Measurement of Event Shapes in Proton-Antiproton Collisions at Sqrt(s) = 1.96 TeV

Material Information

Measurement of Event Shapes in Proton-Antiproton Collisions at Sqrt(s) = 1.96 TeV
Pinera, Lester
Place of Publication:
[Gainesville, Fla.]
University of Florida
Publication Date:
Physical Description:
1 online resource (104 p.)

Thesis/Dissertation Information

Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Committee Chair:
Korytov, Andrey
Committee Members:
Yelton, John M.
Mitselmakher, Gena
Matchev, Konstantin T.
Uman, Martin A.
Graduation Date:


Subjects / Keywords:
Calorimeters ( jstor )
Cumulative distribution functions ( jstor )
Hadrons ( jstor )
Jet thrust ( jstor )
Luminosity ( jstor )
Particle interactions ( jstor )
Protons ( jstor )
Quantum chromodynamics ( jstor )
Quarks ( jstor )
Simulations ( jstor )
Physics -- Dissertations, Academic -- UF
event, qcd, shape
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Physics thesis, Ph.D.


This dissertation presents a measurement of event shape variables in proton-antiproton collisions at a center of momentum energy of 1.96 TeV. The observables studied are the transverse thrust and thrust minor, both defined over final state momenta perpendicular to the beam direction. These variables are calculated using unclustered calorimeter energy measured using the CDF-II detector at the Fermi National Accelerator Lab. In addition to differential distributions , we present the evolution of event shape mean values as a function of the leading jet Et. The data is compared to dedicated theoretical predictions (NLO+NLL) and subsequently to PYTHIA Monte Carlo with and without multiple parton interactions. In the presence of an underlying event the observables are found to significantly depart from the predictions of perturbative QCD. ( en )
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Includes vita.
Includes bibliographical references.
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Thesis (Ph.D.)--University of Florida, 2008.
Adviser: Korytov, Andrey.
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by Lester Pinera.

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I t3)< 8 GeV, >2.5 (default) JET20, R=0.7

.7--- -----.4--.---.4-- .----.I-----4----.-4.. ---

Figure 3-11. The ratio of the transverse moment of "probe" and I1 ,--. i" jets using the
20 GeV jet sample. The curves are obtained using two different methods: the
missing ET projection fraction (red) and the dijet balance technique (black).
The "probe" tri._.r jet is required to be in the region 0.2 < |r\ < 0.6, while
the probe jet is required to be outside that region.

regions of the detector such as the region between the east and west halves of the central

calorimeter (Tr ~ 0), or the region between the central, wall, and plug calorimeters

(TI ~ 1.0). The correction is based on the idea that in an event with only two jets, the

transverse energies of those jets should be balanced. To extract a correction factor as a

function of r1, events are selected with a I .-.-' r" jet that lies in the central part of the

calorimeter (0.2 < |qtrfggerl < 0.6) and a single "probe" jet that lies outside this region.

The ratio of the probe/ptrigger is then plotted as a function of TIProbe; the result is shown in

Fig. 3-11. The correction relies entirely on a good understanding of the calorimeter in the

central region, where individual towers can be calibrated using information from isolated


The second correction is designed to account for multiple pp interactions in the same

bunch crossing. The idea is that energy from additional pp interactions in the same bunch

crossing can fall into the jet clustering cone of the hard interaction thereby increasing

the measured jet's energy. The correction is derived by measuring the transverse energy

2006. Each of the tri ..-- r paths is unique and therefore each of the samples is statistically

independent of the others.

4.2 Event Selection

We select events with the two highest ET jets lying in the central region T]1 < 0.7 with

no further restrictions on the number of additional jets. As mentioned in chapter 3, jets

are reconstructed using CDF's implementation of the Midpoint algorithm. A cut is also

placed on the hardness of the leading jet corresponding to the aforementioned separation

of data into 100, 150, 200, and 300 GeV samples. This cut is imposed after the jet energy

is corrected back to the parton level. As -,i--.- -1. 1 by theorists, no additional cut is placed

on the transverse energy of the second jet [19].

In order to ensure that events selected are not contaminated by high energy cosmic

rays, we apply a standard CDF cut on the significance of missing transverse energy (fr )

in the event. The rT significance is defined as 7T / ZE/ T where ZEET is the scalar sum of

the transverse energy of the event as measured using individual calorimeter towers above

threshold. For the single jet triggers used in this study, this cut has been optimized to 5.0,

6.0, 7.0 GeV1/2 respectively for the 50, 70, 100 GeV triggers.

Finally, to avoid pile-up, we require events with only one reconstructed primary

vertex. The z-position of this vertex is required to lie within 60 cm of the nominal

interaction point. This is done to maximize detector coverage for each event while

guaranteeing high statistics.

4.3 Calorimeter Towers

The measurement of event shapes is ultimately performed with unclustered

calorimeter towers over the detector's full rapidity range (|r]\ < 3.5). Figure 4-1 shows

the T] and Q distribution of towers in Data and MC. Clearly, an excess of towers is present

in Data; however, the shapes of these distributions is well reproduced by the simulation.

[1] M. W. Grunewald, (2007), arXiv:hep-ex/0710 2-:-
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k k k p -+ w~- < (1-4)

and (2) the probability of emitting a soft or collinear gluon is enhanced:

k< k < p w In2p- (1-5)

The emission of a hard parton is, therefore, accompanied by a cascade of secondary

partons at small angles. This stage of the event is referred to as the parton shower. It

is also calculable within pQCD but requires a resummation of terms in the perturbative

expansion to all orders in as.

Within the same proton anti-proton collision it is also possible to have a secondary

parton-parton interaction. This situation is referred to as multiple parton interactions(\!I PI).

Together with the spectator partons from the proton and anti-proton, MPIs contribute to

the O.,./. ;i;, ,,' event (UE). Being closely connected to the internal state of the hadrons

before collision, understanding the UE is not within the realm of pQCD and we must

instead rely on phenomenological models. It is important to recognize that the UE is a

feature of all hadronic collisions and that it is impossible to distinguish on an event by

event basis UE particles from those associated with the hard scattering.

Finally, at energies below ~ 1GeV all quarks in the event undergo a process called

hadronization by which they form colour neutral hadrons. These are ultimately the

particles observed in a detector. From a theoretical point of view, hadronization is the

least understood part of jet fragmentation. However, it is believed to occur locally and

involve only small momentum transfers [11].

bunch 13
bundh 36

3 BSA ticka
spacings n
between bundws bunch

Figure 3-2. Proton and antiproton beam structure at the Tevatron. Each beam is divided
into three 1i 1,,i,-" which are separated by an abort gap.

bunches. Each train is followed by an abort i,'' whose presence is meant to ensure a

safe removal of the beam should conditions become unstable. The beam configuration is

illustrated in Fig. 3-2. Finally, the beams are focused to interact at collision points where

the two i i, i" detectors are centered, with a bunch crossing occurring every 396 ns.

The critical quantity for determining the rate of collisions is the beam ;,;,>. .:'/u ;

which may be expressed as,

L fB NB N(3-1)

where fB is the bunch revolution frequency, NB is the number of bunches per

beam; Np (Np) is the number of protons (antiprotons) per bunch, and ap and up are the

average cross-sectional areas of the bunches. In discussions of instantaneous accelerator

performance the luminosity is often given in units of [cm-2s-1]. For a given physical

process with cross-section a, the luminosity (L) will yield that interaction at a rate of

final state 'f'. In a quantum field theory such as QCD, the matrix element is a sum of

transition amplitudes represented by Feynman diagrams. The diagrams may be grouped

conveniently by the number of strong interaction vertices, each of which contributes a

factor Va- to the corresponding amplitude.

For any given final state, an infinite number of diagrams exist with differing numbers

of loops 4 And for a general N-jet final state, the total matrix element associated with a

hard scattering at a hadron collider is given by

MA(if) Y .M, + Y M, + Y MA, + ... (2-6)

tree 1 loop 21oop
N N N+1
OC as2 a as

Calculating the transition rate, and hence the differential cross section da/dy,

requires multiplying this total matrix element by its complex conjugate. This result can be

calculated analytically, but given the complex gauge structure of QCD and the multitude

of tree level scattering configurations possible at a hadron collider, the number of Feynman

diagrams that need to be accounted for at even the lowest order is significant. As a result,

fixed order calculations are typically performed numerically by Monte Carlo integration

programs. With regard to a general event shape observables y, fixed order calculations

diverge (at all orders) in the limit y -- 0. The fixed order results shown in this dissertation

are the obtained via the MC program NLOJET.

2.3.2 Soft QCD Radiation & Resummation

For event shape variables, fixed order perturbative estimates are only useful in

the region away from y = 0. This is due to the singular behaviour of the fixed order

4 Feynman diagrams containing loops are often referred to as virtual corrections.

of momentum is equal to the vector sum of transverse moment outside the region).

However, preliminary studies showed that there was almost no correlation between

the event shapes (thrust and thrust minor) and the recoil term. As such, its effect was

primarily to shift the mean and smear the distributions. As a result, this alternative

definition was not pursued.

2.3.3 Matching Fixed Order & Resummed Results

For the practical use of resumed results an important step is that of matching

with the fixed-order prediction. At the simplest level one may think of matching as

simply adding the fixed-order and resumed predictions while subtracting out the doubly

counted logarithmic terms. However, it should be noted that there are subtleties involved

in the matching procedure; a discussion of which is beyond the scope of this experimental

dissertation. For the sake of interested parties it will suffice to note that theorists have

emploiv d a in R matching procedure in the matched curves provided.

2.4 Monte Carlo Generators

Thus far, the QCD predictions we have discussed have been concerned with free

quarks and gluons. Before reaching our detector, these partons must hadronize into

bound colourless states. This final phase of the QCD interaction, which occurs at low

characteristic energy scales, cannot be predicted by perturbation theory. Instead we use

numerical simulations based on semi-empirical models. In addition, final state hadrons are

free to decay and interact with detector material. An indispensable tool in understanding

experimental uncertainties are event generation programs based on Monte Carlo methods

[24]. Such programs simulate the production and development of individual hadronic

events according to probability densities.

Table 1-1. Summary of gauge boson properties of the Standard Model.
Boson Spin Electric charge Mass
Photon (7) 1 0 0
W 1 1 80.398 GeV/c2
Z 1 0 91.1876 GeV/c2
Gluon (g) 1 0 0

distances; however, this is a consequence of the gauge structure of the strong interactions

2 The properties of the gauge bosons are summarized in Table 1-1.

In the Standard Model all matter is made up of spin 1/2 fermions which must

therefore obey the Pauli exclusion principle [4]. These point-like particles are classified

as either leptons or quarks and are grouped into three generations of doublets with

successively larger masses. Particles of the higher generations are unstable and therefore

decay to less massive particles of the lower generations. The visible universe is primarily

composed of particles from the first, least-massive group. Curiously, the Standard Model

offers no explanation as to why nature is grouped into these generations.

The leptons are six in number and interact exclusively via the electric and weak

forces. The muon (p) and tau (r) are identical to the electron (e) except for the fact

that they are respectively 200 and 2500 times heavier. In addition to these three charged

leptons, there are three corresponding neutral leptons known as neutrinos (Vt, V1, V')

whose masses are all very small. Furthermore, their cross-sections for interacting with

matter are vanishingly small and so their direct reconstruction in experiment is difficult.

The properties of leptons are summarized in Table 1-2.

The second class of fermionic matter in the Standard Model are known as quarks.

These particles come in six flavours: up (u), down (d), strange (s), charm (c), bottom (b),

and top (t). They are unique in that they participate in all the known forces and are the

2 Gluons themselves carry the li g hdi ,. which allows them to interact with each

2.2 Event Shape Observables

Because the parton's scattering in a hadron collider are not in the center of

momentum frame, the event shapes studied here are defined as sums over final state

moment transverse to the beam direction.

2.2.1 Transverse Thrust

The thrust is often considered the prototypical event shape observable. At a hadron

collider it is defined as:

Tr max i- n (2-1)
nT V


where the sum runs over all particles in the final state and the thrust axis, dT, is defined

as the unit vector in the transverse plane which maximizes this expression. For a perfectly

"pencil-like" event with only 2 outgoing particles, T = 1. In the case of a perfectly

isotropic event the transverse thrust takes on the value T = _. Because the ini ii iily of

event shapes vanish in the two-jet limit, it is convenient to define Ti- = 1 T which shares

this property. Hereafter, any discussion of the observable called thrust shall refer to the

quantity 7-r.

2.2.2 Transverse Thrust Minor

Having defined the transverse thrust axis nT, one can define the transverse thrust



TMi-- i o n ZXz (2-2)


+ Potential wires
Sense wires
.. -- -, ,- X Shaper wires
,' Ill Bare Mylar
,,,, f'Nl, I llii Gold on Mylar (Field Panel)

S52 54 56 58 60 62 64
Layer 1 3 4 8 7 .

Figure 3-6. Cross-sectional views of COT superlayers and individual wires in three COT
cells. The angle between wire-plane of the central cell and the radial direction
is 350.

I i-; -' mixture of argon, ethane, and isopropyl alcohol which provides a small enough

drift time (200 ns) to allow hit read-out between Tevatron bunch crossings.

The COT consists of 30,240 sense wires arranged into 96 1V. rS which are grouped

radially into eight -op. i.;. -, as depicted in Fig. 3-6. The superlayers are divided

azimuthally into cells, each with 12 sense wires held at potentials between 2.6-3.0 kV.

