection of the £° signal on the A+(2593) band. Since plots (a) and (b) represent the same events projected in two different directions, they are fitted simultaneously by constraining the area of the left/right peak in (a) to be the same as the area of the right/left peak in (b) The left peaks in both (a) and (b) are fitted by bifurcated Gaussians, and the right peaks are fitted by single Gaussians. They are all constrainted to have the same widths.

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69 Shapes of the bifurcated Gaussian and the single Gaussian are determined by Monte Carlo studies of A^E c n and E c ->-A+7r decays. The background is expected to be a mixture of two parts: random A+7T+7T combinations and non-resonant A^(2593)^A+7r + 7r~ events. Alhough it is very difficult to predict what its exact shape is, we know this shape has cut-offs at phase space lower limit 139 MeV/c 2 and upper limit about 172 MeV/c 2 ,*. We used a "double-threshold" function y(x) with upper and lower thresholds at a and b (in this particular case a = 139 MeV/c 2 and b = 172 MeV/c 2 ), y(x) = N(x a)(b x ) e Mx-a)+ S 2(x-af e s 3 (b-x)+s 4 (b-x)^ (4.1) to fit the background of Figure 4.5. Here N is a normalization factor and s i5 where i = 1, 2, 3, and 4, determines the shape of the function. The fitted background shape obtained by fitting the plot in Figure 4.5 with floating s^s is very consistent with the shape from the Monte Carlo generated A+tt+tt' non-resonance decay. As we tested, the fitted results are not sensitive to the variation of the background shape as far as a and b are fixed. Reasonably varying the parameters of the double-threshold function (reasonably means still giving a good fit) makes the yields of signals change within 5% of the mean value of fitted areas. We believe that statistical errors dominate the uncertainties of this measurement. The areas of E° and E++ signal we measured from Figure 4.5 are 77±7 and 72±7, respectively. These values are obtained by fitting Figure 4.5 by fixing the background, with shape determined by the Monte Carlo studies of A+ 1 (2593)^A+7r + 7rnon-resonance decay. To obtain the number of A+(2593)'s which decay into E c tt, these numbers need to be subtracted by the number of "independent" E c 's in the 'The lower limit is really the pion mass, and the upper limit, as we can tell in Fi K ure 4 4 depends on the width of the A+ (2593) band.

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70 sideband of the A^(2593) signal. Due to the kinematic limit, only the higher-mass A^(2593) sideband contains E c 's. Therefore we estimated the background as being half. The number of E c 's in the A^(2593) sideband were measured similarly as we did with the number of E c 's in the A^(2593) peak except that the mass-difference range is wider and the kinematic reflections of the peaks are in different massdifference ranges. The sidebands were taken from the range of the mass difference M(A+7r + 7r-) M(A+) between 320 MeV/c 2 and 330 MeV/c 2 . Figure 4.6 shows the histograms and the fits. The fitted yields are 19±4 of E++'s and 15±4 of E°'s. After subtracting one-half of the yield from the sideband, we obtained the number of A;!j(2593)'s which decay to E c 's: 67±8 for the E++ and 65±8 for the E° Compared with the total number of A+ 1 (2593)'s in the mass-difference range between 304 MeV/c 2 and 314 MeV/c 2 , which is 137±22 measured in Figure 4.1, we see that resonance via the E c dominates these transitions. The same methods were applied to measure / Ec 's of the A+^2625) except that in this case there are two A+ 1 (2625) sidebands other than the one in the A+^2593) case. The numbers of E++'s and E°'s inside the A+^2625) signal are measured as shown in Figure 4.7, and the fitted yields are 46±9 for E++ and 36±9 for E° The lower A+!(2625) sideband is chosen to be between 320 MeV/c 2 and 330 MeV/c 2 , which is the same as the one shown in Figure 4.6, and there are 19±4 E++'s and 15±4 E°'s. The higher sideband is therefore in the range between 354 MeV/c 2 and 364 MeV/c 2 , and the number of E++'s and E°'s is measured to be 13±3 and 6±4, respectively. The fit for the higher sideband is shown in Figure 4.8. After the sideband subtraction, the results are 30±10 A^'s decay to E++'s and 25±10 decay to E°'s. These numbers indicate that resonance through E c is very small in the decay of the A+ 1 (2625), since the total number of A+(2625)'s between mass difference 354 MeV/c 2 and 364 MeV/c 2 , 450±29, is much larger.

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71 Figure 4.6: Events and the fits of £°'s and £++'s in the A^(2593) sideband. Plot (a) shows the mass difference M(A+tt~) M(A+), and plot (b) shows M(A+tt + ) M(A+). The peaks in the right at about 168 MeV/c 2 on both plots are the signals of the £° and the £++. In each plot a bump is centered at about 158 MeV/c 2 , representing reflections of the £°(£++) peak seen in the direction of £+ + (£°). Each plot is fitted by two single Gaussians with fixed widths (3.4 MeV/c 2 of the left bump and 1.1 MeV/c 2 of the right peak) from £° -> A+tT (£++ -> A+7T+) Monte Carlo studies and a double-threshold function the same as the one used to fit Figure 4.5, with the lower threshold 140 MeV/c 2 and the higher threshold 185 MeV/c 2 . The areas representing the same combinations are constrainted to be the same, and the two plots are constrained to have an identical background.

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72 0.15 0.16 0.17 0.18 0.19 GeV/c 2 Figure 4.7: The mass difference of M(A+7r + 7r _ ) M(A+) between 337 MeV/c 2 and 347 MeV/c 2 (the A+ 1 (2625) signal). The meanings of the signals are the analog to those in Figure 4.5. The reflection of the peak of one combination is overlaid with the peak of the other combination. These shapes are predicted by A+ 1 (2625)->E c 7r Monte Carlo studies. Each plot is fitted by two single Gaussians and a second-order Chebyshev polynomial. The widths of the Gaussians are fixed by the values from the Monte Carlo (1.2 MeV/c 2 of the peak in the left and 3.4 MeV/c 2 of the bump in the right). The areas representing the same combinations are constrained to be the same, and the two plots are constrained to have the same background.

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73 0.15 0.17 0.19 0.21 GeV/c 2 Figure 4.8: The mass difference of M(A+7r + 7r-) M(A+) between 354 MeV/c 2 and 364 MeV/c 2 (the A+(2625) sideband), fitted in the same way as fitting Figure 4.7. The widths of the Gaussians are fixed by the values from the £ c ->-A+7r Monte Carlo studies (1.3 MeV/c 2 in the left and 4 MeV/c 2 in the right).

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After further considerations of systematic errors, we listed our results of and / E o, compared with the measurements with other experiments, in Table 4.13 and Table 4.14. 4.4.2 A+ -> £+7T° The technique of measuring / Sc+ = B(A+ -> J£**)/B(AS -> A C W), is similar to that of measuring and / E o, and much simpler. Since A+7r°7r° decay only has one substructure, which is A+7r°, instead of two (£+ + 7r~ and £°tt + ), we do not need to do complicated fits to correlate £+ + and £° signals as we did in the A+7r + 7r~ case. The scatter plot of M(A+7r°7r°) M(A+) versus Af(A^"7r°) — M(A^) shown in Figure 4.9 shows the evidence of A+ 1 (2593)^-E+7r° substructure. In the plot, we can see two concentrated clusters of events in the A^i(2593) mass-difference band around 306 MeV/c 2 : one at about 167 MeVc 2 which is consistent with £+ mass difference, and another which is the kinematic reflection of the first, at about 140 MeV/ c 2 just above the kinematic threshold. We cannot see this phenomenon for the A+ 1 (2625) signal. Low statistics and high background do not allow us to report the A+ 1 (2625)->£ c 7r° measurement (the upper limit would be 1). Thus only a / E +(A+ 1 (2593)) measurement was performed. Figure 4.10 shows the histogram and the fit of the signal and its kinematic reflection at the A+!(2593) mass-difference band taken from the M(A+7r°7r°) M(A+) mass-difference range between 304 and 314 MeV/c 2 . The plot was fitted by two single Gaussians with fixed widths (2.9 MeV/c 2 for the left signal and 2.4 MeV/c 2

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75 0.27 I — ^ — 1 — 1 — 1 — 1 — ' — i — i — I — i — i — i i I . I 0.130 0.155 0.180 0.205 0 230 M(A C V) M(A C + ) (GeV/c 2 ) Figure 4.9: Scatter plot of the mass difference M(A+7r°7r°) M(A+) vs. the mass difference M (A+tt°) M(A+). Very visible in the figure is a horizontal band at about 306 MeV/c 2 of M(A+7r°7r°) -M(A+), corresponding to A+(2593) -+ A+ttV. It has two lobes at the kinematic limits: one at about 167 MeV/c 2 of M(A+tt°) M(A+), which is consistent with £+ mass difference; and the other just above the kinematic threshold which is tt 0 mass. We assume there are three other bands in the plot (visible but not obvious) which are not shown clearly: (1) a vertical band at about 167 MeV/c 2 of M(A+tt°) M(A+), corresponding to E+ -> A+tt 0 ; (2) a diagonal band extending from (0.135, 0.308) to (0.2, 0.37), which is the kinematic reflection from band (1), corresponding to the single 7r°'s from the random E+tt° combinations; (3) a horizontal band at about 342 MeV/c 2 of M(A+7r°7r°) M(A+), in which no E+ clustering can be seen, corresponding to A+j(2625) -> A+7r°7r°.

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76 o > CD CO c CD > 50 40 30 20 10 ~i — i — i — r i — i — i — r t — i — i — r t — i — i — r 0 0.130 0.140 0.150 0.160 GeV/c 2 0.170 0.180 Figure 4.10: The mass difference M(A+7r°7r°) M(A+n°) between 304 MeV/c 2 and 314 MeV/c 2 (the A+j(2593) signal). The two peaks correspond to E+'s (left) and independent 7r°'s (right) in the A+j(2593) -> E+tt° decay.