In order to maintain a maximum drift distance of 88 cm between wires, the number of

cells per sul I. i -,, r is required to scale with radius. The sense wires in even-numbered

superlayers are strung parallel to the z direction, thereby providing resolution in the

transverse plane, while odd-numbered sulp' i- ,i, _s use stereo wires strung at small

angles (20) with respect to the z direction allowing for longitudinal resolution. Particles

originating from the nominal interaction point at z = 0 which have |T1 < 1.0 traverse all

eight superlayers while those with |T1 < 1.3 will traverse at least 4 superlayers.

The organization of wires within a cell is shown in Fig. 3-6. Each cell is composed of

high voltage field panels, potential wires, and shaper wires-all of which work to support a

uniform electrostatic field. A charged particle passing through the cells ionizes the gas in

measured data. To this end we begin by considering the definitions of the thrust (Eq. 2-1)
and thrust minor (Eq. 2-2). Separating the final state into hard and soft components and
recognizing that the thrust axis is determined almost entirely by the hard component, the
transverse thrust and thrust minor can be written approximately as:

TH AnT UE+ 1cs (2-7)

q HARDIsinoHARD + UE sin UEI
Ti n (2-8)
TMin HARD I UE + 5E HARD E (28)

where (HARD and (UE represent the angle between the thrust axis and the hard and soft
components respectively. The contribution of the underlying event is expected to be on
average uniform over the transverse plane; therefore,

(|cosUE) = sin UE= (2-9)

Taking a weighted difference between the mean values of the thrust and thrust minor we
arrive at an expression whose numerator is independent of the underlying event.

a (TMin) 3 (r)


Where a (1 (| cos QUE ) and 3 (| sin UE|). The only trace of the underlying
event in this expression is in the denominator, where its contribution is overshadowed by
that of the hard scattering. Nevertheless, an additional factor, 7MC, may be computed

Hard -UE I ES : ql| < 3.5 qjetl|< 0.7
(1 pT )
Haed I
S ard ) ---- NLO+CAESAR (CTEQ6M)
| Tune A Hadron x 7yM
0.04 ---- Data (Unfolded) x y7


S-11 -< (Icos el)
P -- Isin 0l)
100 150 200 250 300
EJet 1

Figure 5-3. Plot of the weighted difference of the mean values of Thrust and Thrust Minor
as a function of the leading jet energy for CAESAR+NLO, PYTHIA Tune A
at the Hadron level and Data unfolded to the particle level.

200 250

EJet 1

100 150 200 250 300
EJet 1

Figure 4-16. Contribution of isolated instrumental effects on the transverse thrust and
thrust minor.

ES : h|<|S 3.5 jjet|< 0.7
-u-- Tune A Hadron
-o |B-Field
S ----- Granularity
i ii -- Resolution

i I


4-7 Monte Carlo track multiplicity in jets before and after track quality cuts. Particles
are counted within a cone of opening angle 0, = 0.5 radians. The label "CDFi'n
refers to MC after full detector simulation. . . . . . 85

4-8 Inclusive momentum distribution of Monte Carlo tracks in jets before and after
track quality cuts. Particles are counted within a cone of opening angle 0c = 0.5
radians . . . . . . . . . . 85

4-9 Distribution in Q of MC charged hadrons relative to the transverse thrust axis,
compared to the same distributions in MC tracks after full detector simulation. 86

4-10 Inclusive momentum distributions of Pythia Tune A tracks for the entire central
region < 1.1 . . . . . . ... . 86

4-11 Difference between Data and Monte Carlo in the distribution of tracks as a function
of the angle between the 2D track pr and the transverse thrust axis nT over the
entire central region < 1.1 . . . . . . . 87

4-12 Relative difference between Data and Monte Carlo in the distribution of tracks
as a function of the angle between the 2D track pr and the transverse thrust
axis nT over the entire central region Ty| < 1.1 .... . . 88

4-13 Relative difference between Data and Monte Carlo in the distribution of towers
as a function of the angle between the 2D tower pr and the transverse thrust
axis nT over the central region < 1.1 . . . . . 88

4-14 The effect of CDF detector simulation on the transverse Thrust (top) and Thrust
M inor (bottom ) . . . . . . . . 89

4-15 The effect of CDF detector simulation on the final observable constructed, the
weighted difference in the mean values of the transverse thrust and thrust minor. 90

4-16 Contribution of isolated instrumental effects on the transverse thrust and thrust
m inor . . . . . . . .... . . 92

4-17 Contribution of isolated instrumental effects on the weighted difference of the
mean values of the transverse thrust and thrust minor. . . ...... 93

4-18 Effect of tower Er threshold on the mean values of the the transverse thrust
and thrust minor plotted against the leading jet energy. . . ..... 94

4-19 Effect of the tower ET threshold on the weighted difference in the mean values
of the transverse thrust and thrust minor. . . . . . 95

5-1 Distributions of the transverse thrust and thrust minor for leading jet energies
100, 150, 200, and 300 GeV. Comparison is made between theoretical predictions
at (NLO+NLL) accuracy, PYTHIA Tune A at the hadron level as well as after
detector simulation, and Data. . . . . . . . 97

- 0.15




ES : | 3.5 j-< 0.7

-u- Tune A Hadron

- ------ ----------------------- ------------------ *- Tune A + C DFSim --
-....... ...... .....................|.. .......................... --....... ..... .

100 150 200 250 300
EJet 1


200 250

EJet 1

Figure 4-14. The effect of CDF detector simulation on the transverse Thrust (top) and
Thrust Minor (bottom).

between these two variables, Fig. 4-15, reveals that on the scale of this final observable a

noticeable systematic effect is present due to the simulation. Possible sources for this shift

have been identified and investigated as follows:

C '!i ged particles traveling through a magnetic field experience the Lorentz force

law which ultimately bends the trajectory of the particle from its straight line path.

As a result, the energy flow of an event at the level of the calorimeter may appear

ES : Iil<3.5 \ietl <0.7

|-u- Tune A Hadron

S-*- Tune A + CDFSim

----i i l i i --- -- -I-- -- ------------------ --------------

Figure 1-1. Diagram of gluon emission off a quark with momentum A.

be ejected from the participating hadrons with large moment transverse to the beam

direction. In these cases, the primary interaction occurs very rapidly compared to the

internal time-scale of the hadron wavefunction and the methods of perturbative QCD

become applicable. This phase of the hadronic collision is referred to as the hard-scattering

stage and is theoretically calculable at some fixed-order in the strong coupling.

The ejected partons then begin radiating soft gluons which can in turn split into

quark anti-quark pairs or emit further gluons. Consider the probability of emitting a gluon

with momentum k and transverse momentum k1 relative to a hard scattered quark with

momentum p (see Figure 1-1):

dwjq-*q = 2CF a [1 + (1 )2] (1-2)
47 p k k{


CF = (N; 1)/2Nc = 4/3. (1-3)

Nc denotes the number of colors and the coupling runs with the gluon transverse

momentum. Two results follow directly from this equation: (1) the probability of emitting

a gluon at large angles relative to the initial parton is low:


Figure 2-3. A cartoon description of the stages of an event simulation.



Figure page

1-1 Diagram of gluon emission off a quark with momentum . . ..... 23

2-1 A three-jet event approaching the two-jet limit. . . . . 28

2-2 Colinear branching of partons within a three-jet event. . . . 30

2-3 A cartoon description of the stages of an event simulation.. . . 36

2-4 Ratio of the mean values of the YZpr of particles between Pythia with and without
multiple parton interactions as a function of the leading jet energy. .. . 40

2-5 Distributions of the transverse thrust and thrust minor for leading jet energies
100, 150, 200, and 300 GeV. Comparison is made between theoretical predictions
at (NLO+NLL) accuracy and PYTHIA without an UE. . . ..... 42

2-6 Evolution of the mean values of the transverse thrust and thrust minor as a function
of the leading jet energy. Comparison is made between theoretical predictions
at (NLO+NLL) accuracy and PYTHIA without an UE. . . ... 43

2-7 The weighted difference of the mean values of thrust and thrust minor as a function
of the leading jet energy. Comparison is made between theoretical predictions
at (NLO+NLL) accuracy and PYTHIA without an UE. . . ..... 44

2-8 Distributions of the transverse thrust and thrust minor for leading jet energies
100, 150, 200, and 300 GeV. Comparison is made between theoretical predictions
at (NLO+NLL) accuracy and PYTHIA with and without an UE. . . 45

2-9 Evolution of the mean values of the transverse thrust and thrust minor as a function
of the leading jet energy. Comparison is made between theoretical predictions
at (NLO+NLL) accuracy and PYTHIA with and without an UE. . . 46

2-10 The weighted difference of the mean values of transverse thrust and thrust minor
as a function of the leading jet energy. Comparison is made between theoretical
predictions at (NLO+NLL) accuracy and PYTHIA with and without an UE. 47

3-1 A schematic picture of the accelerator chain at Fermilab. . . ..... 49

3-2 Proton and antiproton beam structure at the Tevatron. Each beam is divided
into three ii ,i -" which are separated by an abort gap. . . . 52

3-3 Total integrated luminosity delivered by the Tevatron since the beginning of
Run II. Also shown, is the live luminosity, labeled "To tape", which excludes
integrated luminosity during detector dead-times. . . . ... 53

3-4 Diagram of the CDF II detector with a quadrant removed and a zoomed-in view
of the inner subdetectors . . . . . . . 55

The Strong Coupling

In the absence of quark masses the only free parameter of QCD is its coupling

constant, as. The parameter is a measure of the strength of the strong interactions and

is analogous to the fine structure constant a of QED. Theoretical calculations of cross

sections and decay rates are typically calculated as a perturbative expansion in powers of

the coupling constant. However, being renormalizable theories, the term coupling constant

turns out to be a hideous misnomer. In reality, these parameters vary with the energy

scale of the interaction.

In the case of QED, the value of the coupling, a, decreases as the energy of the

interaction decreases. This has a rather intuitive physical interpretation. At small

momentum scales, a photon will resolve a larger volume around a bare electric charge;

virtual e+e- pairs from the QED vacuum act as dipoles, effectively -, i.. Inig" the bare

charge and making it appear less than its true value. At larger momentum scales (i.e., at

smaller distances) we begin to penetrate the dielectric properties of the QED vacuum and

see the bare charge. In field theories this is known as the vacuum polarization.

In Quantum C'! ini. dynamics, the vacuum polarization has the exact opposite effect.

While a similar quark anti-quark screening exists in the QCD vacuum, it is superceded

by an anti-screening effect that is a direct consequence of the gluon self interaction. The

result is that the strength of a8 decreases logarithmically at high energies:

o In(Q2/A CD(-)

where 3o = 11 2nf/3, with nf being the number of quark flavors, and AQCD is

the energy scale at which the strong coupling diverges. This phenomena is known as

1i.ii/ 'I./'I.:. freedom and was first discovered by Wilczek, Politzer, and Gross in 1973

[9, 10]. Conversely, at low energies the strength of the coupling appears to grow without

100 150

200 250

100 150 200 250 300
EJet 1

Figure 4-18. Effect of tower ET threshold on the mean values of the the transverse thrust
and thrust minor plotted against the leading jet energy.

ES: I|<3.5 |jet|< .7

S>pT> 100 MeV
I ---- T > 200 MeV
....................P.........................T > 300 M eV

.. ............... .I. ---------------- -

------ ---- --..--.. --. .-

EJet 1

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

S 1.96 TEV


Lester A. Pinera

August 2008

C('!I i: Andrey Korytov
Major: Physics

This dissertation presents a measurement of event shape variables in pp collisions at

a center of momentum energy of 1.96 TeV. The observables studied are the transverse

thrust and thrust minor, both defined over final state moment perpendicular to the

beam direction. These variables are calculated using unclustered calorimeter energy

measured using the CDF-II detector at the Fermi National Accelerator Lab. In addition

to differential distributions, we present the evolution of event shape mean values as a

function of the leading jet ET The data is compared to dedicated theoretical predictions

(NLO+NLL) and subsequently to PYTHIA Monte Carlo with and without multiple

parton interactions. In the presence of an underlying event the observables are found to

significantly depart from the predictions of perturbative QCD.

Ultimately, our results show that the presence of an underlying event drastically

changes not only the means but also the shapes of the distributions in both observables.

Furthermore, our MC studies -i--.-, -I that the additional particles from the underlying

event dampen the effects of hadronization on the distributions. In the end, data, MC,

and theorists' predictions all coincided in the final observable C((r), (TMi,)), which was

constructed to be insensitive to the underlying event.

y (m) !
CAL 3d0


1. 0 .5 1.0 1.5 20 2.5 3.0 x(m)0


Figure 3-5. Schematic r-z view of the CDF tracking system and surrounding subdetectors.

of 2.5 an 10.6 cm, and the Intermediate Silicon L rs (ISL) consisting of one 1 -, r at

22 cm in the central region and two I1,. rs at 20 and 28 cm in the forward regions. The

silicon 1v. rs are then surrounded by the Central Outer Tracker (COT), a 3.1 m long

drift chamber extending from a radius of 40 to 137 cm. Figure 3-5 is a schematic of one

quadrant of the CDF tracking system in the r z plane. The total system is referred to as

the i ii. I ii. tracking system. In addition to accurately determining the moment of

charged particles, the tracking system also provides a means of determining the locations

of decay and interaction vertices.

Central Outer Tracker

The COT is the anchor of the CDF II tracking system. It provides precise measurements

of the transverse momentum of charged particles in the central region |T1 < 1.0. The

detector is a cylindrical drift chamber whose volume begins at 40 cm from the beam pipe

and extends radially to 138 cm. The chamber spans 310 cm in length along the z direction

and is immersed in a 1.4 T magnetic field. Furthermore, the detector is filled with a

L -v. r 00 is a single-sided radiation hard silicon microstrip detector. It is mounted

directly on the beam pipe, at the inner radius of 1.15 cm and an outer radius of 2.1 cm,

such that it is as close as possible to the interaction point. LOO's primary contribution to

tracking is an increased resolution of the track impact parameter. The impact parameter

do is defined as the shortest distance in the r 0 plane between the interaction point and

the trajectory of the particle obtained by the tracking algorithm fit. Tracks fitted with

a LOO hit need only be extrapolated a minimal distance from their last known position

toward the primary vertex. LOO alone has 13,824 read-out channels.

The SVX is composed of five 1lv.. rS of double-sided silicon microstrip detectors and

provides radial coverage from 2.5 to 10.7 cm. The SVX is built in three cylindrical barrels

each 29 cm long that are placed end to end along the length of the beam pipe. One side

of each microstrip detector provides tracking information in the r 0 plane, while the

other side provides tracking information in the r z plane, therefore the SVX is capable

of reconstructing three-dimensional tracks. Three of the five SVX lv.- r- provide 900 stereo

information, two SVX 1lv. r- provide 1.20 small-angle stereo information. The total

number of channels in the system is approximately 400,000. The SVZ bulkhead design is

shown in Fig. 3-7.

The primary goal of the SVX is to detect secondary vertices from heavy flavour

decays. The secondary goal is to maximize tracking performance by combining the COT

and SVX hit information. Therefore alignment of the SVX detector is critical for track

reconstruction. The process of combined COT and SVX track reconstruction [33] starts

in the COT. After a COT-only track is reconstructed, it is extrapolated through the

SVX. Because the track parameters are measured with uncertainties, the track is more

like a tube of some radius, determined by the errors on track parameters. At each SVX

1~.-.r, hits that are within a certain radius are appended to the track and the re-fitting is

performed to obtain the new set of parameters for the track. In this process there may be

unstable. PYTHIA simulates the decays of these particles based on standard branching

ratios supplied by the Particle Data Group [5].

2.4.4 CDF Simulation

After hadronization, hundreds of final state particles are passed to the CDF

simulation (CDFSim) package. It contains a detailed description of the CDF detector

geometry including the active detector elements as well as passive material, such as

read-out electronics, cables, support structures, etc. The overall framework for the

simulation is done using the GEANT package [29], with some modifications directed

at making the simulation work faster. Once the detector is built in the language of

GEANT, almost any kind of particle can be tracked through it with all appropriate

physics processes taking place to mimic the physical detector response. Some interactions

are handled with specific parametrized models, such as GFLASH shower simulation

package [30], tuned to single particle response and shower shape based on the test beam

and collision data. The i data (digitized physical detector response) after detector

simulation is fed to the algorithm that implements the actual trigger logic to decide if the

event should be accepted. The events passing the trigger simulation go through production

stage, in which the collection of physics objects (tracks, jets, muons, etc.) are created from

the raw data.

2.5 Treatment of Underlying Event

At the time of this writing theorists have yet to include in their calculations of event

shapes a model of the underlying event. As a result, a direct comparison of event shape

distributions between data and the predictions of CAESAR is not possible. However, we

believe that a quantity can be constructed from the average values of the observables that

is independent of the UE. The evolution of this quantity with respect to the leading jet

energy should then allow for meaningful comparison between theoretical predictions and

Leading Jet ET > 100 GeV

10 -

lO-3 IlI < 1.1 L
-4 -2 0 2 4 6
X = In( PT )

Figure 4-2. The transverse momentum distribution of calorimeter towers in the central
region T11 < 1.1, normalized to the number of events in each sample. The label
CDFSim refers to Pythia Tune A MC after full detector simulation.



X = #nT

Figure 4-3. Distribution of towers over the central region I TI < 1.1 as a function of the
angle between the 2D tower p' and the transverse thrust axis n-

3.2.6 Good Run Requirements

CDF data-taking is divided into variable periods of time referred to as runs. In

contrast to the labels "Run I" or "Run II" which denote many years of accelerator and

detector performance, data runs are every-d units of data-taking during which the

detector is known to function in some stable configuration. A single run typically spans

several hours in duration.

The data passing the L3 trigger is segmented into ten streams and written to tape

in real time. However, not all of these events are suitable for physics analysis. For this

reason, sood run" requirements are established to determine periods of data taking when

all detector components are operating properly. If one (or more) detector components is

experiencing problems, a "bad" flag is set for that particular subdetector. The run can

still be used in physics analyses, but only if the analysis does not require information from

the problematic component. The CDF shift crew determines whether a component is

fl ,.-.-. d after reviewing standard plots from that subdetector.

3.3 Jet Reconstruction

Theoretically, a "jet" refers to the collection of partons associated with a hard

scattered quark or gluon at the end of it's perturbative QCD shower. As previously

mentioned, though, the particles observed in experiment are not quarks or gluons, but

rather hadrons; so, at the level of experiment, a jet is a collimated spray of particles

believed to be the signature of a hard scattered parton. However, making quantitative

comparisons between theory and experiment requires going beyond a qualitative

description and defining a precise algorithm for identifying jets.

o 1 methods can be used to define what is meant by a jet and no one method

is best. Jet algorithms typically fall into two categories: a cone based algorithm which

measures the energy deposition in an angular region, or a clustering algorithm based

on combining particle moment. Currently there are three jet clustering algorithms


One of the principle tenets of quantum mechanics is that nature is probabilistic. In

experiment, this means that for a particular type of collision one will encounter all the

allowed interactions within the standard model with relative frequencies. As a result,

studying a particular feature of the standard model first requires isolating events of

interest. For event shape studies, we are specifically interested in interactions mediated

by the strong force-this means events containing jets. Fortunately, at a hadron collider

the overwhelming ii, ii ily of events are born from QCD interactions, and therefore, our

studies benefit from the large data samples available.

This chapter presents a discussion of the measurement of event shapes using the CDF

II detector. The measurement is performed using the detector's calorimeter subsystem,

whose coverage in pseudorapidity makes comparison to theoretically calculable "global"

observables feasible. Additional studies are performed in a restricted central region

(|T| < 1.1) where track information is available. The chapter includes an explanation of

the event selection, a discussion of backgrounds, and at least a qualitative gauge of the

systematic uncertainties in the final observable constructed (the weighted difference of the

mean values of the thrust and thrust minor).

4.1 Data Samples

We report a measurement of event shapes in pp collisions at V/s 1.96 TeV. Events

were produced at the Tevatron collider and recorded by the CDF Run II detector. Results

are presented for leading jet energies of 100, 150, 200, and 300 GeV. The data for the

100, 150, and 200 GeV samples were collected using single jet triggers with respective ET

thresholds of 50, 70, and 100 GeV during the period February 2002 to August 2004. The

events selected for the 300 GeV sample also come from the 100 GeV single jet tri --.-r,

but during a later data taking period corresponding to December 2004 to November

EJet 1

1 -, 1 ES: ql< 3.5 ITj < 0.7

0.3 -u--- Tune A Hadron
-*-- Tune A + CDFSim
--v-- Data

0.2 -

0 .1 .... ......... ..... .................... ......................... ............................ ...........

0. L I . I L. I .. ..I.

100 150 200 250 300
EJet 1

Figure 5-2. Evolution of the mean values of the transverse thrust and thrust minor as a
function of the leading jet energy.Comparison is made between theoretical
predictions at (NLO+NLL) accuracy, PYTHIA Tune A at the hadron level as
well as after detector simulation, and Data.

3-5 Schematic r-z view of the CDF tracking system and surrounding subdetectors. 58

3-6 Cross-sectional views of COT superlayers and individual wires in three COT
cells. The angle between wire-plane of the central cell and the radial direction
is 35 . . . . . . . . . . 59

3-7 Schematic of the SVX bulkhead design. . . . . . 62

3-8 Schematic picture of one quadrant of the CDF calorimeter. . . . 64

3-9 The Cerenkov Luminosity Counter at CDF. The detector modules are located
in the "3-degree l ..!. of the east and west modules. . . . 67

3-10 Functional block diagram of the CDF data flow. ....... . . 69

3-11 The ratio of the transverse moment of "probe" and rli .-.- 2" jets using the
20 GeV jet sample. The curves are obtained using two different methods: the
missing ET projection fraction (red) and the dijet balance technique (black).
The "probe" trigger jet is required to be in the region 0.2 < T11 < 0.6, while
the probe jet is required to be outside that region. . . . . 74

3-12 Average transverse energy deposited in a random cone of R = 0.7 in min-bias
events as a function of the number of primary vertices in the event. .. . 75

4-1 The distribution of calorimeter towers in TI and Q over the full rapidity range
of the detector. The distributions are normalized to the number of events in
each sample. The label CDFSim refers to Pythia Tune A MC after full detector
sim ulation . . . . . . . . . 79

4-2 The transverse momentum distribution of calorimeter towers in the central region
T11 < 1.1, normalized to the number of events in each sample. The label CDFSim
refers to Pythia Tune A MC after full detector simulation. . . . 80

4-3 Distribution of towers over the central region T11 < 1.1 as a function of the
angle between the 2D tower p' and the transverse thrust axis Wn . ... 80

4-4 Distributions of Az for different track reconstruction algorithms. The data is fit
to a sum of two "Gaussians" to determine the width, UA,, of the distributions,
and is later used in track selection. . . . . . . 81

4-5 Illustration of the distance, Rc,,,, from the beam line to the point where the
conversion occurred. Here, do is the impact parameter. . . . 83

4-6 Distribution of the impact parameter do, for different track reconstruction algorithms.
The data is fit to the sum of two "Gaussians" to determine the width, ad0, and
is later used in the track selection. . . . . . . 83

T1= I.O --------

Figure 3-8. Schematic picture of one quadrant of the CDF calorimeter.

|r| Range S 6_ _
0.0 -1.1 150 ~ 0.1
1.1- 1.8 7.50 ~0.1
1.8 -2.1 7.50 ~0.16
2.1 3.64 15 0.2 1 0.6
Table 3-3. Calorimeter segmentation of the CDF II detector.

noting that both types of showers, but particularly the hadronic variety, are subject to

statistical fluctuations that ultimately impair the energy resolution of the detectors.

At CDF, the calorimeters are segmented into towers which are arranged in a

projective geometry pointing towards the primary interaction point (Fig. 3-8). The

entire calorimeter is mechanically subdivided into three regions: central, wall and plug.

The components are denoted central electromagnetic (CEM), central hadronic (CHA), wall

hadronic (WHA), plug electromagnetic (PEM), and plug hadronic (PHA). The central

calorimeter covers the pseudorapidity region |I T < 1.1, while the plug extends coverage out

to IrT = 3.6. The WHA system bridges the gap between the central and plug hadronic

components. The calorimeter segmentation is summarized in Table 3-3.

( I Hap d + UE Parton Levrel |et| <0.7
c a rd) - G lo b a lI
S--- -- Global
S-- -- Central (|| <- 3.5)

I ---- ----- I-

100 150 200 250 300
EJet 1

Figure 2-4. Ratio of the mean values of the Z pr of particles between Pythia with and
without multiple parton interactions as a function of the leading jet energy.

based on Monte Carlo generated with and without MPI to produce an expression entirely

independent of the UE.

%MC HARD I(2- 11)

then we can define a new quantity:

C((r), (TMin)) 7MC (a TMn) /3 ()) (2-12)

The factor 7MC is plotted in Figure 2-4 as a function of the leading jet energy. Finally,

it is the evolution of this quantity as a function of leading jet ET that will allow for a

meaningful comparison between Data and theorists' predictions.


Figure 2-5 shows a comparison of the distributions of Transverse Thrust and Thrust

Minor between dedicated theoretical prediction, labeled "CAESAR+NLO", and PYTHIA

at the parton level and after hadronization. These plots reveal that apart from a shift

away from the 2-jet limit over nearly the entire range of the variables, the Monte Carlo

3.2.1 The CDF Coordinate System . . . . . 56
3.2.2 Tracking and Vertexing Systems . . . . . 57
3.2.3 Calorim etry . . . . . . . 62
3.2.4 Cerenkov Luminosity Counters . . . . . 65
3.2.5 Til-.-.- i System and Data Acquisition .... . . 68
3.2.6 Good Run Requirements . . . . . . 71
3.3 Jet Reconstruction . . . . . . . 71
3.3.1 Jet C -I. g . . . . . . . 72
3.3.2 Jet Corrections . . . . . . ... 73

4 ANALYSIS OF THE DATA . . . . . . . 77

4.1 Data Sam ples . . . . . . . . 77
4.2 Event Selection . . . . . . . . 78
4.3 Calorimeter Towers . . . . . . . 78
4.4 Tracks: I < 1.1 . . . . . . . . 79
4.5 Detector Effects . . . . . . . . 87
4.6 Systematic Uncertainty . . . . . . . 91
4.6.1 Jet Energy Scale . . . . . . ... 93
4.6.2 Containment in the Detector . . . . ... 93
4.6.3 Accelerator Induced Backgrounds . . . . 95

5 R E SU LT S . . . . . . . . . 96

6 CONCLUSIONS . . . . . . . . 100

REFERENCES . . . . . .. .. .. .. .. .. 102

BIOGRAPHICAL SKETCH . . . . . . . . 104

luminosities the probability of having an empty crossing is small, making it difficult to

maintain good precision.