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77 o > if) c > 24 20 16 12 8 4 0 0.135 t 1 r t 1 r i i r t 1 r 0.145 0.155 GeV/c 2 0.165 0.175 Figure 4.11: The mass difference M(A+7r°7r°) M(A+7r°) between 320 MeV/c 2 and 330 MeV/c 2 (the A+^2593) sideband). The positions and shapes of the two bumps are determined by the E+->A+7r° Monte Carlo. The signal at right corresponds to E+^A+tt 0 , and the left bump reflects single tt 0 's from the E+tt° combinations. for the right signal) determined by the A+ 1 (2593)^S+tt° Monte Carlo, and a doublethreshold function which is defined in equation 4.1. The shape of the doublethreshold function with the two thresholds 135 MeV/c 2 and 176 MeV/c 2 is determined by the non-resonance A+ 1 (2593)-^A+7r°7r° Monte Carlo. The areas of the the two Gaussians are constrained to be the same. Finally, the fitted yield is 89±11. Consistent fitting results were obtained when we fitted the background with a floating shape of the double-threshold function. Figure 4.11 shows the M(A+tt 0 ) M(A+) distribution at the A+(2593) side band and the fit to it. The sideband was taken from the M(A+7r°7r°) M(A+) range between 320 and 330 MeV/c 2 . The plot is fitted by two single Gaussians with

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fixed mean values and shapes determined by the £ + — >A + 7T° Monte Carlo, and a double-threshold function with fixed thresholds and other floating parameters. The areas of the these two Gaussians are constrained to be the same. The fitted yield is Mill. We finally calculated that 81±16 of A+ 1 (2593) decays are to £ + 's from a total number of 93±20 A^i(2593)'s in the mass-difference range between 304 MeV/c 2 and 314 MeV/c 2 . This is consistent with what we have seen in the A^(2593)->A+7r7r decay, for which the E c 7r substructure dominates. The result of / E +(A+ 1 (2593)) is presented in Table 4.12 after proper systematic errors are evaluated. 4.5 Search for Other Decays Since isospin is conserved in strong decays, the A + x ->• A+7T 0 is forbidden. If any of the two A + 7r + 7r~ states we observed were excited E c baryons, A+7T decay should be not only allowed but more favorable than A+7T7T decays due to the larger phase space. A^'s are allowed to decay electromagnetically to A+7, and if any A^i's intrinsic width is sufficiently narrow, its decay may be competitive with A+7T7T decays. To search for these decays, we reconstructed A + 7r° and A+7 combination using our previously defined candidates of A+, tt° and 7. Based on the optimization of Monte Carlo signals versus the background from data, a 200 MeV/c n° momentum cut for A+7r° and a 300 MeV/c photon momentum cut for A+7 are used. Figure 4.12 shows the mass-difference spectrum of M(A+tt 0 ) M(A+), and no signal can be observed. To measure the upper limit of decay ratios, three functions are used to fit the distribution. A Breit-Wigner, with fixed 4.7 MeV/c 2 A + j(2593) width, convoluted with a Gaussian with fixed 5.7 MeV/c 2 Monte Carlo predicted resolution, is used to fit at a fixed mean value of 307 MeV/c 2 ; a single Gaussian

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79 100 75 | 50 CM C c i3 25 ~I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T~ 'J] r 0 I — 1 — 1 — 1 — i — i — i — i i i I i ' i i I i i i i 0.290 0.315 0.340 0.365 0.390 GeV/c 2 Figure 4.12: Mass difference of M(A+tt°) M(A+). 0.290 0.315 0.340 0.365 0.390 GeV/c 2 Figure 4.13: Mass difference of M(A+7) M(A+).

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80 Table 4.5: Fitting results on M(A+tt°)-M(A+) and M(A+7)-M(A+) distributions. Decay Yield Yield Upper Limit (90% C. L.) A+(2593)-> A+tt° A+(2625)-> A+tt° A+(2593)^A c + 7 A c + 1 (2625)^A+ 7 26 ±28 -8 ±36 96 ±71 -42 ± 52 160 165 381 120 with 6.7 MeV/c 2 Monte Carlo predicted resolution is used to fit at a fixed mean value of 342 MeV/c 2 ; and the background is fitted with a second-order polynomial. Also, no signal is found at mass-difference spectrum of M(A+7) — M(A+), as shown in Figure 4.13. We used the exact-same fitting procedures as in the M(A+7r 0 ) — M(A+) case, except different Gaussian resolutions, which are 7.4 MeV/c 2 at mass difference 307 MeV/c 2 and 7.9 MeV/c 2 at mass difference 342 MeV/c 2 . The fitted yields and their projected upper limits are shown in Table 4.5. We conclude that we have observed no evidence of A+7r° or A+7 decays from A^. 4.6 Masses and Widths 4.6.1 Systematic Uncertainties One major part of the systematic error of mass measurements is the fitting error, mostly from the uncertainty of the background shape or sometimes even the signal shape. To evaluate this error, we use many different fit types and check the variations of the mean value of the signal. For a particle with a considerably wide natural width, such as the or a particle with an uncertain shape of the signal, such as the A+ x (2593), the fitting error generally dominates the systematic uncertainty.

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81 Since we measure the mass difference between the A+7T7T and the A+ instead of measuring the directly, most of the experimental uncertainties from the reconstruction of the A+ cancel. As we checked, 3 MeV/c 2 change of the A+ mass shifts the M(A+7r + 7r~) M(A+) by no more than 0.01 MeV/c 2 . So the systematic uncertainties other than the fitting errors mostly come from the measurement of the momenta and decay angles of the two extra pions. For charged pions, these errors are dominated by the uncertainties in the magnetic field normalization and the energy loss correction which is applied to the tracks traversing the beam pipe and the drift chambers. For 7r°'s, the errors come from the shower energy measurement by the crystal calorimeters. To evaluate the systematic errors of mass-difference measurements caused by the independent charged pions with low momentum, we measured the mass difference M(D* + ) M(D°) in decay D* + -> D°ir + since the mass-difference measuring technique is the same as M(A+7r + 7r _ ) M(A+) and the independent pion is soft. Our fitted result is 145.39±0.01 MeV/c 2 , in excellent agreement with the PDG value, which is 145.397±0.030 MeV/c 2 . We found that 0.2% momentum change of all charged tracks will shift the M(D* + ) M(D°) by about 0.05 MeV/c 2 , larger than the error of the PDG average. Therefore we believe 0.2% change in momentum is a reasonable amount to study the momentum scale in mass-different measurement with charged soft pions. For the systematic errors caused by the measurement of the soft 7r°'s, similar to the charged ones, we check the photon energy scale by looking at the mass difference of M(D*°)~M(D°), and our fitted value agrees very well with the PDG value, which is 142.12±0.07 MeV/c 2 . We think 1% energy change is a reasonable amount used for an energy-scale study since it shifts M(D*°) M(D°) by about 0.10 MeV/c 2 . In the study of M{D* + ) M(D°) measurement, we find that mass difference is more sensitive to the systematic shifts of the position and angle parameters of

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82 tracks. However, the charged tracks are measured much more accurately. Our vertex constraint program would shift the track positions and angles by fair amounts. We find that calculating the mass difference by constraining the D° and the pion to be from the event vertex, gives up to 0.02±0.01 MeV/c 2 meanvalue difference, compared with the mean value of mass difference reconstructed without vertex constraint. This difference reasonably reflects the systematic error from the decay angle measurement. The systematic error on the width measurement comes from two sources: the fitting error and the mass resolution of the detectors determined by Monte Carlo studies. The fitting error dominates the total error when the natural width of a particle is wide, and it can be evaluated by varying parameterizations of the background and the signal shapes. The detector resolution becomes important when it is close to, or bigger than the natural width, and its correctness can be checked by fitting the signals of other particles with well-known widths and comparing the results with corresponding Monte Carlo signals. As we tested, the CLEO Monte Carlo program does a very good job with tracks with medium-to-high momentum spectra, but for tracks with low-momentum spectra, it tends to overestimate the detector performance and therefore predicts a mass resolution with a lower value than the real resolution. But by the time this research work was performed, we are unable to make corrections, since it is very difficult to detect what the exact reason is and by exactly how much the Monte Carlo is wrong. So we have to be very careful and conservative with our estimates of the uncertainties on narrow-width measurements.

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83 4.6.2 A+j(2625) Mass and Width Limit The result presented on the A^j(2625) mass difference with the A+, 341.80±0.10 MeV/c 2 is our measured mean value by fitting the A+7r + 7r~ signal with a widthfloat single Gaussian. By fitting the A+7r°7r° signal, we obtained a value of 342.9 ± 0.9 MeV/c 2 . We have also checked the fits to the A+7r + 7r~ signal using a double Gaussian, a bifurcated Gaussian, and a Breit-Wigner convoluted with a Gaussian, with variations of different shapes. All fitted means agree within 0.13 MeV/c 2 . In the momentum-scale study, we find that a 0.2% momentum change for all charged tracks shifts M(A+ 1 (2625)) M(A+) by about 0.22 MeV/c 2 . We find that the mass difference M(A+ 1 (2625)) M(A+) shifts for about 0.2±0.1 MeV/c 2 if we do not constrain the A+ and the two pions to be from a single vertex compared with constraining them into the main vertex. This proved that the uncertainty of the pion decay angle does not bring large systematic errors. We also compared M(A+7r + 7r-) M(A+) with M(A+7r+7r-) M(A+), and their mean values agree within statistical errors. According to Table 4.1, the fitting error due to the background parameterization with the signal fitted by a single Gaussian is about ±0.04 MeV/c 2 , which is tiny compared with the uncertainty of the soft pion momentum measurement. Considering all these sources of errors, we conservatively estimate that the systematic uncertainty is 0.35 MeV/c 2 . With the width of 0.7±0.3 MeV/c 2 extracted from the Breit-Wigner convoluted with a Gaussian fit, considering that our Monte Carlo predicted resolution should not be larger than the actual one, we calculated the upper limit of the A+ 1 (2625) width to be 1.4 MeV/c 2 at 90% confidence level.

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84 Table 4.6: Measurements of the (2625) mass and width limit. Experiments [M(A c + 1 )-M(A+)](MeV/c :i ) r A + (MeV/c 2 ) E687[29] CLEO-II[30] ARGUS[32] CLEO-II(this) 340.4±0.6±0.3 342.2±0.2±0.5 342.1±0.5±0.5 341.80±0.10±0.35 < 1.9 < 3.2 < 1.4 Table 4.7: Measurements of A^(2593) mass and width together with the mass resolutions in the corresponding experiments. All quantities are in units of MeV/c 2 . Note that E687[31] fitted their signal using a single Gaussian and the fitted Gaussian width is consistent with that A+^2593) has a zero intrinsic width. Experiments Resolution [M(A+) M(A+)](MeV/c 2 ) T A+] (MeV/c 2 ) CLEO-II[30] E687[31] ARGUS[32] CLEO-II(this) 2.0 1.8 1.8 1.62 307.5±0.4±1.0 309.2±0.7±0.3 309.7±0.9±0.4 308.8±0.4±0.4 O Q+1.4+2.0 °y -1.2-1.0 o q+2.9+1.8 z y -2. 1-1.4 A 7+1.3+1.4 4 '-1.1-0.9 The results of mass difference with the A+ and the upper limit of the width are listed in Table 4.6. A comparison with the previous experiment results is given in the table. 4.6.3 A+(2593) Mass and Width In Figure 4.1, we fit the A+ 1 (2593)^A+7r + 7rsignal in the same manner as the previous experiments: using a Breit-Wigner function convoluted with a Gaussian. The results of the mass and width are listed in Table 4.7, together with the measurements of previous experiments. Here the systematic errors are mostly fitting errors, evaluated based on Table 4.1. Although our measurements agree with previous experiments, we doubt the results, and the most obvious reasons comes from the following facts: (1) A+ x (2593)

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85 has a nearly 100% dominating decay channel, £ c 7r; (2) the combination of H°7r + (or £^ + 7r ) has a kinematic limit at the mass difference of about 307 MeV/c 2 ; (3) the fit to the A^(2593) signal in Figure 4.1 is poor. Because of these and some other thoughts which will be stated later, we feel that using a full Breit-Wigner distribution to parameterize the S°7r + (or E c 7r") decay very close to the kinematic threshold may not be correct. We will describe a new way to parameterize the signal in the next chapter, since the new method uses the £+ + and £°masses and widths. 4.7 Fragmentation Functions As stated in Chapter 1, all quarks "fragment" into hadrons. The initially produced pair of hadron and anti-hadron should be expected to have more energy than the subsequent hadrons produced further in the decay chains. Each hadron, as it is produced, carry away a fraction, z, of total energy of the corresponding original quark. A fragmentation function (~, where N is the number of hadron produced from a type of specific physical process) proportional to the probability a hadron being produced in the interval of [z, z + dz). In e + e~ annihilation experiments, measurement of the fragmentation functions of heavy quarks provides information about non-perturbative particle production in a variety of experimental environments. Many forms of functions have been suggested to describe the normalized momentum spectra for heavy quarks. Among those, the functional form given by Peterson et al.[33] is the most widely used. The Peterson function has form dN _ 1 ~dz~~ z[l-(l/*)-e P /(l -*)]*' where z = (E + p\\) hadron /{E + p Q ), and p\\ is the longitudinal momentum and p Q is the total momentum of the heavy quark. The quantity z is not experimentally accessible, and in CLEO experiments a close approximation is made by using the