3.2.5 Trigger System and Data Acquisition

In Run II, Tevatron beam bunches are separated by 396 ns, which corresponds to

a bunch crossing rate of 2.5 MHz. The i_ i, in l y of the data used in this analysis was

taken early in Run II when the instantaneous luminosity was around 40 x 1030 cm -2s-1

corresponding to about one interaction per bunch crossing. However, in later runs, the

CDF detector experienced luminosities up to 200 x 10o0cmr-2s-1 which corresponds to

about 6 interactions per bunch crossing. With the typical size of an event being about 250

kilobytes (KB), data would have to be stored at a rate well over 400 GB/s. At present, the

maximum storage rate is about 30 MB/s.

Fortunately, not all these events are interesting for physics analysis and most can

be discarded. The framework for selecting or rejecting specific types of events as they

are read from the detector, is known as the trigger system. The CDF data acquisition

(DAQ) system and triggers are designed to efficiently identify interesting events and record

data from relevant channels of the detector. Such manipulations are said to occur at the

"online" level in contrast to offlinee" analysis of data which has already been stored.

A successful DAQ system must clearly minimize the fraction of time during which

new collisions are occurring but the detector is unable to record them. The fact that

events can only be written to tape at a rate of ~75 Hz, necessitates a buffered system;

that is, while the properties of one event are being surveyed, the information from all

subsequent events must be temporarily stored until each can be considered in turn. The

CDF tri -.-. r uses a three tier system in which events are examined in increasing detail as

they pass through the stages. An event is passed to the next trigger level only as long as it

is accepted by the preceding one. The data flow of the CDF DAQ is shown schematically

in Fig. 3-10.

Table 3-1. Summary of current Tevatron performance characteristics.
center-of-mass energy 1.96 TeV
bunch crossing separation 396 ns
number of protons per bunch 240 x 109
number of antiprotons per bunch 25 x 109
peak luminosity 290 x 1030 cm-2s-1

time. This is generally due to the direct pp annihilation as well as long-range interaction

between the beams which leads to larger emittances and lost particles. A Tevatron store

is typically discarded when the luminosity has decreased by a factor of ~ 5, so long as

there are sufficient antiprotons collected to begin anew. Summary of current Tevatron

performance characteristics is given in Table 3-1. The design goal for the Tevatron is to

collect 8 fb-1 by the end of 2009.

3.2 The CDF II Detector

The data for this analysis was collected using the CDF-II detector [32], one of the

two principle detectors located on the Tevatron ring. The generic nature of CDF's full

name, "Collider Detector at Fermilab" reflects the fact that it was the first detector built

at the Tevatron for the pp era. The CDF-II name refers to the present incarnation of the

detector, which underwent ii i" upgrades in many of it's components to coincide with

the Tevatron's increased collision rate and center of mass energy during Run II.

The detector is capable of precision measurements of the energy, momentum, and

position of particles produced in pp collisions. Rather than being designed for one

specific class of high-energy physics measurement, CDF is designed to be a versatile

"multi-purp,-, detector capable of studying many fundamental processes. The detector is

axially symmetric about the beamline covering almost all solid angles except those closest

in angle to the beam. It is about 10 meters high, extends about 27 meters from end to

end, and weighs over 5000 tons. A diagram of the CDF-II detector is shown in Fig. 3-4.

S.Hard + UE ES : hI| < 3.5 |jetl < 0.7
KXpT )
i. IYMC = Hard PT > 100 MeV x ymc
A |PT > 200 MeV x yMc
I -- 2 0 .0 4 ... ....................... .. _- P > 3 0 0 M e V x 7 _
S 0 .0 4 --------------------

0 .0 2 ........................................................ ........................... ............................ ...........

ca|l -I (Icos9l
P Isin el)
100 150 200 250 300
EJet 1

Figure 4-19. Effect of the tower ET threshold on the weighted difference in the mean
values of the transverse thrust and thrust minor.

the detector. As a result, the further a collision occurs from the nominal interaction point

the greater the possibility that particles fall beyond the detector's coverage. To evaluate

the uncertainty due to this effect we require a tighter cut on the z position of the primary

vertex. The difference in the observable between the default and the tight cut is then

assigned as a systematic uncertainty.

4.6.3 Accelerator Induced Backgrounds

In the event selection we specifically require events with a single vertex; however, it

is possible that two vertices that lie very close to each other can be reconstructed as a

single vertex. This "pile-up" effect is especially likely at high values of the instantaneous

luminosity. To evaluate the uncertainty due to this effect we separate events in each

data sample into high and low luminosity subsets. The final observable is then compared

between subsets and the difference is taken as a measure of the systematic uncertainty.

Leading Jet ET> 100 GeV
Pythia Parton (CTEQ5L)
Pythia Hadron

10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35


I| rtl< 0.7 Leading Jet ET> 150 GeV
Pythia Parton (CTEQ5L)

Pythia Hadron


101 0

10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35


Ijet I 0.7
ES : Global

Leading Jet ET > 300 GeV
Pythia Parton (CTEQ5L)
Pythia Hadron

S Ijet I 0.7
ES : Global

Leading Jet ET> 100 GeV
Pythia Parton (CTEQ5L)
Pythia Hadron

0.1 0.2 0.3 0.4 0.5 0.6 0.7
X = TMin

IletW < 0.7
ES : Global

0.1 0.2

Leading Jet ET > 150 GeV
Pythia Parton (CTEQ5L)
Pythia Hadron

0.3 0.4 0.5 0.6 0.7
X = TMin

IrtlI < 0.7 Leading Jet ET > 200 GeV
Pythia Parton (CTEQ5L)
Pythia Hadron

0.1 0.2 0.3 0.4 0.5 0.6 0.7
X = TMin

I I t< 0.7
ES : Global

0.1 0.2 0.3


Leading Jet ET > 300 GeV
Pythia Parton (CTEQ5L)
Pythia Hadron

0.2 0.4 0.6
X = TMin

Figure 2-5.

Distributions of the transverse thrust and thrust minor for leading jet energies

100, 150, 200, and 300 GeV. Comparison is made between theoretical

predictions at (NLO+NLL) accuracy and PYTHIA without an UE.

| jet 0.7
ES : Global


In this work we have presented an analysis of event shapes in pp collisions at /s

1.96 TeV. The measurement was performed using the CDF II detector at Fermilab's

Tevatron accelerator complex. The data were divided into 4 statistically independent

samples based on the transverse energy of the leading jet in the event-100, 150, 200, 300

GeV. The two observables studied were the transverse thrust and thrust minor and were

constructed from unclustered calorimeter energy over the entire pseudorapidity range of

the detector (|11 < 3.5).

The large data sets made it possible to study the distributions in both observables

over all 4 jet ET samples. Furthermore, the mean values of the event shapes as a function

of the leading jet energy were also presented. This quantity is expected to have a strong

dependence on the QCD coupling, as. In addition, we constructed an auxiliary observable,

C((r), (TMi})), from the weighted difference in the mean values of the transverse thrust

and thrust minor, and plotted its evolution with the leading jet energy. This quantity is

expected to be independent of the underlying event, thereby allowing direct comparison

between theory and data.

Theorists' predictions for the transverse thrust and thrust minor were provided at

NLL+NLO accuracy. However, these predictions do not incorporate hadronization effects

or an underlying event-both of which are expected to alter the energy flow in the final

state. As a result, comparison to data for these observables was performed in three stages.

First, theorists' predictions were plotted alongside the results of PYTHIA 6.216 without

multiple parton interactions. Next these results were compared to PYTHIA Tune A

which includes a model of the underlying event. And finally, all of these predictions were

compared to data. Along the way, the effects of hadronization on the distributions were

studied using the Monte Carlo simulations.

SHaird +UE ES : | < 3.5 Iet 0.7
c.. IH ard )Tune A Hadron x MC

a 0.04 ................... ........... .......... --....... Tune A + CDFSim x yM ....

0 .0 2 .................................................................................... ........................................

a- 1 ( Icos el
SIsin el)
100 150 200 250 300
EJet 1

Figure 4-15. The effect of CDF detector simulation on the final observable constructed,
the weighted difference in the mean values of the transverse thrust and thrust

broader than in the absence of a magnetic field. To estimate the magnitude of this
effect on the final observable, MC particles at the hadron level were propogated to
the first active 1-v. r of the calorimeter under the influence of a 1.41 Tesla B-field.
The direction of the particle at this point is taken to be the location of the particle
relative to the z position of the primary interaction point.
The processes leading to electromagnetic and hadronic showers in a calorimeter are
largely statistical in nature and therefore the energy resolution of the detector is
subject to statistical fluctuations. To estimate the effect of the resolution, if any, on
our final observable we smear (according to a gaussian distribution) the energy of the
final MC particles by la. For photons and electrons JEM/ET 13.5'. / ET while
for all other particles uHAD/ET = 7". / T
In the central region each calorimeter tower is Aq x A 0.1 x 15 in size while
in the plug region the calorimeter towers are 0.2 0.6 x 15 in spatial dimensions.
When a particle above threshold is detected, the location returned by the system is
the center of the tower whose PMT read-out the energy deposition and not the exact
location of the shower within the tower. As a result, there is a mismeasurement
associated with the granularity of the calorimeter. In an effort to understand this


Quantum Field Theory. A theoretical framework for constructing quantized
models of field-like systems, or equivalently, many body systems. In this
dissertation, the term specifically refers to systems combining the principles
of special relativity and quantum mechanics.

pertubative Quantum Ch'!i ii.ndynamics. Refers to calculations involving the
strong force at large energies (small distances) when the coupling a8 is small.

Multiple Parton Interactions. In hadron-hadron collisions refers to the
possibility of more than one parton being involved in a scattering.

Next-to-Leading Order. Refers to the level of accuracy of a calculation
within fixed order perturbation theory.

Next-to-Leading Log. Refers to the level of accuracy of a calculation that
involves a resummation of the perturbative expansion.







The priestess presiding over the Oracle of Apollo at Delphi in ancient
Greece. Also a computer program based on stochastic methods which
simulates high energy particle collisions, the production of hadrons, and
the decays of short lived particles.

The process by which free quarks become colour neutral states
consisting of 2 or 3 quarks hadronss). This process occurs at low
energies and its details are not well understood.

Anomalous events observed in cosmic ray detectors characterized by an
excess in the ratio of charged to neutral particles.

Disoriented C'!ii I! Condensate refers to the notion that a region of
pseudo-vacuum might occasionally form in high energy hadronic collisions
where the chiral order parameter is misaligned from its vacuum orientation
in isospin space. Such an event would manifest itself as an .i-vi iii 1, ry in the
charge to neutral ratio of particles.

Collider Detector at Fermilab. A multipurpose detector located at one of
two collision points in the Tevatron accelerator complex. Also, refers to the
collaboration of scientists that operate and maintain the detector.

Proton-antiproton accelerator located at the Fermi National Accelerator Lab
in Batavia, IL. At the time of this writing, it is the world's highest energy
collider with Vs = 1.96 TeV.






numbers which exist exclusively as bound states. Below is a brief overview of the latest

state-of-the-art in particle physics, the Standard Model.

1.1 The Standard Model of Particle Physics

The interactions of matter are described by four forces: the gravitational, electromagnetic,

weak, and the strong force. While gravity pl ,- an important role on macroscopic scales,

at the subatomic level it is sufficiently weak that it can be neglected. The remaining three

forces account respectively for familiar phenomena like the interactions of particles with

electric charge, the decays of long-lived heavy particles (~ 10.7 10-13s), and in a residual

way, the binding of protons and neutrons in atomic nuclei.

Classically, interactions between matter are understood in the context of waves

which are continuously emitted and absorbed. This is an adequate description at large

distances, but at smaller scales the quantum nature of the interaction must be taken

into account. The Standard Model is an example of a quantum field theory [3] which

is to that it is a marriage of quantum mechanics and special relativity. In this view,

interactions are described by the discrete exchange of bosons (i.e., particles of integer

spin). The electromagnetic force is mediated by massless photons (7) whose effects are

observed from subatomic to macroscopic distances. The weak force is carried by three

bosons (W' and Z) which are massive, a fact which ultimately limits the range of

its influence to subatomic distances. Furthermore, the W' carries electric charge and

therefore also couples to the electromagnetic interactions 1 The strong force is mediated

by eight massless bosons known as gluons (g) whose influence is also limited to subatomic

1 Todiv the Electromagnetic and Weak force appear to be separate forces, but earlier in
the history of the universe they were in fact part of a single "Electro-Weak" force.

Hai Hard+UE. ES : |l < 3.5 Ijetl 0.7
SMC H.- ard Tune A Hadron x Y
0.04T ( p7 B-Field x 7MC
S. |-- -- Granularity x MC
0 I------- Resolution x 7MC

0.02 ------- ------- -............................----------- --- ............................--------- ---- --- ....................- -- --- -........ .............................--...........--

a--=1 < Icos el
SI Isin el)
100 150 200 250 300
EJet 1

Figure 4-17. Contribution of isolated instrumental effects on the weighted difference of the
mean values of the transverse thrust and thrust minor.

C( (r), (TMin) )deviated 2
C((r), (TMin))d fault

The difference between C((r), (TMi,)) in the Data with and without this scale factor

is then taken as a measure of the systematic uncertainty

4.6.1 Jet Energy Scale

To evaluate the uncertainty due to the jet energy corrections, we use a parametrization

that under- and over-estimates the jet energy by one standard deviation in the jet energy

scale and then re-run our event selection. The difference between the default and the

deviated observable is assigned a systematic uncertainty.

4.6.2 Containment in the Detector

The primary interaction vertex is required to lie within 60 cm from the center of the

detector in order to ensure that the ii, i, ii ity of the event is contained within the detector.

The analysis of event shapes uses calorimeter information in the far forward regions of

Figure 3-9. The Cerenkov Luminosity Counter at CDF. The detector modules are located
in the "3-degree li. .! of the east and west modules.

where app is the total pp cross-section at =/s 1.96 TeV (60.7 mb); and fBc is the

frequency of bunch crossings at the Tevatron (1.7 MHz). At CDF, measuring p is done by

measuring the number of "empty" bunch crossings (i.e., bunch crossings with zero primary


The number of primary interactions per bunch crossing n follows Poisson statistics

with mean p.

P(p)w = (3-6)

The probability of having an empty bunch crossing is then Po(p) = e. Thus,

measurement of the probability of having an empty crossing is enough to determine

the average number of interactions p, and, consequently, the value of the instantaneous

luminosity. This probability is measured by dividing the number of empty crossings

(corrected for detector acceptance) by the total number of bunch crossings in a certain

time interval. For a crossing to be considered empty there should be no hits in either

the East or West CLC modules. The disadvantage of this method is that at very high


- 1.96 TEV






ACKNOW LEDGMENTS ................................. 4

LIST O F TABLES . . . . . . . . . 9

LIST OF FIGURES .. .. .. ... .. .. .. .. ... .. .. .. .. ... .. .. 10

LIST OF SYM BOLS .................................... 14

A B ST R A C T . . . . . . . . . . 15


1 INTRODUCTION .................................. 16

1.1 The Standard Model of Particle Physics ................... 17
1.2 Quantum Chromodynamics .......................... 20
1.3 Structure of Hadronic Collisions ........................ 22

2 EVENT SHAPES ............................... .. 25

2.1 Motivation and Historical Perspective ..................... 25
2.2 Event Shape Observables ............................ 27
2.2.1 Transverse Thrust . . . . . . . 27
2.2.2 Transverse Thrust Minor . . . . . . 27
2.3 Theoretical Predictions . . . . . . . 29
2.3.1 Fixed Order Calculations . . . . . . 30
2.3.2 Soft QCD Radiation & Resummation . . . . 31
2.3.3 Matching Fixed Order & Resummed Results . .... 34
2.4 Monte Carlo Generators . . . . . . . 34
2.4.1 Q CD 2 to 2 . . . . . . . 35
2.4.2 Parton Showers . . . . . . . 37
2.4.3 Hadronization . . . . . . . 37
2.4.4 CDF Simulation . . . . . . . 38
2.5 Treatment of Underlying Event . . . . . . 38
2.6 NLL+NLO vs PYTHIA . . . . . . . 40
2.7 PYTHIA Tune A . . . . . . . . 41


3.1 A ccelerator . . . . . . . . 48
3.1.1 Proton Source . . . . . . . 48
3.1.2 M ain Injector . . . . . . . 50
3.1.3 Antiproton Source . . . . . . . 50
3.1.4 Tevatron . . . . . . . . 51
3.2 The CDF II Detector . . . . . . . 54

energy is distributed isotropically. Furthermore, they have the advantage that they are

free of the arbitrariness associated with the jet definition (being of either cone or cluster

type, then defining the size of the cone, splitting/merging fractions, etc.).

The first study of an event shape traces back to 1964 and actually predates the

advent of QCD or knowledge of jets. Physicists back then proposed a "principal axis" as

a means of understanding the multitude of particles emerging from hadronic collisions

[12]. However, it was not until 1977 that theorists recognized that this i::1i:;,i:: directed

ii. ,ii, iii :i:, represented a calculable quantity in perturbative QCD. It was around

this time that event shape studies began in earnest as a simple, quantitative way of

understanding the nature of gluon bremsstrahlung. In fact, it was event shape observables

which provided the first indication that gluons were vector particles and not scalars [13].

Since then, event shapes have enjoi, .1 a long and impressive history at e+e- and

Deep Ineslatic Scattering (DIS) experiments. In these two environments they have

provided a plethora of measurements of the strong coupling [14], as well as tests of the

colour structure of QCD [15], and validation of Monte Carlo (\ C) event generators [16].

Moreover, they've improved our understanding of the dynamics of soft pQCD and have

even provided insights into hadronization through the study of power corrections [17], [18].

By comparison, event shapes at hadron colliders have, thus far, received much less

attention. Primarily because the presence of the underlying event casts some doubt as

to whether these observables can even be used to study the dynamics of pQCD, much

less non-perturbative corrections to the theory. This dissertation represents the first

attempt to measure ,jl..1/',' event shapes at a hadron collider. Irrespective of whether direct

comparison to theory is possible, the measurement of event shapes should provide an

additional means of tuning MC at hadron colliders.


The goal of high energy physics is to understand the physical universe at it's most

fundamental level. Perhaps inevitably though, what mankind has regarded as fundamental

has met with repeated revision and refinement throughout history. From the indivisible

particles postulated by the ancient Greeks, to the cataloguing of the chemical elements,

to the modern theory of quarks and leptons, scientists have forged chains of explanations

leading downward from the scale of ordinary life to the increasingly microscopic.

This evolution, however, has not been motivated by a naive reductionist sense for

fewer and fewer fundamental particles, but rather by a desire to understand the patterns

that have emerged in nature at every given epoch. The periodic table, for instance,

arose from the observation that elements with similar physical properties naturally

group together when arranged according to mass. This result along with others gave

way to the 19th century model of atomic chemistry. But the realization that matter was

composed of atoms lead to even more fundamental questions about the nature of the

atoms themselves-questions which were investigated by the first scattering experiments

of the 20th century. These tests revealed that atoms consisted of a cloud of negatively

charged electrons orbiting a dense nucleus which was itself discovered to be a composite

of positively charged protons and electrically neutral neutrons. But this model too proved

incomplete-what force overcame the electrical repulsion between protons in the nucleus?

And how were protons and neutrons related in the first place?

The picture of particle physics which has emerged is tod w known as the Standard

Model. It is a theory which describes with remarkable precision the interactions of matter

at the smallest scales. However, despite its many triumphs [1, 2], the theory is not without

its own peculiarities. It includes point like particles just like the electron, but hundreds

of times heavier as well as particles with fractional electric charge and internal quantum

stack until it reaches ~ 0(1012) particles, at which point they are sent back to the Main

Injector with 8 GeV energy. The Main Injector then accelerates the antiprotons to 150

GeV and subsequently injects them into the Tevatron.

The newer Recycler ring inhabiting the same tunnel as the Main Injector is an

extension of these facilities. It was designed to literally "recycle" the valuable antiprotons

left at the end of a collider store. The Recycler is also equipped with additional electron

(... 111 .- where a beam of "cold" dense electrons is intermingled with "hot" antiprotons

to again reduce the spread in their kinetic energy. Unlike stochastic ...1i,.- whose

effectiveness is inversely proportional to the linear particle density of the beam, electron

cooling is independent of the beam density. Although the recycling function of this ring

has yet to be implemented, it's cooling and storage attributes have contributed to an

increased luminosity since August 2005.

3.1.4 Tevatron

The Tevatron is the final component of the acceleration process, and is currently the

highest energy collider in the world 1 It accelerates counter-rotating beams of protons

and antiprotons individually to an energy of 980 GeV, resulting in collisions at /I= 1.96

TeV. It is also the worlds first superconducting synchrotron and was constructed in the

early 1980's to supersede the older Main Ring, a proton only synchrotron for fixed-target

experiments limited to ~ 500 GeV.

The Tevatron is housed in an underground tunnel of mean radius 1.0 km and is

surrounded by repeating sequences of cryogenically cooled superconducting magnets for

bending and focusing the beams. Protons and antiprotons from the Main Injector are

accelerated by RF cavities. Each beam is divided into three Ii11 1-s" consisting of 12

1 The Large Hadron Collider is a proton-proton synchrotron located at the CERN
laboratory in Geneva Switzerland. It's collisions will occur at =-s 14 TeV and is
scheduled to come online in 2008

bound, a fact that points towards (but does not prove) con,,. i,. o1 4 Furthermore in

this regime (Q~ 1 GeV) the traditional methods of QFT (i.e. perturbation theory) are

no longer valid. In particular, the process of hadronization, by which free quarks are

converted into observable hadrons, is known to be a low-energy phenomena and is not well


1.3 Structure of Hadronic Collisions

The measurement described in this thesis involves proton anti-proton collisions at the

Tevatron accelerator. As previously mentioned, protons (antiprotons) are composites of

three valence quarks (anti-quarks) and are not themselves point-like particles. However,

they are not only comprised of valence quarks, but also have a contribution from a "sea"

of gluons and quark anti-quark pairs that are constantly being created and annihilated.

Each of these quarks and gluons, collectively referred to as a partons, carries a fraction

of the total energy of the hadron. In addition to being a many body problem, specifying

the proton's internal state is further complicated by the fact that the interactions between

partons involve low momentum transfers and are not calculable within perturbative

QCD. Nevertheless, theoretical predictions can be made by specifying functions that

describe the probability of finding a certain constituent with a particular fraction of the

hadron's energy. Such functions are known as parton distribution functions (PDFs) and

are ultimately determined from experimental data. In this way, we arrive at a description

of proton anti-proton collisions in terms of parton-parton interactions.

When colliding hadrons with hadrons at very high energy, most of the collisions will

exclusively involve soft interactions of the constituent partons; with the final hadrons

moving primarily along the beam direction. However, in some collisions two partons will

4 Confinement refers to the fact that isolated quarks have never been observed.

cone R=0.7 et7vn12
Entries 126B946e407
12 Mean 1.675
S2/I ndf 16.75/4
po -0.510.002141

0 B

A 4-

2- -

1 2 3 4 5 6 7 8 9
Number of primary vertices

Figure 3-12. Average transverse energy deposited in a random cone of R = 0.7 in min-bias
events as a function of the number of primary vertices in the event.

in a random cone in minimum bias events. These are events whose only requirement is

coincidence between east and west modules of the CLC. The average transverse energy in

the cone is parametrized as a function of the number of primary vertices in the event and

is shown in Fig. 3-12.

The next correction is referred to as the "absolute" correction and is meant to account

for any non-linearity and energy loss in the detector. Quite generally, the response of a

calorimeter tower depends on the momentum, position, incident angle, and species of the

incident particle. Moreover, the response of the CDF calorimeter is non-linear, which is to

-Z.I that the energy recorded by a tower for a particle with momentum pi is different than

for two particles with moment P2 + i3 pi. While the CDF detector simulation has been

carefully tuned to include these effects, meaningful comparison to theory requires that the

measured jet energy be independent of these. To this end, Monte Carlo with full CDF II

detector simulation is used to reconstruct jets at the calorimeter level and at the hadron

l-a Leading Jet ET > 100 GeV
CDFSim Tracks
Charged Hadrons


Pythia Tune A
|hi < 1.1
0 1 2 3
X = pnT

Figure 4-9. Distribution in Q of MC charged hadrons relative to the transverse thrust axis,
compared to the same distributions in MC tracks after full detector simulation.


X = In( PT)

Figure 4-10. Inclusive momentum distributions of Pythia Tune A tracks for the entire
central region |T1 < 1.1

The CEM and PEM systems consist of 23 1l,- i of 4.5 mm lead interspersed with 4

mm polystyrene scintillator, for a total thickness of about 20 X, (radiation lengths). Lead

is chosen for its large EM cross section, and its thickness ensures that punch-through of

electrons and photons into the hadronic calorimeter is minimal. Both electromagnetic

calorimeters are embedded with proportional wire chambers at the approximate depth

of maximum shower development. This system along with a preshower detector greatly

enhances electron identification. The EM calorimeters achieve energy resolutions of

approximately CE/E ~ 15'. -/vE for particles at normal incidence .

The hadronic calorimeters consist of alternating l-v.. -i of iron absorber and

naphthalene scintillator. Because they rely on nuclear interactions which have a much

smaller cross section, the hadronic 1l.- -,i must be thicker than the EM components

to achieve a useful depth of interaction lengths. Iron is used because its nuclear cross

section is comparable to that of lead while being lighter and less expensive. In the central

region the CHA's thickness is approximately 4.5 nuclear interaction lengths (A), while

in the plug region the PHA's thickness is 7 A The WHA is designed to compensate the

limited forward coverage of the CHA, and covers the region 0.7 < |q| < 1.3. It too is

iron/scintillator based with the thickness of 4.5 nuclear interaction lengths. The energy

resolution of hadronic calorimeters is further degraded by the loss of secondary neutrinos

and muons and by the energy expended in exciting and breaking up the absorber nuclei.

The resolution of CDF's hadronic calorimeters is approximately CE/E ~ 50 I' '- /V

for particles at normal incidence. Table 3-4 summarizes properties of the CDF calorimeter


3.2.4 Cerenkov Luminosity Counters

While the luminosity does not directly feed into the calculation of event shapes, the

University of Florida group designed and maintains the detector which performs this

'0 10 M 111



F *%f

beam line

Figure 4-5. Illustration of the distance, R,,,,, from the beam line to the point where the
conversion occurred. Here, do is the impact parameter.



Figure 4-6. Distribution of the impact parameter do, for different track reconstruction
algorithms. The data is fit to the sum of two (; i--i ,in- to determine the
width, edo, and is later used in the track selection.







In the course of writing this dissertation, it has become overwhelmingly obvious to me

the multitude of people to which I am indebted. And unfortunately, as I sit down to write

these acknowledgements I am painfully aware of first, my own shortcomings as a writer,

and second, the limited space I have to thank so many. And so, as with most endeavors in

my life, I undertake the writing of these acknowledgements with some anxiety.