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86 Table 4.8: Efficiencies and productions of A^'s for different x p 's. The statistical errors on efficiencies are negligible. Xp Efficiency (%) Yield Normalized Yield A+j(2593) 0.5-0.6 5.45 34 ± 16 0.13 ±0.06 0 6-0 7 6 44 1 '-t HZ io U.iO X u.uo 0.7-0.8 7.07 91 ± 18 0.27 ±0.05 0.8-0.9 7.11 71 ± 15 0.21 ±0.05 0.9-1.0 5.47 35 ± 11 0.14 ±0.05 A c + ! (2625) 0.5-0.6 5.63 114 ± 13 0.18 ±0.02 0.6-0.7 6.47 217 ± 16 0.30 ±0.02 0.7-0.8 7.08 214 ± 16 0.27 ±0.02 0.8-0.9 7.78 161 ± 14 0.19 ±0.02 0.9-1.0 7.48 48 ±8 0.06 ±0.01 scaling variable x p = p/p max , as denned for A+ in the last chapter. e P physically represents the "hardness" of the heavy quark fragmentation. The smaller the value of e P is, the larger the portion of the total momentum the heavy quark carries. Although the Peterson function agrees pretty well with the fragmentation of D° and D* + measured in the experiments [34] [35], there is no reason why any charmed particle momentum spectrum should follow an analytical curve of this type, as many particles are the decay results of excited states. However, the measurement of e P of Peterson function remains useful for comparing the spectra of different particles. To measure the Peterson function of a particle, we fit the distribution of efficiencycorrected cross section at a different x p range and extract the parameter e P . Table 4.8 shows the yields and Monte Carlo derived efficiencies at different x p ranges. Also listed are the efficiency-corrected yields normalized to x p > 0.5. Figure 4.14 shows the ^ (N is the efficiency-corrected number of A&'s for x p > 0.5) distribution for the A+^2593) and the A+(2625) based on the efficiencycorrected yields listed in Table 4.8. Only statistical errors are shown in Table 4.8. Systematic errors are dominated by fitting procedures and are found to be a little

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87 0.0 0.2 0.4 0.6 0.8 1.0 Figure 4.14: Normalized spectra of scaled momentum for A+ x samples. The data for the A+ t (2593) (diamonds) and the A+^2625) (triangles) are fitted to the Peterson function overlaid as the solid and dashed curves, respectively. smaller than the statistical errors. The error bars shown in Figure 4.14 are the total errors. Also shown in the figure are the curves obtained by fitting the distributions by Peterson function. The measurement results are listed in Table 4.9 compared to the previous measurements. The measurements show that A^ fragmentation at 10 GeV/c 2 is close to the fragmentation of D* + , which was measured to have e P = 0.078 ±0.008(36].

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88 Table 4.9: Measurements of the fragmentation of A^'s using Peterson functions. Experiments ep A c + 1 (2593) CLEO-II[30] ARGUS[32] CLEO-II(this) 0.057±0.023±0.016 0.069±g-git ± 0.040 0.064l8fJ A c + !(2625) ARGUS[28] CLEO-II[30] CLEO-II (this) 0.044±0.018 0.065±0.016±0.013 0.1081q;oo9 4.8 Decay Ratios and Production Ratios 4.8.1 Systematic Errors on Yields and Efficiencies To calculate the branching ratios and productions, the yields on the signals and the Monte Carlo derived efficiencies are used. Both bring systematic errors to the result. The systematic errors on the yield of a signal come from the fitting procedures, including the signal and background parameterizations and the mass resolution determined by the Monte Carlo. As we explained in the last section, for the £*(2593)->>A+7r + 7r~ signal, the systematic error is dominated by the uncertainty of the signal shape, and background parameterization is also a factor since the signal is just at the kinematic threshold. Based on Table 4.1 and other fit results, the fitting errors of the £«(2593)-fA+7r+7r yield are ±15% from the peak parameterization and ±8% from the background parameterization. As we tested, varying the Gaussian resolution by a reasonable amount only changes the A+^2593) yield by 2%. We therefore estimate the fitting error on the A+ 1 (2593)^A+7r + 7ryield to be ±17%. For A+ 1 (2625)->A+7r + 7r-, we have a clean signal at very low background, so the systematic error comes mostly from the Monte Carlo predicted resolution or

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89 equivalently, the uncertain natural width of this state. We finally estimate that the fitting error of the A+ 1 (2625)->A+7r + 7ryield is t\°%. As the A^— ^A+7T 0 7r° signals are poor, both statistical and fitting errors are very large. The fitting errors are mostly due to the uncertainty of the mass resolutions and the natural widths of the states. We expect the A+ 1 (2593)->A+7r°7r° signal to be nearly a full Breit-Wigner convoluted with a Gaussian, since the kinematic threshold is at 301 MeV/c 2 . The fitting errors are evaluated by reasonably varying the background parameterizations, the mass resolutions, and the widths of the states. From the results listed in Table 4.3 and some further tests, we estimate the fitting errors on A+^A+tt 0 ^ 0 signals are ±13% for A+^2593) and tf %. Since we measure the branching fractions by ratios, the systematic errors on the efficiencies of A+ reconstruction will cancel. Based on comprehensive studies by the CLEO collaboration, the systematic errors on efficiencies are 1% on finding one charged track and 5% on finding a 7r°. 4.8.2 A+ttV, A+tt 0 , and A+ 7 Decays Since the yield of A^-^A+tt+ttwas the best measured for AJ, the branching ratios we measured are all given relative to this decay mode. This is the first time that the decay A+j-^A+ttV is reported. Of interest is the branching ratio #(A+7r 0 7r°)/#(A+7r + 7r-). If only isospin symmetry is applied on these states, this ratio should be 1/2. Based on the discussion in the last subsection, we assign the systematic errors on S(A c + 7r° 7 r 0 )/fi(A c + 7r+7r-) to be ±26% for the A+(2593) and ±™% for the A+(2625). Table 4.10 gives the result calculated from the yield and the Monte Carlo predicted efficiency of each decay mode.

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90 Table 4.10: Branching ratios of A+7r°7r° relative to A+7r + 7r . Particle 5(A+7r°7r°)/B(A+7r + 7r-) (2593) A+(2625) 2.6±0.6±0.7 1.0±0.3±S;| Table 4.11: Limits on branching ratios of A+ x — >-A+7r 0 and A^— >-A+7 relative to A^-^A+Tr+Tr . All values are evaluated at 90% C.L. Experiments 5(A+7r°)/5(A+7r + 7r-) £(A+ 7 )/£(A+7r + 7r-) (2593) A+(2625) CLEO-II[30] CLEO-II(this) CLEO-II[30] CLEO-II(this) < 3.53 < 1.1 < 0.91 < 0.45 < 0.98 < 3.0 < 0.52 < 0.36 The result on the A^(2625) is larger than 0.5 but consistent with it, but the number on the A^(2593) is significantly larger than 0.5. This can be explained by the phase-space suppression. The A^(2593) mostly decays into E c 7r first then goes to the final state A+7T7T. Since the mass of the A^(2593) is just at the threshold to decay into a E c plus a charged pion, so the decay A+ x (2593) — > £+ + 7r~ and A^(2593) — > E^7r + will be suppressed. On the other hand, isospin symmetry is not exact, so the n° mass is about 5 MeV/c 2 lower than charged ones, so the decay A^(2593) -> £+7T° is not suppressed by phase space. Thus for the A^(2593), we expect B(A^ -4 A+7r°7r°)/5(A+ 1 -> A+tt+tt") to be higher than 1/2. We will discuss this more in the next chapter. According to Table 4.5, taking the systematic errors on A+7r + 7r~ yields into account, we estimated the upper limits of A+7r° and A+7 decay ratios relative to A+7T+7T".

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91 Table 4.12: Branching fractions of substructure E+ in A+j— »A+7r + 7r decays. Note the A^i yields are smaller than the fitted results in Figure 4.1 since we measure the E c yields from 304 MeV/c 2 to 314 MeV/c 2 of the A+^2593) peak and from 337 MeV/c 2 to 347 MeV/c 2 of the A+j(2625) peak. Decay A+ Yield E c Yield A+(2593) E++7TE°7T+ E+7T 0 137 ±22 ±22 137 ± 22 ± 22 93 ± 20 ± 22 67 ± 7 ± 5 65 ± 7 ± 5 74 ±11 ±10 0.45 ±0.12 ±0.11 0.47± 0.12 ±0.11 0.73 ±0.20 ±0.20 A+x(2625) S++7T" E°7T+ 450 ± 29 ± 9 450 ± 29 ± 9 24 ± 10 ± 7 32 ± 10 ± 7 0.05 ±0.02 ±0.02 0.07 ±0.02 ±0.02 Table 4.13: Comparison of measurements of branching ratios of E+ + and E° substructures in A^(2593)^A^7r + 7r" decays from different experiments. Experiment /ej> E687[29] CLEO-II[30] ARGUS[32] CLEO-II(this) 0.36 ± 0.09 ± 0.09 0.37 ±0.12 ±0.13 0.45 ±0.12 ±0.11 0.42 ±0.09 ±0.09 0.29 ±0.10 ±0.11 0.47 ±0.12 ±0.11 > 0.51 90% C.L. 0.66±8;ii ± 0.07 4.8.3 E c 7r Decays The A(1405), the spin 1/2 strange baryon, decays 100% to E7r; and the spin 3/2 state A(1520) decays to both E7r and Ann. We have observed the similar phenomenon for the A;!; (2593) and the A+ 1 (2625). Measurements of f Ec = B{A^ -> E c tt)/B(A+ 1 -> A+tttt) for E++, E+, and E° are tabulated in Table 4.12. The systematic errors are dominated by the fitting errors on E c yields on A£ signals and backgrounds. Our observation is close to the previous CLEO measurements and consistent with the prediction that the A+ x (2593) and A+^2625) have J p 1/2" and 3/2", respectively. The A+j(2593) can decay through both Swave E c n and P-wave nonresonance A+7r + 7rchannels, but the 5-wave is preferred. However, angular mo-

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92 Table 4.14: Comparison of measurements of branching ratios of E^" + and £° substructures in A^(2625)— >-A+7r + 7r~ decays from different experiments. Experiment /s++ ARGUS[28] E687[31] CLEO-II[30] CLEO-II(this) < 0.08 90% C.L. 0.05 ±0.02 ±0.02 < 0.07 90% C.L. 0.07 ±0.02 ±0.02 0.46 ±0.14 < 0.36 90% C.L. Table 4.15: Measurements of A^— ^A+7r + 7r production ratio relative to the total inclusive A+ production. Experiment A+(2593) CLEO[30] ARGUS [32] CLEO(this) 1.44 ±0.24 ±0.30 2.1±f;$ ±1.1 1 /.fi+0.23+0.29 1 4O -0.22-0.29 A+(2625) ARGUS[28] CLEO[30] CLEO(this) 4.1 ± 1.0 ±0.8 3.51 ±0.34 ±0.28 3.47 ±0.1718$ mentum and parity conservations require Al 1 (2625)— >T, c ir to be jD-wave, so for the A^(2625), the P-wave non-resonance Al7r + 7r~ is preferred and expected to have a smaller width. 4.8.4 Production Ratios Since we do not have good statistics with Al7r°7r° decay channels, we only present the A+^A+n+n' production as a fraction of A+ baryons in the 10 GeV/c 2 e + e" annihilations. We have only measured the number of A+'s and A^'s at x p (A^) > 0.5, so we need to extrapolate the Peterson function to zero momentum. Fortunately, the two A^'s are fragmented very hard (only about 20% are fragmented below x p = 0.5,) so the systematic errors from extrapolation are not very large. Based on our estimation, the sources and their values of systematic errors of the A^(2593)

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93 are 15% for the peak parameterization, 8% for the background parameterization, and 10% for the x p = 0 extrapolation. We estimate the total systematic error of the A^(2593) production ratio measurement to be 20%. For the A+ 1 (2625), the fitting errors are dominated by the uncertainty of the detector resolution. The total fitting error is estimated to be t\ 0 %, and the x p = 0 extrapolation uncertainty is estimated to be 7%. Thus the total systematic error of the A^(2625) production ratio measurement is estimated to be lg 2 %Our results are consistent with the previous experiments.