First and foremost, I would like to thank the countless scientists that have contributed

to the CDF collaboration and to the operation of the Tevatron accelerator. When I stop

to think about the complexity of colliding subatomic particles at such high rates and the

dedication required to maintain the detectors that record these collisions I am humbled.

It literally takes hundreds of people working in concert to achieve such a feat. That a few

brilliant minds had the clarity of vision to believe it could be done and the courage to

gather the wherewithal to build such an instrument is truly inspiring.

It would be a brutish oversight not to specifically thank here my advisor, Professor

Andrey Korytov, who -ir.-.- -Il. 1 event shapes as a thesis topic. His patience, optimism,

and encouragement were often sources of great comfort. Needless to ,-', his guidance over

the past three years is in the pages of this dissertation.

I am most indebted to my friend and office-mate Sergo Jindariani and his wonderful

wife Oksana. Whether discussing the finer points of jet fragmentation or our shared dream

of managing a Publix supermarket, Sergo's knowledge and humility have alv-i-, brought

perspective to my own thoughts. His daily presence has been sorely missed this past year.

Many thanks are also due to Craig and Nicole Group for their friendship and support.

Craig's positive attitude in the face of difficult times was annoying to the least, but

more often than not, just what I needed to get through the div. I cannot imagine having

survived my years at Fermilab without all four of you. Mazal Toy!

Being a part of the University of Florida High Energy Experimental group, I also had

the privilege of working directly with a number of talented scientists; particularly, Roberto

level. The jets are then matched in TI 0 space (AR < 0.4) and a correction factor derived

as a function of jet energy at the calorimeter level.

Finally, the last correction applied to the measured jet energy is the so-called

"out-of-cone" correction. It is meant to account for the fact that partons during

fragmentation may fall outside the clustering cone used for jet definition. The correction

effectively returns the "jet ( i, i ;, back to the parent parton's energy and is entirely

derived from Monte Carlo simulations.

Table 4-2. The resolution of the impact parameter, -do, evaluated for different categories
of tracks based on the number of SVX and COT hits.
Algorithm cdo, mm
COT-only 0.110
Inside-Out (10) 0.013
Outside-In rf 0.020
Kalman Outside-In rf 0.020
Outside-In stereo 0.014
Kalman Outside-In stereo 0.014
Outside-In 3D 0.0095
Kalman Outside-In 3D 0.0095
SVX Only 0.020

hadrons and after full detector simulation and reconstruction. The results are shown in

Figures 4-7 and 4-8. Note that the momentum in the later plot is expressed in terms

of the observable which is defined as t 1/x In Ejet with Ejet being the jet
energy and Pparticde the particle's momentum. Note that in these plots the label "CDFSim

li I.- refers to reconstructed tracks after MC hadrons have been propagated through the

detector using the full CDF simulation package which includes simulation of conversions

and in-flight decays. The agreement in the distributions confirms that our cuts remove

most of the backgrounds. The tracks considered in these figures lie in a small cone around

the jet axis, but the result is valid over the entire central region (|r| < 1.1) as evidenced in

Fig 4-9

Curiously, if we relax the cuts on d do, and Rco,, and compare Data and Pythia

Tune A, we observe that there are many more rejected tracks in the Data than there

are in the simulation (see Fig. 4-12). Furthermore, this excess is distributed uniformly

(Fig.4-11), but is clearly most prominent in the region away from the primary energy flow

( r ~ 7r/2) where the relative overage is -~ A- i',. (tracks are measured with pr > 300

MeV). The same plot for calorimeter towers reveals a similar excess of ~ 40',. in the

region away from the transverse thrust axis (towers are measured with ET > 100 MeV).

Additional studies -,-. -1 that this excess is the result of an underestimation in the

amount of detector material in the CDF simulation package.

[25] T. Sjostrand et al., Comput. Phys. Commun. 135, 238 (2001), hep-ph/0010017.
[26] Z. Nagy, Phys. Rev. D68, 094002 (2003), hep-ph/0307268.
[27] Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977).
[28] B. Andersson, G. Gustafson, and B. Soderberg, Z. Phys. C20, 317 (1983).
[29] R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P. Zanarini,
[30] G. Grindhammer, M. Rudowicz, and S. Peters, Nucl. Instrum. Meth. A290, 469
[31] CDF, R. Field and R. C. Group, (2005), hep-ph/0510198.
[32] CDF Collaboration, R. Wagner and et. al., FERMILAB-PUB 96/390-E (1996).
[33] CDF Collaboration, K. A. Bloom and, FERMILAB-CONF 98-370-E (1999).
[34] J. Elias et al., Nucl. Instrum. Meth. A441, 366 (2000).
[35] E. J. Thomson et al., IEEE Trans. Nucl. Sci. 49, 1063 (2002).
[36] CDF Collaboration, F. Abe and et al., Phys Rev. D45, 1448 (1992).
[37] S. D. Ellis and D. E. Soper, Phys. Rev. D48, 3160 (1993), hep-ph/9305266.
[38] A. Bhatti et al., Nucl. Instrum. Meth. A566, 375 (2006), hep-ex/0510047.
[39] C. Hays et al., Nucl. Instrum. Meth. A538, 249 (2005).

7.6 MHz Synchronous pipeline
5544ns latency
<50 kHz Accept rate

Level 2:
Asynchronous 2 stage pipeline
~20gs latency

DAQ Buffers

LI+L2 rejection: 20,000:1

Figure 3-10. Functional block diagram of the CDF data flow.

At the first level (LI) new events are loaded into a buffered pipeline with a depth

of 42 slots. With each Tevatron clock cycle (132 ns), the events are moved up one slot,

implying that an accept/reject decision must be reached within 5.5 ps for each event. Only

the most rudimentary pattern matching and filtering algorithms are applied to data from

the calorimeters, the COT, and the muon chambers. The calorimeter stream's decision

is based on the total energy deposited in towers as well as the magnitude of unbalanced

L1 Storage
42 Clock
Cycles Deep

L2 Buffers:
4 Events


In order to study the smallest known structures, particle physicists must collide

ordinary matter at very high energies. Doing so, in a controlled fashion requires a facility

that can accelerate particles to velocities close to the speed of light and then collide

them together on-demand. Such an environment can be found in the far western suburbs

of Chicago, Illinois at the Fermi National Accelerator Laboratory (or Fermilab). The

lab is funded by the U.S. Department of Energy and is home to the Tevatron, which

has stood for two decades as the world's highest energy collider. The Tevatron directs

counter-rotating beams of protons and antiprotons through an underground tunnel 4

miles in circumference until they are focused into head-on collisions at a center-of-mass

energy of =s/ 1.96 TeV. The Collider Detector at Fermilab (CDF) is centered on one

such interaction point, where its multiple specialized 1.,riS detect the passage of outgoing

remnant particles to provide a multifaceted view of the event collision. In this chapter we

give a brief overview of the accelerator chain and the CDF detector used to collect the

data for the measurements.

3.1 Accelerator

The creation and isolation of protons and antiprotons and the acceleration of each

beam to an energy of 980 GeV is a complex process that must be performed in multiple

stages. In fact, the Tevatron is only the last leg of the particle's journey through various

low and intermediate energy accelerators. A schematic of the accelerator chain is shown in

Fig. 3-1.

3.1.1 Proton Source

The process leading to the pp collisions must begin with readily available forms of

matter. Hydrogen gas is a useful starting material because its nucleus is comprised of a

single proton. Electrodes in the dome of a Cockcroft-Walton generator ionize hydrogen

Hard+UE Global njiet1< 0.7
S(1 PT )
7 'MC --- Hard
-e-- Pythia Parton (CTEQ5L)
E Tune A Parton x 7Mc
I- 0 .0 4 .... .......................... ......................... ....
Tune A Hadron x 7MC


a -- Icos el)
P I k Isin el)
100 150 200 250 300
EJet 1

Figure 2-10. The weighted difference of the mean values of transverse thrust and thrust
minor as a function of the leading jet energy. Comparison is made between
theoretical predictions at (NLO+NLL) accuracy and PYTHIA with and
without an UE.

Table 1-2. Summary of lepton properties.
Particle Spin C'! irge Mass
1st Generation e- 1/2 -1 0.511 MeV/c2
Ve 1/2 0 <3x 10-6
2st Generation p 1/2 -1 105.7 MeV/c2
uP 1/2 0 < 0.19
3rd Generation 7- 1/2 -1 1777 MeV/c2
_V7 1/2 0 < 18.2

only matter fields to interact via the strong force. Each of the six quarks carries one of

three quantum numbers metaphorically known as colour and usually denoted red, blue,

and green Interestingly, quarks have never been observed isolated in nature and exist

exclusively in colour-neutral bound states known as hadrons which come in two varieties:

1i, i. -u, and mesons. Baryons consist of a triplet of quarks with one quark of each color

while mesons consist of a quark anti-quark pair of opposite colours (e.g. red and anti-red).

Protons and neutrons are the most familiar 1'. ii, -.i, but dozens of such bound states

exist, albeit with much smaller lifetimes[5]. Of the mesons, pions are the most common,

but even their lifetimes are short (< 10-7s). The properties of quarks are summarized in

Table 1-3.

The only particle predicted by the Standard Model yet to be discovered is the Higgs

boson (H). It is the only scalar particle in the theory and pl .1i- a key role in explaining

the origin of mass for all other elementary particles. Particularly the difference between

the massless photon and the very heavy W and Z bosons. The Higgs mechanism [6] also

provides a means of dynamically generating fermion masses in a gauge invariant way.

The search for the Standard Model Higgs boson remains one of the top priorities at the

Tevatron and the future Large Hadron Collider experiments.

3 These have nothing to do with the spectrum of visible light and could just as well
have been called chocolate, vanilla, and strawberry.

Table 1-3. Summary of quark properties.
Particle Spin C'!0 irge Mass
1st Generation u 1/2 2/3 1.5-4 MeV/c2
d 1/2 -1/3 4-8 MeV/c2
2st Generation c 1/2 2/3 1.15-1.35 GeV/c2
s 1/2 -1/3 80-130 MeV/c2
3rd Generation t 1/2 2/3 170.9 1.8 GeV/c2
b 1/2 -1/3 4.1-4.4 GeV/c2

1.2 Quantum Chromodynamics

Quantum Ch!i iindynamics (QCD) is the dynamic theory of the strong interactions.

Possibly the most fundamental tenet of the theory is that all hadronic matter is made up

of quarks. The idea of quarks was first proposed by Gell-Mann and Zweig in the 1960's

to explain the apparent flavour symmetry of the lowest-mass mesons and '. ,i .1' [7].

However, in their schema the existence of the A++ particle, a spin 3/2 baryon believed to

be a bound state of three u quarks, required the introduction of an additional quantum

degree of freedom known as "colour" [8]. Obviously, the introduction of an additional

degree of freedom would lead to a proliferation of states and so the colour hypothesis had

to be supplemented with the requirement that only colour singlets could exist in nature.

The fact that these singlet states were composed of either three quarks (baryon) or a

quark anti-quark pairs (meson) directly lead to the mathematical formulation of QCD as a

gauge theory based on an SU(3) colour symmetry.

Formally, QCD is a renormalizable quantum field theory [3] constructed in close

analogy with Quantum Electrodynamics (QED). Just as particles with electric charge

interact via the exchange of massless photons, quarks interact with each other through the

exchange of massless gluons. However, a prominent difference between the two theories is

that the generators of the SU(3) gauge group do not commute with each other. Physically,

this means that the gluons themselves carry a colour charge and can interact with each

other. The gluon-gluon interactions of QCD have no analogue in QED and have very

significant consequences for the theory.

Year 2002
-4500 '






2003 2004 2005 2006 2007 2008

1000 2000 3000 4000 5000 6000
Store Number
Figure 3-3. Total integrated luminosity delivered by the Tevatron since the beginning of
Run II. Also shown, is the live luminosity, labeled "To tape", which excludes
integrated luminosity during detector dead-times.

R =L


with sigma in [cm2] and R in [Hz]. This quantity gives rise to integrated luminosity

which better characterizes the amount of data delivered over time. The cross section for

some process is typically quoted in units called "barns" (lb = 10-28 m2) and so integrated

luminosity is more often quoted in units of inverse cross-section. The total integrated

luminosity measured at CDF since the beginning of Run II is shown in Fig. 3-3. The live

luminosity, which excludes integrated luminosity during all detector dead-times is also


Recent performance has the Tevatron regularly achieving peak luminosities of 2.5-2.75

x 1032 cm-2s-1. The instantaneous luminosity is at it's peak at the beginning of a store

when the beams initially begin colliding and decreases approximately exponentially with

In this analysis we use the Monte Carlo program PYTHIA 6.216 [25] to simulate

multihadronic events in our detector. The simulation of each event proceeds in four

distinct stages; a schematic of which is shown in Fig. 2-3.

The hard QCD 2 -+ 2 scattering of partons from the colliding proton and antiproton.
This involves parton distribution functions and a knowledge of the leading order
QCD matric element.
A p irton shev, i in which the initial outgoing partons radiate gluons which in turn
radiate more gluons or split into new qq pairs. This stage incorporates soft pQCD
Hadronization of the final partons. This is followed by the decay of short lived
particles like 7r and Ks.
Interaction of particles with detector material and simulation of detector response.