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CHAPTER 5 STUDIES OF E c AND E* BARYONS 5.1 Introduction The isospin triplet (E+ + , £+, £[!) is the charm counterpart of the E triplet with the two light quarks antisymmetric under exchange. The quark-model-predicted spin-parity J p for the triplet is l/2 + with the two light quarks in a J p = 1 + configuration. Although all three states have been observed by many experiments[37, 38, 39, 40, 41, 42, 43, 44], only the mass splittings and production ratios of the E+ + and the E° are reported, and no attempt has been made to measure their intrinsic widths. With a much larger data sample and the improved resolution of the CLEOII detector, we are now able to measure the widths and production ratios of all three states. The 3/2+ excitation of the E c is the E* triplet. CLEO has recently made the first observation of the E* ++ and the E*°[21]. Here we present an update of the measurements of these two particles and give evidence of the observation of the previously undiscovered E* + . In this chapter we first describe the observations and the fits of E c and E* signals in section 2.2, then in later sections we present the results of masses, widths, fragmentation functions, and production ratios of these particles. The physical significance of these measurements is also discussed. Finally, we describe a tentative measurement on the mass and width of the A+j(2593) in a new way, different from the methods used in previous experiments. We present this last because it requires the knowledge of the E c mass and width. 94

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95 5.2 Signals All E c 's and E*'s have one decay mode: A+7T. To obtain the signals, we combine each A+ candidate with a pion, then measure the mass difference M(A+n) — M(A+). The A+ candidates are selected in the same way as we did in observing A^'s. To improve the signal to background ratio, a cut of x p > 0.5 for A+n* and a harder cut of x p > 0.6 for A+7T 0 are used, since the A+7r° combination has much larger background and is more difficult to observe. Here x p is defined in the same way as the x p of the A+ x . All charged tracks are used to be the independent candidates. In order to suppress the large background from these low-momentum charged pions, a cut on cos(9 dec ) is used for A+n* modes. 9 dec is defined to be the angle between the the pion momentum measured in the rest frame of the A+tt*, and the direction of the A+7r ± in the laboratory frame. According to Monte Carlo studies, 9 dec cut is more efficient than simply cutting on 7r ± momentum to improve the signal to background ratio of the E* ++ and the E*°. We used cos(9 dec ) > -0.4 which is the optimization from the E*-»E c 7rMonte Carlo studies. When reconstructing A+tt* invariant mass, we constrain the A+ and the independent pion to be from the event vertex, whose finding procedure was described in Chapter 3. This improves the mass resolution by roughly 5% for both the E++ and the E°. 7T° selection is described in Chapter 3. To suppress the large background, a 7r° momentum cut is needed. The Monte Carlo shows that a direct tt 0 momentum cut is slightly more efficient than 9 dec cut for the E*+ observation and predicted that a 150 MeV/c cut gives largest signal to background ratio. Sufficient Monte Carlo events have been generated. The mass differences we used are 167.87 MeV/c 2 for the E++, 168.70 MeV/c 2 for the E+, 167.30 MeV/c 2 for the

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96 E°, and 233 MeV/c 2 for all three E*'s. We found that slightly varying the generated mass does not affect the Monte Carlo prediction for either width or efficiency. We first generated events with zero width to get the resolution of the signal; then after we extracted the width from real data, we generated events with the found width. Efficiencies are calculated using the latter Monte Carlo events. Using the same signal-fitting functions, the same natural width can be extracted from the Monte Carlo signal. All reconstructed mass differences in Monte Carlo shift by less than 0.03 MeV/c 2 relative to the generated ones. 5.2.1 A+tt* Figure 5.1 shows the mass-difference spectrum of M(A+7r ± ) M(A+). The clear peaks near 167 MeV/c 2 are E c 's, and wide bumps near 233 MeV/c 2 are E*'s. In addition, we should expect broad enhancements below 205 MeV/c 2 which are A+7r combinations from A+ 1 (2625)^A+7r + 7r _ decays. It is because of this background that we did the A^ analysis before the E^'s. It is calculated from A+ 1 (2625)->A+7r + 7rsignal and Monte Carlo predicted efficiencies that the excess from this source yields 728 events between 150 MeV/c 2 and 205 MeV/c 2 . In the same plots shown as solid histograms are the mass-difference spectra using the sidebands of the A+signal. The sidebands are taken from the A+ combinations in the mass-difference region 3 4.6 a M away from the known A+ mass, 2286.7 MeV/c 2 . No enhancement can be observed from these histograms, and they can be very well fitted by second-order polynomials. In Figure 5.1, E c and E* signals are fitted with Breit-Wigners convoluted with a Gaussian with a fixed resolution width of 1.04 MeV/c 2 for the E c or 1.53 MeV/c 2 for the E*. The Gaussian resolutions are determined by the Monte Carlo studies. The broad excesses in the region below 205 MeV/c 2 are fitted by a double-threshold

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97 250 125 "i — n — r ~\ — i — i — i — i — i — i — i — i — i — i — i — i — r o > V CO c CD > 125 (a)+_+ A/7T GeV/c 2 Figure 5.1: Mass difference for (a) M(A+tt+) -M(A+), and (b) M(A+tt-) -M(A+). The solid histogams are the spectra of M(A+7r ± ) -M(A+ "side"), where a "A+ side" is from Aj" sidebands.

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98 function with a fixed shape determined from A+7r shapes in A+ 1 (2625)— >A+7r + 7r~ Monte Carlo (with thesholds at 139 MeV/c 2 and 205 MeV/c 2 ), and a fixed area, 728, determined by the efficiency-corrected A+ 1 (2625) production. The rest of the background is fitted by a second-order polynomial with all parameters floated. The results are sensitive to different fitting procedures. The extracted parameters from some variations of fits are listed in Table 5.1. Fit Type 1, which has the fitted curves shown in Figure 5.1, provides the presented results. Type 2 fixes the convoluted Gaussian width of the E c 's to be 1.25 MeV/c 2 , widening the Monte Carlo predicted resolution of the E c 's by 20%. Type 3 reduces the area of the double-threshold function by 50%, and Type 4 enlarges it by 50%. Type 5 uses a third order of polynomial instead of the 2nd order to fit the background. Type 6 fits the region in the plot below 200 MeV/c c and Type 7 fits the region above 200 MeV/c 2 . Type 8 uses 4 MeV/c 2 bin size instead of 1 MeV/c 2 . The statistical errors given in the table are only for fit Type 1 since the errors for the other types are roughly the same. Besides the fit types listed in Table 5.1, many other fitting procedures are used, such as varying and floating the parameters of the double-threshold function (we found that our results are much more sensitive to the area than the actual shape of the double-threshold function), using higher-order Chebychev polynomials to fit the entire background, using a single Gaussian, a double-Gaussian, or a bifurcated Gaussian to fit the peaks to check the variation of the means, fitting the two peaks separately in different mass-difference ranges and with different backgrounds. The measured parameters from all reasonable fits are within the range listed in Table 5.1. Also, we measured the same parameters with different o M cuts around the A+ mass and found that the signals we have are consistently associated with the A+. To study the fragmentation function of these particles, we divide the 0.5 1.0 x p range into 4 bins and add an extra bin from 0.4 to 0.5, then fit each mass-difference

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99 Table 5.1: The yield (Y), mass difference AM, and extracted width T measured from various fits to A+7r ± . Fit Type y AM(MeV/c 2 ) r(MeV/c 2 ) 1 880±™ 167.34 ±0.10 2.1 ±0.3 2 845 167.35 1.7 3 915 167.35 2.3 4 851 167.33 2.1 5 875 167.34 2.1 6 908 167.36 2.2 1 895t& 167.24 ±0.11 o q+0.4 ^•°-0.3 2 870 167.23 1.9 3 942 167.24 2.1 4 925 167.22 2.0 5 879 167.22 2.3 c 0 oyo 10/ .2,1 2.3 1 231.4 ±0.8 14 ±3 2 825 231.4 15 3 649 231.6 12 4 931 231.2 16 5 829 231.4 15 7 715 231.4 13 8 821 231.7 15 Ef 1 10151^ 231.9 ± 1.2 203 2 769 232.8 16 3 811 233.1 16 4 1249 231.6 24 5 822 232.7 17 7 1193 231.9 23 8 1116 231.7 22

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100 Table 5.2: The yield (Y), efficiency, and normalized production of A+tt* events for different x v cuts. Xp Y Efficiency (%) Normalized Production 0.4 1.0 1094 ± 54 6.64 16988 ± 813 0.4 0.5 211 ±29 6.57 3212 ± 441 0.5 0.6 246 ± 27 6.61 3722 ± 408 0.6 0.7 295 ± 26 6.69 4410 ± 389 0.7-0.8 232 ± 23 6.64 3493 ± 364 0.8 1.0 137 ± 16 6.42 2134 ±249 0.4 1.0 1109 ±55 6.64 16702 ± 828 0.4 0.5 214 ±28 6.57 3257 ±426 n ^ n fi v.o u.u 941 -197 O.Ol o040 ± olo 0.6 0.7 289 ± 27 6.69 4319 ± 403 0.7-0.8 209 ± 23 6.64 3148 ± 346 0.8 1.0 120 ± 14 6.42 1869 ±218 0.4 1.0 1097 ± 121 7.06 15538 ± 1714 0.4 0.5 244 ± 67 7.07 3451 ± 948 0.5 0.6 321 ± 55 7.23 4440 ± 761 0.6 0.7 282 ± 46 7.09 3977 ± 649 0.7-0.8 155 ± 33 6.70 2313 ± 493 0.8 1.0 70 ± 15 6.88 1017 ±218 0.41.0 1348 ± 189 7.06 19093 ± 2677 0.4 0.5 311 ±79 7.07 4399 ± 1117 0.5 0.6 384 ± 71 7.23 5311 ± 982 0.6 0.7 277 ± 60 7.09 3907 ± 846 0.7 0.8 227 ±47 6.70 3388 ± 701 0.8 1.0 134 ± 34 6.88 1948 ± 494

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101 spectrum individually. Each Gaussian width is fixed by the predicted resolution from corresponding Monte Carlo events. If we float the masses and the BreitWigner widths of all signals, both mass and width of the same particle vary considerably due to poor statistics. However, if we fix all the masses to the measured values in the 0.5 1.0 x p range, all widths vary around our presented values, measured in the 0.5 1.0 x p range, within statistical errors. If we fix all the widths to be our presented values, E c masses vary within 0.16 MeV around our presented masses with statistical errors about ±0.20 MeV/c 2 , and E* masses vary within tlx MeV/c 2 around our presented masses with statistical errors of about ±2 MeV/c 2 . Table 5.2 listed the yields and efficiency-corrected productions with all widths fixed. Each efficiency is determined by the Monte Carlo, and its error is within 0.01%. We also fitted the mass-difference spectra with variations of the 9d ec cut and, almost equivalently, of the n 4 momentum cuts to see if there are any systematic changes in masses and widths. We find the signals of the data are consistent with Monte Carlo studies, and all extracted parameters agree within statistical errors. 5.2.2 A+tt° For A+7T 0 combinations, 7r° momentum cut is very important to reduce the background. The 150 MeV/c 2 cut we used is the prediction from the Monte Carlo. Table 5.3 displays signal-to-background ratios of A+7r° combinations for different 7r° momentum cuts. In the table S"s are the fitted areas of the E c or the E* from the Monte Carlo plots; £Ts are the size of the background from the E c or E* sidebands from A+7r° combinations of real data. The plot of mass difference M(A+tt°) M(A+) is shown in Figure 5.2. The two signals and the background are fitted by the same four functions used in Figure 5.1. The convoluted Gaussian widths are determined by Monte Carlo stud-

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102 Table 5.3: Signal versus background of A+7r° combinations for different 7r° momentum cuts. In the table S is the fitted area of the E c or the E* signal from the Monte Carlo events; B is the area of the background (taken from the E c or E* sidebands) from A+7T 0 combinations of real data. P(7T°) (GeV) 5 E+ 0.05 2877 2610 5448 9977 39.0 26.1 0.10 2873 2526 5376 7760 39.3 28.7 0.15 2734 2398 4685 6068 40.0 30.8 0.20 2363 2010 3676 4685 39.0 30.7 0.25 1929 1694 2632 3654 37.6 28.0 ies: 1.92 MeV/c 2 for the E+ at 167 MeV/c 2 and 3.71 MeV/c 2 for the E*+ at 229 MeV/c 2 . The shape of the double-threshold function is determined by A+7r° shape in the A+ 1 (2625)->A+7r 0 7r 0 Monte Carlo, and the two thresholds are fixed to be at 135 MeV/c 2 and 216 MeV/c 2 . The area of the double-threshold function is the number of A+ 1 (2625)->A+7r°7r° feed-down, and it is calculated (from the efficiencycorrected A+ 1 (2625)->A+7r°7r°) to be 216. The solid histogram in the plot shows the spectrum of the combination of 7r°'s and the A+ sidebands, taken from the same mass-difference region (3 4.6 a M ) as in the A+ir* case. Fitting procedures affect the extracted parameters. Many different fits were performed to investigate the stabilities of the signals using different fitting methods. Table 5.4 shows some results from different fit types. Fit Type 1 is the procedure just described whose fitted curve is shown in Figure 5.2, and the fitted results are our presented values. Type 2 fixes the width of the convoluted Gaussian of the E+ peak to be 2.20 MeV/c c , 15% larger than the Monte Carlo predicted resolution; and Type 3 fixes it to be 2.50 MeV/c 2 , 30% larger than the Monte Carlo value. We found that the fitted T of the E*+ is insensitive to the change of the convoluted Gaussian width. In fit Type 4 the double-threshold function representing the feed-down of A^i(2625) is taken away; and in Type 5 its area is enlarged by 100%. Type 6 uses a

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103 240 r — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 2 40Ld 0 C — l 1 1 1 I l l l I I l l l l I I ' ' ' 0.14 0.19 0.24 0.29 0.34 GeV/c 2 Figure 5.2: Mass difference M(A+tt°) M(A+). Table 5.4: The yield Y, mass difference AM, and extracted width T measured from various fits to the A+7r° signal. Fit Type Y AM(MeV/c 2 ) r(MeV/c 2 ) 1 367±^ 166.9 ±0.5 4.5±& 2 356 166.9 3.9 3 343 167.0 3.2 4 415 167.0 5.4 5 329 166.8 3.9 6 337 166.8 4.0 7 376 166.9 4.7 9 352 166.9 3.7 10 355 167.1 4.5 1 236+^ 9 229.2 ± 1.3 r o+().4 °-°-4.6 2 224 229.2 5.2 3 231 229.2 5.1 4 190 229.2 3.3 5 297 229.0 7.7 6 203 229.4 3.7 8 215 229.5 4.2 9 238 229.3 5.5 10 217 229.4 4.1

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104 third-order polynomial instead of the second order in Type 1 to fit the background. Fit Type 7 and 8 try to eliminate the influence of one signal to the other. Type 7 excludes the region from 200 MeV/c 2 to 250 MeV/c 2 so only the E+ signal is fitted. Type 8 fits the region above 200 MeV/c 2 so the E+ signal is excluded. All the above fit types fit the spectrum with 2 MeV/c 2 bin size. Types 9 and 10 are the fits to plots with the bin size 1 MeV/c 2 and 4 MeV/c 2 , respectively. The statistical errors for all fit types are roughly the same as the ones given in Type 1. As in the A+7r ± cases, we have used more variations of fits, and the variations on all measured parameters do not exceed the ranges of those listed values in Table 5.4. It is worth mentioning that although the yield of the E* + , which is 236l7° 9 , does not seem statistically significant, if we fit the signal by a single Gaussian with floated width, a 162±™ signal is obtained with a mean value of 229.4 ±1.4 MeV/c 2 . We also notice that if we fit the mass-difference region from 190 MeV/c 2 to 290 MeV/c 2 (E+ signal only) in Figure 5.2, the x 2 obtained in our best fit is 31.5 for 44 d.o.f. (degrees of freedom), whereas in a fit with no signal allowed, the \ 2 rises to 49.5. The fit strongly supports the existence of a signal, and this represents the first evidence for the particle E* + . When we vary 7r° momentum cuts from 50 MeV/c to 250 MeV/c, we found that the mass difference shifts from 166.1 to 166.9 MeV/c 2 for the E+ and from 233.5 to 229.7 MeV/c for the E* + ; and the extracted width varies from 3.4 to 4.8 MeV/c 2 for the E c and from 5.0 to 8.4 MeV/c 2 . Also, for the yield in the E+ signal, the data agrees fairly well with the Monte Carlo. Although we have obtained the best statistical significance for the E*+ signal at 200 MeV/c7r° momentum cut, the Monte Carlo optimized 150 MeV/c cut is actually used. To prove the consistency of our signal with A+ samples, we looked at the signal with different o M cuts around the A+ mass, and the measured masses, widths, and yields agree very well.

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105 Table 5.5: The yield (Y), mass difference (AM), efficiency, and normalized production of the E+ for different x p cuts. Both M and T are in units of MeV/c 2 . Xp AM Y Efficiency(%) } '/Efficiency 0.5 1.0 167.1 ±0.4 559 ± 60 2.77 20181 ±2166 0.5 0.6 167.4 ±0.7 208 ± 38 2.45 8490 ± 1551 0.6 0.7 167.2 ±0.8 168 ± 34 2.82 5957 ± 1206 0.7-0.8 166.4 ±0.7 182 ± 28 2.88 6319 ± 972 0.8 1.0 168.2 ± 1.3 72 ± 18 2.85 2526 ± 632 We tabulated the masses and the yields of the E+ for different x p ranges in Table 5.5. For the E* signal, lacking statistics makes it very difficult and not quite meaningful to fit the mass-difference spectra at different x p bins. The numbers in the table are all obtained by fixing the BreitWigner width to be 4.5 MeV/c 2 and fixing the width of the convoluted Gaussian to be the number obtained by Monte Carlo, ranging from 1.80 MeV/c 2 to 2.32 MeV/c 2 . All statistical errors on efficiencies are no larger than 0.01%. 5.3 Masses The masses we present are the mean values of the BreitWigner convoluted with a Gaussian. We have checked that fitting with a single Gaussian, a double Gaussian, or a bifurcated Gaussian (constraining the two width difference no larger than 15%) gives the mean value within 1 a of the statistical error. As discussed in the last chapter, the uncertainties in the magnetic field normalization and the energy-loss correction applied to the charged soft pions, or the uncertainty of the shower energy calibration applied to the neutral pions, bring systematic errors on mass measurement for M(A+7r) M(A+). We find that 0.2% change of charged track momentum shifts M(£ c ) M(A+) by about 0.10 MeV/c 2 and M(E*) M(A+) by about 0.30 MeV/c 2 , 1.0% change of photon energy shifts

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106 Table 5.6: Measurements of mass differences between E c 's and the A+. All numbers are in units of MeV/c 2 . Experiment M(E++) M(A+) M(E+) M(A+) M(E») M(A+) ARGUS[41] CLEO-II[42, 43] E687[45] E791[44] CLEO-II(This) 168.2 ± 0.5 ± 1.6 168.2 ±0.3 ±0.2 167.6 ±0.6 ±0.6 167.8 ±0.3 ±0.2 167.3 ±0.1 ±0.2 168.5 ±0.4 ±0.2 166.9 ±0.5 ±0.3 167.0 ± 0.5 ± 1.6 167.1 ±0.3 ±0.2 166.6 ± 0.5 ± 0.6 167.4 ±0.3 ±0.2 167.2 ±0.1 ±0.2 M(E+) M(A+) by about 0.13 MeV/c 2 and Af(E*+) M(A+) by about 0.38 MeV/c 2 . Reconstructing mass M(A+7r) using vertex constraint on the A+ and the independent pion shifts M(E C ) M(A+) by about 0.05±0.10 MeV/c 2 . For the E c , M(A+tt + ) M(A+) and M(A+tt + ) M(A+) are about 0.2±0.10 MeV/c 2 higher than M(A+7r") M(A+) and M(A+7r~) M(A+), respectively. For E c 's which have clean signals and narrow widths, fitting errors are less important than the errors from other sources, but for E*'s which have very wide widths, fitting errors dominate the systematic uncertainties. Based on Table 5.1, Table 5.4, and more other fitting results of M(A+7r)-M(A+), we conclude that the systematic errors due to fitting procedures are ±0.03 MeV/c 2 for both M(E++)-A/(A+) and M(E°)-M(A+), ±0.2 MeV/c 2 for M(E+)-M(A+), ±8:1 MeV/c 2 for M(E: + +)-M(A+), ±0.5 MeV/c 2 for M(E*+)-M(A c +), MeV/c 2 for M(E; ++ ) Af (A+). To be conservative, we finally assign the total systematic errors to be 0.2 MeV/c 2 for M(E++) M(A+) and M(E C °) M(A+), 0.3 MeV/c 2 for M(E+) M(A+), ^ MeV/c 2 for M(E C * ++ ) M(A+), ±0.7 MeV/c 2 for M(E^) M(A+), ±JJ MeV/c 2 for M(E: ++ ) M(A+).