Below is a brief description of the implementation of each of these stages in the event


2.4.1 QCD 2 to 2

In PYTHIA the hard scattering consists of the matrix element described above

calculated at leading order. This means that two incoming partons interact via the

dynamics of QCD at "tree-level" (i.e., no loops in the Feynman diagrams) and the final

state consists of two outgoing partons. Additional hard emissions are introduced by

imposing an artificial cutoff on the development of the parton shower which is described in

the next section. Relatively recently though, next-to-leading order(NLO) O(a ) MC has

become available which includes one-loop corrections to LO processes as well as additional

hard radiation (fully becoming a 2 -- 3 process) [26]. However, to be clear, the Monte

Carlo simulation used in this dissertation (PYTHIA) calculates the hard scattering at

leading order. As previously noted though, predictions provided by theorists incorporate

NLO results.

extraordinary individuals they raised. My aunts and uncles have shown support for me

throughout my life and I hope they know what a huge comfort and source of strength they

are to me.

Finally, I would like to dedicate this work to my mother, father, and brother who

have sacrificed so much.


*0 ijetI l 0.7
I ES : Global

Leading Jet ET > 100 GeV
Pythia Parton (CTEQ5L)
Tune A Parton
Tune A Hadron

X.I' Iet I < .7
-ln ES : Global

Leading Jet ET > 100 GeV
Pythia Parton (CTEQ5L)
Tune A Parton
Tune A Hadron

X = TMin


X = TMin

X = TMin

I|etl< 0.7 Leading Jet ET > 300 GeV
Pythia Parton (CTEQ5L)
Tune A Parton
Tune A Hadron

Ietl< 0.7
ES : Global

0.1 0.2 0.3


Leading Jet ET > 300 GeV
Pythia Parton (CTEQ5L)
Tune A Parton
Tune A Hadron

0.2 0.4 0.6
X = TMin

Figure 2-8.

Distributions of the transverse thrust and thrust minor for leading jet energies

100, 150, 200, and 300 GeV. Comparison is made between theoretical

predictions at (NLO+NLL) accuracy and PYTHIA with and without an UE.

Global 1jet_< 0.7

-e- Pythia Parton (CTEQ5L)
0.1 Pythia Hadron


100 150 200 250 300
EJet 1

E Global jet< 0.i7
0.3 -e--.................................. Pytha Parton (CTEQ5L)
Pythia Hadron

0.2 ......

0.1 -

0 1 . I .I .I ,
100 150 200 250 300
EJet 1

Figure 2-6. Evolution of the mean values of the transverse thrust and thrust minor as a
function of the leading jet energy. Comparison is made between theoretical
predictions at (NLO+NLL) accuracy and PYTHIA without an UE.

energy, Fig. 2-9, we observe in comparing Tune A at the parton and hadron levels, that

the underlying event appears to dampen the effects of hadronization on the distributions.

In some sense, the additional particles from the underlying event saturate the event shapes

distributions to a point where the "re-shuffling; of moment that occurs at hadronization

has little effect on the observable. Finally, we note that in the final observable constructed,

C((r), (TMi})), the contribution from the underlying event cancels (as expected) and good

agreement is seen between theorists' predictions and Pythia Tune A.

it's vicinity allowing freed elections to drift toward the sense wires. The 1/r dependence of

the electric field around the wires implies that the field is largest close to the sense wires.

The high field strength then results in an avalanche discharge as the originally ionized

electrons acquire enough energy to free other electrons which are themselves accelerated.

This effect provides a gain of ~ 104 for the collected charge. However, because the COT

is immersed in a magnetic field the drift is not precisely in the direction of the electric

field lines. To compensate for this bending the supercells are tilted by a Lorentz angle of

a ~ 35 with respect to the r vector such that the drift trajectories remain azimuthal.

The signals on the sense wires are processed and the location of hits recorded. The hit

times are later processed by pattern recognition software to reconstruct helical tracks. The

hit resolution of the COT is approximately 140 pm, which translates into a transverse

momentum resolution -P ~. 0.0015 PT
pT GeV/c

Silicon Detectors

The silicon tracking detectors are located closest to the beam interaction point to

provide precise position measurements along the trajectory of the charged particle. This

is particularly crucial for the reconstruction of displaced secondary vertices. In essence,

the silicon detector is a reverse-biased p-n junction. C1i irged particles passing through a

silicon wafer induce ionization, which in the case of semiconductors produces electron-hole

pairs in the junction's depletion region. In the presence of an electric field, the electrons

travel toward the positively biased anode while the holes drift toward the cathode,

producing an electric signal. All the CDF silicon tracking components are implemented as

microstrip detectors, where the typical distance between two strips is on the order of 60

pm and each 1-vr has a nominal thickness of 300 pm. As a result, the silicon detectors

have a much better resolution than the COT. Their proximity to the beam imposes

an additional constraint that the detector should be able to withstand large doses of


Rossin, Yuri Oksuzian, Sasha Sukhanov and Song Ming Wang. I thank each of you for

your dedication to the CLC and the friendly environment you fostered. I would also like to

thank Bobby Scurlock, Mike Schmitt, and Karthik Shankar for listening to my rants these

past few months. These three gentlemen convinced me to forgo a a handsome salary in

order to write this dissertation ... I will never forgive them.

Throughout my life, I have had the good fortune of being surrounded by positive

people who have inspired and motivated me. It would be impudent not to thank them

here also. These are people who were not directly involved in this research, but without

whom this dissertation could not have been written. First, I would like to thank my great

friend Tony Cuadra, who took a 1500 mile road trip with me when it mattered most-your

attempts to cover your genius with reckless abandon are not fooling .-,n one. To Jon

Lawrence, who makes the best pad thai this side of Bangkok, your friendship and support

have helped me through some tough times. To Shawn Allgeier, who still wrestles bears

naked in the woods, one d4i- you will win and when you do I will be there to sit on you.

To Alexandra King and her cousin Becky Sue, thank you for making me laugh and please

stop inbreeding. To Ed K ., i,-1: ,, t, who's graduate career has unfortunately paralleled

mine in too many v- i-, thank you for understanding, and believe me when I the best

is yet to come. To Sagar Mungekar, who's skewed memory has lent itself to some of the

funniest writings I have ever read, thank you for reminding me of all the great times I've

had. And to Rebecca Hyde, who has known me better than most anyone, thank you for

not running away so many years ago.

Because so much in life depends on where you start, I have to take this opportunity

to also thank my family. I am immensely grateful for having been born into such a loving

and caring group. To have such a concentration of good, decent, hard-working people

in your camp cannot be the result of chance or coincidence; and so, I begin by thanking

the grandparents I barely knew-Ramon and Rita Llanes, whose values are in the 13

the resumed results with fixed order calculations can be quite complicated. Furthermore,

the property of exponentiation described above relies on a kinematic factorization of

phase space that is intricately linked with the details of the observable. As a result,

predictions within this framework have, until now, been calculated analytically by hand.

However, recently methods for automating resummations have been developed [22]. The

theoretical predictions presented here are the product of the "Computer Automated

Expert Semi-Analytical Resummer" (CAESAR).

At present, a technical restriction of these automated resummations, and indeed of

all fully NLL analytical resummations, is that the observable must be ./l'./ that is, it

must be sensitive to emissions in all directions including arbitrarily close to the beam

line. This requirement is in direct conflict with the experimental realities of the hadron

collider environment-namely the limited detector coverage in the forward region. However,

for sufficiently large values of the maximum accessible pseudo-rapidity5 the excluded

kinematic region is expected to give at most a small contribution to the observable [23]

that would ultimately be significant only at very small values. For example, the full global

predictions for the transverse thrust and thrust minor should remain valid for In y < ,max

where Trmax is the maximum detector coverage [19].

It should be noted that theorists first proposed an alternative definition for event

shapes at hadron colliders to specifically deal with the issue of limited detector coverage.

As originally envisioned, the event shapes were to be defined over particles in some

reduced central region and rendered "indirectly" global by the addition on an event by

event basis of a i ... .!" term. Such a term would be defined over particle moment in

the same central region as the rest of the observable but would introduce an indirect

sensitivity to moment outside that region. The proposed recoil term was essentially

the vector sum of the transverse moment in this central region (which by conservation

The definition of pseudo-rapidity is provided in ('!i Ipter 3.

coefficients in the limit y -- 0. In this case, each power of a8 is accompanied by a

coefficient which grows as L In2 1 thus enhancing the importance of higher order terms

in the perturbative expansion. The naive requirement that a8 < 1 is no longer sufficient

to render these terms negligible. This breakdown of the perturbative expansion arises

because requiring y to be small essentially places a restriction on real emissions without

a corresponding restriction on virtual contributions-the resulting incompleteness of the

cancellations between logarithmically divergent real and virtual diagrams is the origin of

the order by order enhancement in the perturbative expansion. To obtain a meaningful

answer in the region y -- 0 it is then necessary to perform an all-orders resummation of

the enhanced terms.

Before discussing resummation any further it is helpful to establish some of the

more common nomenclature. One convention is to refer to all terms oc a7L2' as leading

logarithms (LL), terms oc a'L2,-1 as next-to-leading logarithms, etc.. Within this

hierarchy a resummation may account for all LL terms, or all LL and NLL terms and so

forth. Such a resummation gives a convergent answer up to values of L ~ 1/ Va-, beyond

which terms that are formally sub-leading can become as important as the leading terms.

For example, if L ~ 1/as then the NNLL term a L4 is of the same order as the LL term


However, most event shape observables share the property of exponentiation. For such

observables, the term "(next-to-)leading lc-;,,l iii!, acquires a different meaning-NPLL

now refers to all terms oc aLf+-'-P. The crucial difference between a resummation for

an observable that exponentiates and one that does not, lies in its range of validity. A

resummation that exponentiates will remain convergent up to L ~ 1/as [21]. In this

dissertation, we deal with observables which exponentiate and so NPLL shall refer to the

latter meaning.

In some sense, resummation is merely a reorganization of the perturbative expansion;

however, understanding which terms will appear, how to resum them, and how to combine

aP3b > P3

Figure 2-2. Colinear branching of partons within a three-jet event.

the observable is small typically contain large logarithms-a reflection of the importance

of soft and collinear emission. A successful prediction in this region requires an all-order

resumed perturbative calculation.

Finally, there is at least one significant restriction on the type of observables that are

calculable within perturbative QCD (in either regime). In order to ensure the cancellation

of real and virtual divergences associated with low-energy radiation, observables must

to be infrared and collinear (IRC) safe; that is, the observables must be insensitive to

the emission of a soft gluon or the branching of a parton into two collinear partons (see

Fig. 2-2). This requirement, which originally emerged from the discussions of Sterman

and Weinberg [20], has proven a necessary condition for guaranteeing finite perturbative

predictions. Moreover, the criterion of IRC safety, though posed on theoretical grounds,

has a basis in experimental reality-the results of a measurement should be as insensitive

as possible to small changes in a detector's resolution or granularity. Both of the event

shapes presented in this dissertation are defined to be infrared and collinear safe.

2.3.1 Fixed Order Calculations

Fermi's Golden Rule tells us that the transition rate from an initial state 'i' to a final

state 'f' is given by

2M.(if) 2p(pI,p2,...pN), (2-5)

where M(if) is the matrix element connecting states 'i' and 'f' in the perturbed

Hamiltonian, and p is the density of possible momentum states in phase space for the

Success is overrated. Failure is how we learn.



Lester Pinera was born in Colon, Cuba, on January 12, 1979. He moved to the

United States in 1980 and primarily grew up in Miami, FL. He attended Southwest

Miami Senior High school and graduated valedictorian of the Class of 1997. He earned

his B.A. in physics with a concentration in math from Cornell University in 2001. He

began his graduate work at the University of Florida that year and joined the High Energy

Experimental Group there in 2004. He earned his Ph.D. in 2008.

2.4.2 Parton Showers

In PYTHIA the cascade of partons produced around a hard scattering is simulated

using a numerical implementation of the DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi)

equations [27]. This is a system of differential equations devised to describe the sequence

of emissions from a parton as it evolves from a hard scattering down to lower energy

scales. They are based on a set of -plaIting 1:. ii. !- Pa-bc(as,z), which define the

probability of a parton a splitting to produce partons b and e with the momentum fraction

z and (1 z) respectively. The model includes various features to incorporate coherence

effects, the simplest of which is i.'j,la, ordering which requires that the opening angle Obc

of each branching (a -+ be) be less than that of the previous branch in the cascade.

The shower continues until the virtuality of the partons reaches some lower limit Qo,

which is a tunable parameter set by default to 1 GeV. The final parton configuration is

then passed to the non-perturbative hadronization stage. A more detailed discussion of

parton shower physics can be found in Ref.[13].

2.4.3 Hadronization

Hadronization is simulated in PYTHIA using the Lund string model [28]. Unlike

the electromagnetic field patterns formed by distributions of charge and current, the

corresponding fields in QCD are expected to be confined in narrow regions stretched

between colour charges; this is a result of the gluon's self coupling. According to the

string model, the field lines will eventually 'break' at several points to form new qq or

diquark-antidiquark pairs which lead to meson and baryon production. The model has

many tunable parameters which have been set by default to values determined by the LEP


Finally, some of the hadrons produced are expected to decay very close to the

interaction point. The MC itself treats particles with lifetimes less than 3 x 10-10 s to be

V-l@ 10 Leading Jet ET > 100 GeV -0 Leading Jet ET > 100 GeV
-Iz -lz
Data Data
10 -
1" -- ---j -

Towers Towers
I|ql < 3.5 hi < 3.5
10-5 0 -4 -2 0 2 4
X=0 X=O

Figure 4-1. The distribution of calorimeter towers in TI and Q over the full rapidity range
of the detector. The distributions are normalized to the number of events in
each sample. The label CDFSim refers to Pythia Tune A MC after full
detector simulation.