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107 Table 5.7: Measurements of mass splitting of the E c triplet and comparison with theoretical calculations. All numbers are in units of MeV/c 2 . M{Zt ) M ( s ") IT/ -4\ H I" / 0 \ M(£+) M(E°) Theory Chan[46j 0.4 -0.7 Hwanef47l 3.0 -0 5 Wright [48] -1.4 -2.0 Deshpande[49] -3.3 -2.5 Sinha[50] 1.5 -0.3 Capstick[51] 1.4 -0.2 Experiments ARGUS[41] 1.2 ±0.7 ±0.3 E791[44] 0.38 ±0.40 ±0.15 CLEO-II[42, 43] 1.1 ±0.4 ±0.1 1.4 ±0.5 ±0.3 CLEO-II(this) 0.1 ±0.1 ±0.1 -0.3 ±0.5 ±0.1 Table 5.6 summarizes the measurements of the E c masses from different experiments. Note that we have larger errors on M(E+) -M(A+) than the previous CLEO measurement. This is because we have fitted the mass difference with a floated natural width (Breit-Wigner function) instead of the assumed negligible natural width in the previous works. For E++ and E° mass differences, we have better statistical errors due to the significant improvement of the resolution of soft charged pions. The experimental measurements of mass splitting among the three E c states together with some theoretical predictions from these models are listed in Table 5.7. Our M(E°) result is in vary good agreement with previous results. Our M (E++) result is lower than the average of the previous results, but nearly equal to M(E°). Only CLEO has observed E+, and our measured mass is obviously lower than the previous result. Theoretical predictions about E c isospin mass splitting range from -6.5 MeV/c 2 to ±18.0 MeV/c 2 . Table 5.7 lists the predictions which are close to our measurements. These models have considered the following effect: (1) the intrinsic mass difference between the u and d quarks; (2) electromagnetic interactions consisting

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108 Table 5.8: Measurements of mass difference between E*'s and the A+, in unit of MeV/c 2 . Experiment M(E; + +) ~ M(A C +) M(Z*+) M(A+) M(E*°) M(A+) CLEO-II[21] CLEO-II(this) 234.5 ±1.1 ±0.8 231.4 ±0.8^ 229.2 ± 1.3 ±0.5 232.6 ± 1.0 ±0.8 231.9 ± 1.2j£? of Coulomb interactions between every pair of quarks and spin-spin interactions; (3) contributions of QCD effects (in some of models). CLEO is the only experiment which has reported the measurements on E*'s. Table 5.8 compared the mass differences measured in this work with the recent reported values. Both measurements used the same datasets, but the latter used the recompressed data in which the charged tracks are processed differently and supposed to be measured better. In this work we have roughly the same errors since we could not take much advantage of better charged track resolution due to the large natural width of these states. We have strongly confirmed the existence of the E* + + and the E*° and shown the first evidence of the existence of the E*+. 5.4 Widths As discussed in Chapter 3, the measurement of a particle's natural width depends on the Monte Carlo simulated resolution of the detector, especially when the width is narrow. Also as stated in Chapter 3, we know that the real detector resolution of the M(D* + ) M(D°) measurement is, in the worst case, 15% larger than the Monte Carlo predicted one. We also found that the A;ti(2625) actual resolution is likely bigger, and can be up to 10% larger than the Monte Carlo predicted resolution if A^i (2625) intrinsic width is negligible. Since the momentum spectrum on the soft charged pion for the E++ or the E° is similar to the two independent pions in the A+ 1 (2625)->A+7r + 7rdecay, we should expect that the Monte Carlo predicted

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109 Table 5.9: Measurements of widths of E c 's. r(E++)(MeV/c 2 ) r(E+)(MeV/c 2 ) r(E°)(MeV/c 2 ) Fitted Value Limit 2.1 ±0.3t£ij > 0.6 (90% C.L.) A r-KU + l.U 4 -°-1.7-1.5 0 0+0.4+0.3 ^^-O.S-O.b > 0.7 (90% C.L.) resolution on M(A+7r ± ) M(A+) may be lower than the actual one by roughly the same amount and take this into account when we evaluate the systematic errors. The Monte Carlo resolution on both the E+ + and the E° is 1.04 MeV/c 2 . To make sure that we have seen the finite widths of these states, we fit the M(A+7r + ) M(A+) signal, which is slightly narrower than M(A+7r~) -M(A+) signal, by a width-floated single Gaussian. The fitted widths range from 1.81 to 1.95 MeV/c 2 , depending on how the background is parameterized. We get obviously bad fits if we fit the signal by a single Gaussian with a fixed width lower than 1.6 MeV/c 2 . We have also tried to fit the signal by a double-Gaussian, with a fixed shape determined by Monte Carlo, and could only get reasonable fits by enlarging the Monte Carlo width by at least 50%. Therefore we believe that our detector resolution, which should not be poorer than 1.35 MeV/c 2 , has enabled us to extract finite widths of E c 's from the fits. Even conservatively, we are very certain that the detector resolution must be better than 1.35 MeV/c 2 , which is 30% worse than the Monte Carlo predicted resolution. Then we looked at the x 2 distribution of fits to the mass difference using different Breit-Wigner widths convoluted with a single Gaussian with fixed 1.35 MeV/c 2 width. It can be concluded that at 90% confidence level, T(E+ + ) > 0.6 MeV/c 2 and r(E°) > 0.7 MeV/c 2 . Table 5.9 gives the results on E c widths measurements. The fitted values and their errors are based on Table 5.1 and Table 5.4. Uncertainties of the detector resolution dominate the systematic errors. No other experiments has reported E c

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110 Table 5.10: Measurements of widths of E*'s. Experiment t(e; ++ ) t(e; + ) t(e:°) CLEO-II[21] CLEO-II(this) 17.9^ ± 4.0 14 ± 3 ± 3 °-5-2 13.0ljj;S ± 4 -0 20±l ± 5 Table 5.11: CLEO Measurements of fragmentation functions using the Peterson function for the E c and the E*. Particles E++ E° E++ + E° E c Average o.2ai*|B 0 9
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Ill 0.0 0.2 0.4 0.6 0.8 1.0 x P Figure 5.3: Normalized production spectra of scaled momentum for E c samples. The data for the £++ (triangles), the E+ (circles), and the £° (inverted triangles) are fitted to the Peterson functions overlaid as solid, dotted, and dashed curves, respectively.

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112 0.0 0.2 0.4 0.6 0.8 1.0 Figure 5.4: Normalized production spectra of scaled momentum for £* samples. The data for the £*++ (triangles), and the £*° (inverted triangles) are fitted to the Peterson functions overlaid as solid and dashed curves, respectively.

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113 x p range. The distributions are fitted using the Peterson function. Table 5.11 gives the measured values of e for E c 's and E*'s. Our value of ep(E+ + + E°), 0.28±0.03, is in agreement with the previous result, 0.29 ± 0.06, done by ARGUS[41] also in the 10 GeV/c 2 e + e~ experiment. Our E* values are also agree with the previous value, ep(E* ++ + E*°) = 0.301°;^ . Based on the measurements, it seems that E^'s are fragmented slightly harder than A+, which has e P = 0.25±0.03[1] from 10GeV/c 2 e + e~ annihilation. A^'s are obviously fragmented much harder. This is possibly because many A^'s are directly created from the annihilation, whereas a much larger fraction of E^'s are the decay products from higher excited states. 5.6 Production Ratios To calculate the ratio of the A+ production from E c and E* decays relative to the total inclusive production, the reconstruction efficiencies of the A+, the E c , and the E* from the Monte Carlo simulation are used. Our calculation covers the x p region of 0.4 1.0 for SW ++ and E^ 0 , and 0.5 1.0 for the E+. Since we measure the productions by ratio, most of the systematic errors on the A+ reconstruction cancel. We estimate that the efficiency errors are 3% for E(* )++ or E(* )0 and 6% for the E+. The statistical errors on the Monte Carlo efficiency calculation are tiny. The uncertainty of the detector mass resolution brings large errors in the calculation of E+ + and E° productions. We estimate this uncertainty by reducing and increasing the Monte Carlo resolution by 25% and comparing the areas of the BreitWigner distributions. We estimate this error to be t\Vo. Other fitting errors are mostly due to different background shapes, and they are tested to be no more than 3%.

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114 Table 5.12: Measurements of the E c production relative to total inclusive A+ production from different experiments. All numbers are in units of %. Experiment Beam E691 145 GeV 7 5±3±2 13±4±2 E687 220 GeV 7 6.7 ± 1.9 7.8 ±2.1 NA32 230 GeV 7T" < 5.2(90%C.L.) < 5.3(90%C.L.) E791 500 GeV tt6.7± 1.0 ± 1.0 7.9 ± 1.1 ± 1.0 CLEO-I.5 10 GeV e + e~ 6±3 6±3 CLEO-II(this) 10 GeV e + e7.2 ±0.5 ±0.7 7.3 ±0.5 ±0.7 Fitting procedures dominate the systematic errors for the E+ and E*'s, and the uncertainties on the resolution are much less important. We estimate the fitting errors are t\ 2 % for the E+, ±25% for the two E*'s. We extrapolate the production distribution down to x p = 0 of the Peterson function. The uncertainties on fragmentation function measurements bring large errors. This is not only because we lack the statistics to measure the fragmentation function accurately, but also because there is no reason to expect the Peterson function to perfectly represent the data. We estimate the errors in the extrapolations are 6% for the E++ and the E°, 22% for the E+ and 18% for E*'s. We finally assign the total systematic errors on production ratio measurements to be tl°% for the E++and the S c °, ±™% for the E+ and ±31% for E*'s. The background is not simply formed like the phase space of arbitrary particle combinations. We already know that there is wide enhancement around the region between 140 MeV/c 2 to 210 MeV/ 2 due to a feed-down of A+!(2625)->-A+7r7r decay. Very likely there are some other unknown physical processes making non-phase space contributions elsewhere in the mass-difference spectra, for instance, feed-down from more higher states of the A+ and the E c which decay into A+'s. Table 5.12 lists the measurements of
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115 Table 5.13: Measurements of E* production ratio relative to total inclusive A+ production in units of %. Experiment (7 e;++/ (7 a+ cr S^°/ f7 A+ CLEO-II 1996 CLEO-II (this) 5.9lJi ± 1.8 7.8+l;i ± 2.4 12.8^3 ±3.2 13.71?:? ± 3.0 for the first time we have calculated that (T Ec+ /ct a + = 10.3 ± 1.6 ± 2.7%. Note if we fit the signal with fixed natural width the same as the E° signal, the result would be 7.5 ± 1.1 ± 2.0. Also, if we assume that E c 's do not have natural widths and fit the signals with width-floated single Gaussians, the results on the El + and the E° are 15% smaller and the result on the E+ is 20% smaller. Table 5.13 lists the cr^-/a A + measurements from CLEO. The new result, which agrees with the previous one, shows that the E* and the E c are nearly equally produced. According to their spins, which are 1/2 for the E c and 3/2 for the E*, the number of E*'s created should be two times as large as the number of E c 's from the e + e~~ annihilation. Then why is the number of E c 's in CLEO experiments even larger than 1/2 of E*'s? As the E* has higher mass, its creation should be slightly more suppressed than the creation of a E c ; however, we expect this to be a small effect. We think the real reason is very likely that there are more higher states which decay to the E c than decay to the E*. For instance, we know the decay Al 1 (2593)->E c 7r contributes about 20% of the E c production.

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116 5.7 New Measurements of A+ 1 (2593)^A+7r + 7r According to our measurements, A+ 1 (2593) decays almost 100% to E c 7r, and using our average £+ + and £° mass value, we can calculate that the kinematic threshold of + 7r~ and S°7r + is at a mass difference of 306.86 MeV/c 2 . Since this threshold is very close to the central mass of the resonance, the shape of the signal will not be an "ordinary" BreitWigner. We believe this is the reason why a BreitWigner convoluted with a Gaussian resolution does not fit the A^(2593)— >A+7r + 7r" signal well as shown in Figure 5.5. The fit gives a ln(Likelihood)* value of 48.0 for 30 d.o.f. If we assume that A^(2593) decay 100% to E c 7r, a reasonable way to fit the A+ 1 (2593)— >A+7r + 7r~ signal is to use a relativistic BreitWigner form[l, 52] with the amplitude where M is the invariant mass of the E c 7r in the final state that results from the decay of the A+!(2593), M r is the mass of the A+j(2593), and r r (7r°) and r r (?r ± ) are the mass-dependent widths of A+ x (2593) corresponding to the decay A+7r°7r° and A+7r + 7r", respectively. Note both r r (7r°) and T^n*) are in the denominator but only r r (7r ± ) is in the numerator. This is because we must put the "full" width in the denominator, and A^(2593) has both A+7r°7r° and A+7r + 7r _ decay channels, but here we are only measuring the signal of the A+7r + 7r~ decay. We need a factor \JM in the numerator of the BreitWigner, because the phase space factor is a factor times dM 2 = MdM, and we are fitting the data as a function of M. The factor would not be present if we fit the data as a function of M 2 . For A;|i(2593), M » T r , so this y/M factor virtually does not affect the BreitWigner shape. The normalization factor in equation 5.1 is omitted, and it is evaluated numerically in the fit procedure. *ln(Likelihood) is the same as x 2 for large statistics. (5.1) M 2 M 2 iM r {r r (ir°) + r r (7r±)]'

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117 Figure 5.5: The fit to the A+ 1 (2593)->A+ 7 r + 7rsignal using a simple Breit-Wigner function convoluted with the detector resolution. The mass-difference spectrum and the fit are the same as Figure 4.1, but here we only fitted A+ x (2593) in order check the likelihood of the fit, and 1-MeV/c 2 bin size is shown instead of 1-MeV/c 2 in order to get a clearer view near the threshold.

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118 For this relativistic Breit-Wigner function, the width parameter of the resonance is mass dependent. For a decay by a partial wave of orbital angular momentum L, the width can be described as T r = (p*/M) 2L p*a, (5.2) where p* is the momentum in the rest frame of the resonance of either one of the daughters, and a is a mass-independent parameter. It has been tested in experiments that the width parameterization of equation 5.2 can reasonably fit to the massdependent width of Pwave decay of the p[53, 54]. A^(2593)— )-E°7r~ is two-body decay, so we have p*^-) = [(M 2 (M £ o + A/„-) 2 )(M 2 (M s o A/,-) 2 )] 2 (5 3) p*(£+7T°) and p*(E+ + 7r + ) can be expressed similarly. In our fit procedure we assume that M s ++ = M s o; thus we have p*^) = p*(£°7r _ ) = p*(E+ + 7r + ). Since A cl (2593)— >E c 7r is 5-wave decay, according to equation 5.2, r r (*±) = P^Mtt*), (5.4) r r (7r°) = pV)a(A (5.5) From isospin symmetry, we can assume that a(7r°) = fax*). Now we have three parameters to fit the data: M r , a(7r ± ), and the area of the signal. To fit the A+ 1 (2593)-)'A+7r + 7r _ signal, we used the relativistic Breit-Wigner function as in the equation 5.1, smeared with a single Gaussian and a regular BreitWigner function. The Gaussian is used to parameterize the detector resolution of A+ 1 (2593)^A+7r+7r-, 1.28 MeV/c 2 , determined by Monte Carlo studies; and the

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119 2.580 2.590 2.600 2.610 M(A/tt*tO (GeV/c 2 ) Figure 5.6: New fit to the A^i(2593)-)-A+7r + 7r _ signal using the relativistic BreitWigner function described in the text convoluted with the detector resolution and the E c width. Breit-Wigner represents the natural width of E+ + or E°, with an average value of 2.2 MeV/c 2 . To input a E c mass, we used the mass difference, 167.3 MeV/c 2 , which is our measured average of E+ + and E°. The background is fitted by a second order polynomial with the area and shape floated. Figure 5.6 shows such a fit. The ln(Likelihood) value for the fit is 30.4 for 30 d.o.f, much better compared with 48.0 from the fit using the regular Breit-Wigner function. The results of the fit shown in Figure 5.6, which are used as our presented values, are listed in the first row of the values in Table 5.14. In the following rows of the table, we tabulated the results obtained by different types of signal parameterization. The first three numbers in each row are input values of the fit and the last three

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120 Table 5.14: Fit results of A+ 1 (2593)— A+7r + 7r _ signal in Figure 5.6. The E c mass difference (with A+) AM Sc , the E c width r Ec , and the A^ 1 (2593)-)'A+7r + 7r _ mass resolution er A + are fixed as the input to the fitting function. The mass difference (with A+) of the A^(2593), a(7r ± ) and the yield of the signal are the measured parameters. All mass differences and widths in the table are shown in units of MeV/c 2 . Fixed parameter Fitted parameter A.Uv, rv, AM A + a(7r±) Yield 167.3 2.2 1.28 305.3 ±0.4 83™ 195i£ 167.0 2.2 1.28 305.2 96 194 167.6 2.2 1.28 305.4 73 198 167.3 0.7 1.28 305.9 16 164 167.3 1.5 1.28 305.0 68 187 167.3 2.8 1.28 305.4 98 195 167.3 2.2 1.00 304.8 90 195 167.3 2.2 1.70 305.7 82 183 numbers are the extracted parameters. In each row except the first, there is a number shown in boldface in order to emphasis that this is the number we reasonably altered from the central value. Note that the mass, but not the mass difference, is used in the fit. So A+ mass is actually used here. We proved that varying mass of A+ by a few MeV/c 2 virtually does not changed the measured parameters. Although the A+j (2593) mass is measured, we still present the mass difference since it is a more accurate value. From Table 5.14, we see that the measured mass slightly varies when other input parameters change. So all input parameters, within reasonable ranges, do not influence the value of the mass very much. Also note that the yield measured here is almost the same as the measurement described in Chapter 4 with similar statistical error and fitting error, thus all the A+!(2593) related branching ratios and production ratios measured in Chapter 4 still hold.

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121 a(7r ± ) is very sensitive to changes of any input parameter, but we also notice that the shape of the resonance varies only slightly when a(7r ± ) changes. It seems that the a parameter is not proportional to the "width" of the signal, and the value of a is very sensitive to any change of parameterization near the threshold. We think the measurement of the a parameter in our fit is not very reliable, and the systematic error we quote is large. Using the measured value of a(7r ± ) and assuming a(7r ± ) = 2a(7r°), we can predict the branching ratio r(A+7r°7r°)/r(A+7r + 7r-) using the Asw^^) formula in equation 5.1 and the similar formula for £+7r° decay, 0 yjMr r (ir°) ABw{n ] ~ M?-M*-iM r [r r {*°) + r r {«±)Y (5 ' 6) We found that r(A c + 7rV)/r(A c +7r + 7r-) = 2.2 if a(7r ± ) = 100, 3.1 ifa(7r ± ) = 84, 4.0 ifa(7r ± ) = 60. This proves that the range of a(ir ± ) in Table 5.14 is consistent with our our measured r(A+7r°7r°)/r(A+7r + 7r-) in Chapter 4, which is 2.6 ± 0.6 ± 0.7. Similar to the A+ 1 (2593)->A+7r + 7r _ case, we can also fit the A,?j(2593)->A+7r 0 7r 0 signal using a Breit-Wigner function with the amplitude A bw (tt°) in equation 5.6. Note that A bw (-k°) is very close to a regular Breit-Wigner amplitude since the £+7r° threshold is at about 302 MeV/c 2 , 4 MeV/c 2 below the center mass, and therefore fitting the A+ 1 (2593)->A+7r°7r° signal using A bw (-k q )* obtains almost the same mass "Another way to do the measurement is to fit the A+7r + 7r~ and A+7r°7r° signals simultaneously by constraining them to have the same a's, but since A+7r°7r° signal is much poor, the measured parameters would be almost determined by the A+7r+7r _ signal. We think it is more reasonable to fit them separately.

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122 2.580 2.590 2.600 M(A c Vtt°) (GeV/c 2 ) 2.610 Figure 5.7: New fit to the A+ 1 (2593)^A+7r°7r° signal using the relativistic BreitWigner function described in the text convoluted with the detector resolution and the E c width. and yield as the fit in Figure 4.3. Figure 5.7 shows such a fit. In the fit, we used a convoluting Gaussian with a width of 2.4 MeV/c 2 , representing the A+7r 0 7r° mass resolution, and the same convoluting Breit-Wigner as we used to fit the A+7r + 7r~ signal*. However, due to low statistics, this fit measures the a parameter with enormous statistical error, so we cannot get more information about A B w(n°) and Abw^) by directly fitting them with the A+7r°7r° signal. Figure 5.7 shows a very good fit by fixing Abw^) to be 83. 'Since the S+ width is very poorly measured, we assume that it is the same as the E++ and E°. The fit does not change much even if we use = 4.5 MeV/c 2 .

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123 Finally, using a new method never used on A+ 1 (2593) in any previous experiments, we have measured A^(2593) with the results M(A+(2593) M(A+) = 305.3 ± 0.4 ± 0.6 MeV/c 2 , a( 7 r ± ) = 831J 0 ± 40. The fitting error, 0.5 MeV/c 2 evaluated from Table 5.14, dominates the total systematic error of A^(2593) measurements. The error estimated from the momentum scale study is 0.2 MeV/c 2 . The value of mass is significantly lower than the previously measured values using a normal BreitWigner as the fit function listed in Table 4.7. But the value is consistent with our mean value of A^(2593)— >A+7r 0 7r 0 , 306.3 ±0.7 MeV/c 2 . The fit using the lower limit of the i\ c , 0.7 MeV/c 2 , gives a very small a. Although the fit is acceptable, it is not used to evaluated the systematic error of the a(7r ± ) value because the 0.7 MeV/c 2 limit is far beyond one unit of standard deviation. More careful studies are needed about the a parameter of A^(2593) in both theoretical models and experiments.

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CHAPTER 6 SUMMARY AND DISCUSSION In this research, we have made a complete study of eight charmed baryons: the A^j doublet, which decays to A+7T7T, and the E c triplet and the E* triplet which decay to A+7r. With a large data sample and improved detector resolution, we measured the E c masses more accurately than previous experiments, and the results are 167.3 ± 0.1 ± 0.2MeV/c 2 for E++, 166.9 ± 0.5 ± 0.3MeV/c 2 for E+, and 167.2 ± 0.1 ± 0.2MeV/c 2 . Our results do not indicate any noticeable isospin mass splittings among this triplet. Studying the mass splitting among baryons containing different-valence quarks is a good way to understand hadronic structure and the forces which determine the structure. The mass splittings in the charm baryon system are especially interesting since the large mass of the c quark simplifies the component structure in theoretical models so the experimental tests are more meaningful. The E c is the first baryon isospin multiplet for which the intrinsic light-quark mass difference is not the dominating factor of the isospin mass splitting. However, the theoretical predictions vary largely for different models. Our results support that the splittings are very small, and the numbers are close to the prediction by Chan [46]. In this work, the E c widths were measured for the first time, and the results are 2.1 ± 0.3i°j MeV/c 2 for £++, 4.5^};° MeV/c 2 for £+ and 2.3±g:|±g;| MeV/c 2 for E°. These values are in very good agreement with the prediction of heavy-quark chiral perturbation theory[16]. We measured the E* widths r(E*++) = 14 ± 3 ± 3 MeV/c 2 and r(E*°) = 20±f ± 5 MeV/c 2 . These are consistent with the previous measurement by CLEO[21]. Note that based on equations 1.3 and 1.5, the E c and 124

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125 E* widths are correlated with each other through the coupling constant g 2 Our results agree with the g 2 value predicted by many theoretical models. We have confirmed the previous E* ++ and E*° observation made by CLEO, with masses measured to be 231.4 ± 0.8^| MeV/c 2 for the £* ++ and 231.9 ± 1.2tJ;| MeV/c 2 for the E*°, and the widths measured to be 14 ± 3 ± 3 MeV/c 2 for the £*++ and 20^ ± 5 MeV/c 2 for the E*°, all consistent with previous results. In addition, for the first time we observed the E* + evidence, with the mass measured to be 229.2 ± 1.3 ± 0.5 MeV/c 2 and the width measured to be 5t^ MeV/c 2 . We have measured the ratios of the A+ productions from relative to the total inclusive A+ production from the 10GeV/c 2 e + e~ production, and the results are 7.2 ± 0.5 ± 0.7% from E++, 10.3 ± 1.6 ± 2.7% from E+, 7.3 ± 0.5 ± 0.7% from E°, 5.91^ ± 1.8% from E* ++ , and 7.8±i;§ ± 1.8% from E^ 0 . We are unable to make a E*+ measurement since the signal is too poor. This is the first time that a E+/ a A+ ' s measured, and all the other ratios measured are in agreement with previous experiments. Based on our measurements, we can conclude that 25 ± 4% of A+'s are from E c decays. If we assume the three E*'s are equally produced, then about 20% of A+'s are produced from E* decays. The following evidences provide very strong proof that these two states are indeed A+! baryons with light degrees of freedom having L = 1: (1) the A + 7r° signals are not seen; (2) the E c 7r channel transition dominates the A+(2593) decay and the same channel is measured small for A+j(2625); and (3) the A+7r°7r° channel is observed for both A^i's. This is the first time the A+7r°7r° decay channel has been observed, and the relative decay ratio B(A+7r°7r°)/,B(A+7r + 7r-) is measured to be 2.6 ± 0.6 ± 07 for A+(2593) and 1.0 ± 0.3l<^ for A+(2625). The value for A+(2593) does not agree with isospin symmetry but can be explained by phase-space suppression.

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126 The A+i(2625) mass was measured to be 341.80 ± 0.10 ± 0.35 MeV/c 2 . We measured the upper limit of the A+ x (2625) width to be 1.4 MeV/c 2 at 90% confidence level. These values agree with previous experiments. By fitting the A^(2593)— >A+7r + 7r~ signal the same way as the previous experiments, it is measured to have a mass 308.8 ± 0.4 ± 0.4 MeV/c 2 and a width 4.7l};itJ;9 MeV/c 2 which are consistent with previous results but not consistent with our A+ 1 (2593)— »A+7r°7r° measurements, in which we measured the mass to be 306.3 ± 0.7 MeV/c 2 . But these measurements are based on the signal parameterization using an ordinary Breit-Wigner function. Because A^j(2593) resonance is just at the £ c 7r ± kinematic threshold, a relativistic Breit-Wigner function should be used. In this function, the width of a resonance is mass dependent and can only be parameterized by the a parameter. Using the new method, we obtained very good fit and measured the A^(2593) to have a mass 305.3 ±0.4 ±0.6 MeV/c 2 . Assuming that g(7t ± ) = 2a(n°) based on isospin symmetry, we measured a(7r ± ) = 83lg° ± 40. These new measured values are consistent with our r(A+7r°7r°)/r(A+7r + 7r _ ) result, 2.6 ±0.6 ±0.7. The non-relativistic quark potential model [6] fails in its prediction of the A£ masses. The relativized model is close, but their 10 MeV/c 2 spin-orbital mass splitting is too small. The mass splitting between the two A^ states is 36.5 ± 0.4 ± 0.6 MeV/c 2 from our measurements, about 4 MeV/c 2 larger than 32.4 ± 1.0 ± 0.7 MeV/c 2 measured by ARGUS[32]. From heavy-quark symmetry, we should expect that M(A+(2625)) M(A+(2593)) = M( J D 2 *(2460)°) M(A(2420)°). The PDG[1] average value of M(Z^(2460)°) M(A(2420)°) is 37 ±3 MeV/c 2 . We see that HQET works quantitatively very well in this case.

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127 To date, few theoretical models directly predicted the A^j widths. The most recent calculation was made by Tawfiq et al.[55]. They used a light-front constituent quark model which utilized the SU(2iV/)xO(3) diquark symmetry, where Nf represents the number of light flavors. Assuming the mass of a light quark to be 340 MeV/c 2 , they predicted that r(A+!(2593) -> E c 7r) is around 1.6 ~ 2.5 MeV/c 2 . They also predicted the D-wave transition rate r(A+ 1 (2625) — > S c 7r) to be about 0.7 MeV/c 2 . But our measurements contradict these values. No model has directly predicted the widths of non-resonance two-pion transitions. Better Monte Carlo simulation and detector resolution are needed to perform further measurement of the A+!(2625) width. Theoretical computations[56] give small values of of decay rates of the radiative decays: 0.016 MeV/c 2 for A+^2593) and 0.021 MeV/c 2 for A+^2625). According to these values we should not be able to see A^(2593)->A+7 smce its width is obviously large, and we might be able to see A;Jj(2593)->A+7 if T(A+ 1 (2625)) A+7T+7T is very narrow. We did not find any evidence of A^-^A+7 decays. The upper limit we measured is too large to provide any indications.

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REFERENCES [1] Particle Data Group. Review of particle physics. The European Physical Journal C, 3(1-4), 1998. [2] K. Wilson. Phys. Rev., D10:2445, 1974. [3] J. Kogut and L. Susskind. Phys. Rev., D9:3501, 1974. [4] S. Capstick and N. Isgur. Phys. Rev., D34:2809, 1986. [5] K. Maltman and N. Isgur. Phys. Rev., D22:1701, 1980. [6] L. Copley, N. Isgur, and G. Karl. Phys. Rev., D20:768, 1979. [7] H. Politzer and M. Wise. Phys. Lett, B208:504, 1988. [8] H. Politzer and M. Wise. Phys. Lett, B206:681, 1988. [9] N. Isgur and M. Wise. Phys. Lett, B232:133, 1989. [10] N. Isgur and M. Wise. Phys. Lett, B237:527, 1990. [11] E. Eichten and B. Hill. Phys. Lett, B234:511, 1990. [12] H. Georgi. Phys. Lett, B240:447, 1990. [13] B. Grinstein. Nucl. Phys., B339:253, 1990. [14] N. Isgur and M. Wise. Nucl. Phys., B348:276, 1991. [15] H. Georgi. Nucl. Phys., B348:293, 1991. [16] T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y. Lin, and H.-L. Yu. Phys. Rev., D46(3):1148, 1992. [17] A. Manohar and H. Georgi. Nucl. Phys., B234:189, 1984. [18] A. Chodos. Phys. Rev., D10:2599, 1974. [19] M. Khanna and R. Verma. Z. Phys., C7:275, 1990. [20] S. Coleman and S. Glashow. Phys. Rev., 134B:670, 1964. 128

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129 [21] CLEO Collaboration. Phys. Rev. Lett, 78:2304, 1997. [22] D. Pirjol and T.-M. Yan. Phys. Rev., D56(9):5483, 1997. [23] CLEO Collaboration. Phys. Rev., D57:4467, 1998. [24] C. Prescott. The knvf secondary vertex finding package. CLEO CSN, 97/353, 1997. (unpublished). [25] Brock I. Mn_fit a fitting and plotting package using minuit. L3 Note, 918, 1995. [26] Minuit function minimization and error analysis. CERN Program Library, D506. [27] CLEO Collaboration. Phys. Rev., D43:3599, 1991. [28] ARGUS Collaboration. Phys. Lett, B317:227, 1993. [29] FNAL E687 Collaboration. Phys. Rev. Lett, 72:961, 1994. [30] CLEO Collaboration. Phys. Rev. Lett, (74):3331, 1995. [31] FNAL E687 Collaboration. Phys. Lett, B365:461, 1996. [32] ARGUS Collaboration. Phys. Lett, B402:207, 1997. [33] C. Peterson, D. Schlatter, I. Schmitt, and P. M. Zerwas. Phys. Rev., D27:105, 1983. [34] CLEO Collaboration. Phys. Rev., D37:1719, 1988. [35] ARGUS Collaboration. Z. Phys., C(52):353, 1991. [36] CLEO Collaboration. Phys. Rev., D37:1719, 1988. [37] BNL. Phys. Rev. Lett, 34:1125, 1975. [38] COLU and BNL. Phys. Rev. Lett, 42:1721, 1979. [39] BEBC TST Neutrino Collaboration. Phys. Lett, 93B(4):521, 1980. [40] E400 Collaboration. Phys. Rev. Lett, 59(24) :2711, 1987. [41] ARGUS Collaboration. Phys. Lett, B211(4):489, 1988. 42] CLEO Collaboration. Phys. Rev. Lett, 62(11):1240, 1989. 43] CLEO Collaboration. Phys. Rev. Lett, 71(20):3259, 1993. 44] E791 Collaboration. Phys. Lett, B379:292, 1996.

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130 [45] E687 Collaboration. Phys. Lett, B365:461, 1996. [46] L-H. Chan. Phys. Rev., D31:204, 1985. [47] W-Y. Hwang and D. Lichtenberg. Phys. Rev., D35:3526, 1987. [48] A. Wright. Phys. Rev., D17:3130, 1978. [49] N. Deshpande. Phys. Rev., D15:1885, 1977. [50] S. Sinha. Phys. Lett, B218:333, 1989. [51] S. Capstick. Phys. Rev., D31:204, 1985. [52] J. Jackson. II Nuovo Cimento, XXXIV: 1644, 1964. [53] J. Pisut and M. Roos. Nucl. Phys., B6:325, 1968. [54] V. Chabaud. Nucl. Phys., B223:l, 1983. [55] A. Tawfiq, P. O'Donnell, and J. Korner. On p-wave to s-wave pion transitions of charmed baryons. UTPT, 98-08. (Unpublished). [56] C. K. Chow. Phys. Rev., D54:3374, 1996.

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BIOGRAPHICAL SKETCH Jiu Zheng was born in Tangshan, Hebei province, China on October 7, 1965. After ten years of elementary education in Beijing, he enrolled in the Department of Physics of Peking University in 1983. After obtained his Bachlor of Science degree in 1987, he worked as an electrical and cryogenic engineer in the Natural Constant Group of the National Institute of Metrology for six years. He began studying at the University of Florida in 1993, and he has conducted research in the CLEO collaboration since 1994. 131

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. J. Yelton, Chairman Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of DoctaToTPhilosophy P. Avery Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. JlA ^ P. Sikivie Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. G. Mitselmakliff Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. D. Hintenlang Associate Professor of Nuclear and Radiological Engineering This dissertation was submitted to the Graduate Faculty of the Department of Physics in the College of Liberal Arts and Sciences and to the Graduate School and was accepted as partial fulfillment of the requirments for the degree of Doctor of Philosophy. May 1999 Dean, Graduate School