That is, the excess is uniformly distributed in TI 0 space and was found not to be the

result of "hot" towers. Restricting ourselves to the central region (|r]\ < 1.1) we observe

that the excess appears over a wide range of transverse momentum (100MeV< pr < 5

GeV), but is most prominent below 1 GeV (see Fig. 4-2).

Plotting the distribution of towers as a function of the angle between the 2D tower

PT and the transverse thrust axis nT (Figure 4-3) we observe that the relative difference

between data and MC is greatest in the region away from the primary energy flow (i.e.,

away from of the transverse thrust axis, OTT ~ -7/2). We return to the curious incident of

the excess towers in the ix i' region after a discussion of tracks in the central region.

4.4 Tracks: |qI < 1.1

While our ultimate measurements are based on calorimeter information in the

pseudorapidity range |T| < 3.5, restricting ourselves to the central region |y| < 1.1 makes

possible the use of precision tracking to supplement our understanding of the flow of

energy in dijet events. The primary advantage to this being that tracks allow us to focus

on particles originating from the primary vertex while rejecting those produced by other


System TI Coverage Thickness Resolution (E in GeV)
CEM q| < 1.1 19Xo 13.5' /v E- .
PEM 1.1 < q < 3.6 21Xo t1I.'./0e1 1.
CHA r\1 < 1.1 4.5A 7-'. / -,- .
WHA 0.7< |q<1.3 4.5A 7.7/ O : .
PHA 1.3 < |9 < 3.6 7A si'r./E '.

Table 3-4. Summary of quantities characterizing CDF II calorimetry. Thicknesses are
listed in terms of radiation (Xo) or interaction (A) lengths. The E symbol
indicates a constant resolution term to be added in quadrature to the energy
dependent term.

measurement for the entire CDF collaboration. Hence, my involvement in the up-keep of

this detector over the past 3 years merits its inclusion in this dissertation.

The Cerenkov Luminosity Counter (CLC) was a Run II addition to the CDF detector

intended to provide precise measurements of the instantaneous and integrated luminosity

[34]. The detector consists of two modules (east and west) that are located in the far

forward region 3.75 < |q| < 4.75 of the CDF detector. Each module is comprised of 48

cone-like Cerenkov counters arranged in three concentric li. rs (16 counters per livr)

around the beam pipe focused on the primary interaction point (Fig. 3-9). The entire

module is then enclosed in a thin aluminum shell that is filled with pressurized isobutane

gas. The arrangement makes the detector significantly more sensitive to particles coming

directly from the interaction point because they transverse the full length of a counter

and hence generate more light. This is in contrast to particles coming from secondary

interactions with detector material or from beam-halo interactions; these particles pass

through the counters at large angles resulting in a shorter path through the cones and

hence a less light. The signal is ultimately read out by photomultiplier tubes.

The luminosity is calculated by measuring the number of interactions per bunch

crossings, p, and applying the relation:

p fBc = pp L, (3-5)

implemented at CDF. These are JetClu [36], a cone algorithm that combines objects based

on relative separation in ] Q space; Midpoint, an algorithm similar to JetClu, but defined

to be infrared and colinear safe; and KT [37], an algorithm combining objects based on

their relative transverse moment as well as their relative separation in T] 0 space.

This analysis utilizes jet identification exclusively for the purpose of event selection.

As a result, the jet algorithm used is not expected to significantly affect the final results.

That being said, this dissertation employs CDF's implementation of the Midpoint Jet


3.3.1 Jet Clustering

Jets at the detector level are constructed based on calorimeter tower information.

Before beginning any clustering it is necessary to specify a cone size, R,,,,,e that

determines the maximum amount of angular separation particles can have in T] 0 space

and still be combined into a jet. Typical cone sizes employ, ,1 at CDF are Rc,,e = 0.4,

0.7, and 1.0. The algorithm begins by considering "seed" objects above some threshold

(1 GeV) and constructing a cone of radius R = Rc,,,,/2 around each seed 2 The

momentum four-vectors of all objects located within the search cone are then summed.

This four-vector sum is referred to as the centroid of the cluster. The four-vector of the

centroid is then used as a new cone axis. A cone is drawn about this new axis and the

four-vectors of all particles in this new cone are summed. The process is iterated until

the cone axis and centroid coincide, indicating that the configuration is stable. Once the

stable configuration is found the cone axis is expanded to the full cone size (R = R ,)

and the four-vector of a protojet is formed by adding the four-vectors of all objects in the

2 It is worth noting that this reduced cone size is not a feature of the standard Midpoint
algorithm and is a feature implemented by CDF.

effect on our final observable, the segmentation of the calorimeter is imposed on MC
particles at the hadron level.

The results of these ii 11. ", detector effects are shown for the event shapes in

Figure 4-16 and for the final observable in Figure 4-17. The granularity of the calorimeter

appears as the primary source of the instrumental effect observed in the full detector

simulation (i.e., Fig. 4-15). Other detector effects include the sharing of energy between

towers and the energy response of the calorimeter. However, all of these effects are

incorporated into the full GEANT detector simulation. Ultimately, the difference in the

final observable between the MC at the hadron level and detector level shall be quoted as

a correction factor to the data.

Finally, the event shapes are defined theoretically over all particles in the final state,

including those with arbitrarily small moment. In an effort to understand how a cut on

the transverse energy affects the observables, we vary the ET threshold on towers from 100

MeV (default) through 200 and 300 MeV. Figure 4-18 shows the result of this variation on

the mean values of the thrust and thrust minor. Clearly the events appear narrower as we

cut-out more towers. However, Figure 4-19 shows that for the leading jet energies studied

in this dissertation, the final observable is rather insensitive to the cut on transverse


4.6 Systematic Uncertainty

The sensitivity of our final observable to various uncertainties in the event selection

procedure is evaluated as follows. For each source of systematic uncertain, a "default"

and "deviated" observable is constructed. The "default" observable is the result of the

standard set of cuts defined earlier in this chapter, while the "deviated" observable is the

result of varying a particular parameter by some amount within it's uncertainty. For each

leading jet energy sample a scale factor is produced by taking the ratio of the "deviated"

and "default" values of the final observable:

transverse energy. Information from the COT stream is processed by the Extremely Fast

Tracker (XFT) [35] which partially reconstructs tracks allowing for event decisions to be

made based on track multiplicity and transverse moment. The muon stream combines

hits in the muon chambers with XFT tracks to identify events with muon candidates.

These simple cuts remove a significant in i iP ily of the background, reducing the accepted

event rate to about 30 kHz.

Events which meet the requirements of the LIt ri .r are then passed to the Level-2

trigger(L2). At L2, an event is written into one of four buffers within the DAQ electronics

for each detector component. These buffers differ from the data pipeline used in LI, in

that an event remains in the buffer until the decision is made; that is, while an event

is being processed, it cannot be overwritten by another event from LI. If a LI accept

occurs while all four L2 buffers are occupied deadtime is incurred. In order to minimize

this deadtime, the latency of the L2 decision must be less than approximately 1'. of the

average time between LI accepts. This creates a ~ 20 ps window to accept or reject a

candidate event. Decisions at L2 combine information from LI in addition to data from

other subdetectors like the SVX and CES subsystems. The algorithms at L2 cut the

acceptance rate down to 300 Hz.

At Level-3 (L3) data from the entire detector is combined by the Event Builder

system for a more computationally intensive examination of the events. The arranged

event fragments are distributed across a farm of almost 1000 processors which allows for

approximately Is per decision. L3 takes advantage of full detector information and bases

its reject/accept decision on detailed particle identification and event topology. The full

trigger system reduces the 2.5 MHz event rate to approximately 75 Hz, which amounts to

~ 20 MB/s of data delivered to storage for eventual offline analysis.

3.1.2 Main Injector

The beam extracted from the Booster is then passed into the Main Injector, a second

synchrotron 3.3 km in circumference that serves as an important hub for coordinating

beams in the accelerator complex. In addition to accelerating protons to an energy of 150

GeV, the Main Injector produces 120 GeV protons for antiproton production, receives the

resulting antiprotons and accelerates them to 150 GeV, and injects both beams into the

Tevatron. As a five-year construction effort ending in 1999, the Main Injector stands as

the n ii' r upgrade to the laboratory during the Tevatron era.

3.1.3 Antiproton Source

The number of available antiprotons has ahv--ix placed an upper limit on the

performance of the Tevatron. Preparation of a collection large enough to justify colliding

beams requires several hours. In fact, the most time-consuming activity of the Main

Injector is in support of antiproton production. Even as the Tevatron is generating

collisions, the Main Injector and Antiproton Source are usually working together to

prepare antiprotons for the next store.

The Antiproton Source consists of a fixed nickel target assembly and two small

synchrotrons called the Debuncher and the Accumulator. Antiprotons are created when

120 GeV protons from the Main Injector are incident upon the nickel target. The impact

produces a spray of secondary particles that is focused by a lithium lens and antiprotons

are selected using a pulsed dipole field. The overall production efficiency is about 2 x 10-5

antiprotons per incident proton. The antiprotons coming off the target have a wide range

of energies and are said to be "hot". The Debuncher then serves to collect and "cool"

the antiproton beam, reducing the spread in it's kinetic energy. The system uses the

methods of stochastic cooling, in which the transverse or longitudinal motion of the beam

is measured at one point on the ring and precisely timed negative feedback is applied at

another point. In addition to further <...1. i:. the Accumulator maintains the antiproton


.- ..-. SU



\-- MSK
CMX (miniskirt)

(CSW) e


Figure 3-4. Diagram of the CDF II detector with a quadrant removed and a zoomed-in
view of the inner subdetectors.


2.3 Theoretical Predictions

In an experiment, one measures the value of each event shape observable for every

event selected 2 Being a quantum theory, QCD makes physical predictions for event

shapes in the form of frequentist probabilities. For a generic observable y, theorists can

statistically estimate the form of the differential cross section, dc/dy. This quantity

describes the expected number of events, per unit luminosity, at a given value of the event

shape y. Dividing this by the total cross section for multihadron production, o-tot, gives the

corresponding probability density function for the observable y.

The calculation of an event shape distribution in perturbative QCD is divided into

two regimes: fixed order and resummed results. Almost all event shapes, including those

considered in this dissertation, have the property that large values of the observable

coincide with the emission of one or more hard partons at large angles relative to the

initial outgoing partons. In this regime, the differential cross section is well described by

a traditional perturbative expansion in powers of the strong coupling. Such predictions

are referred to as fixed order calculations and are valid up to some specified order in the

coupling (e.g. O(a,)). This method provides an accurate description for much of the range

of the observable3

Conversely, in the region where the event shape value is small (y
primarily to gluon emission that is soft compared to the hard scale of the event and/or

collinear to one of the hard partons. Such radiation, as previously discussed, has relatively

large emission probabilities due to logarithmic enhancements as well as the larger value

of the coupling. Therefore, predictions for event shape distributions in the region where

2 A precise definition of the event selection criteria is presented in C!i Ipter 4.

3 Incidentally, prior to advancements in resummation techniques fits for various QCD
parameters were typically performed over a limited range of the observable where the fixed
order calculations were known to be reliable.

---* P2

------ ---- P 3


Figure 2-1. A three-jet event approaching the two-jet limit.

The thrust axis dit and the beam direction z together define the event plane in which the

primary hard scattering occurs. Thus, the thrust minor can be viewed as a measure of the

out-of-plane transverse momentum. Clearly, TMi, = 0 for a pencil-like event; when the

momentum of both particles is directed entirely along the thrust axis. For an isotropic

event the thrust minor assumes the value 2
When a three jet event approaches the two-jet limit, as shown in Fig. 2-1, it becomes

clear that the observables have differing sensitivities to the opening angle 0:

T ~ 1 cos 0 ~ 02 (2-3)

TMin, sin0 0 (2-4)

Hence, it is expected that the thrust minor should be more sensitive to the effects of

hadronization and particle decay than the thrust.

Theorists have proposed a number of other event shapes [19] whose definitions

include some dependence on the longitudinal component of the final state particles'

moment. However, preliminary studies showed these observables to be sensitive to

detector mismeasurement, particularly in the forward regions. As a result, we have chosen

to focus on those observables defined exclusively in the transverse plane.

actually reproduces the shape of the distributions reasonably well. The shift can be seen

more concisely in Figure 2-6 which shows the mean values of the observables as a function

of the leading jet ET. We note that the discrepancy between theorists' predications and

PYTHIA at the parton level decreases with increasing jet energy. This difference is likely

the result of the amount of ISR present in the MC which is set to the Tune A setting

(Parp[67] = 4), but may also be the result of the relatively large parton shower cutoff (Qo

= 1 GeV) in the MC6 Furthermore, we note that the hadronization model in PYTHIA

has the effect of shifting the distributions towards larger event shape values-a result

expected from LEP studies [18]. Finally, though, we see that these discrepancies vanish

from the final observable constructed, C((r), (TMi)), (see Fig. 2-7).

2.7 PYTHIA Tune A

In order to achieve a closer description of the data at a hadron collider, the hard

scattering and parton shower in the MC simulation must be supplemented with a

phenomenological model of the underlying event. At the Tevatron, arguably the

most successful of these models is the so-called "Tune A" of PYTHIA [31] which

utilizes multiple parton interactions to enhance the activity of the underlying event.

The parameters of this simulation have been tuned to reproduce the charged particle

multiplicity and momentum spectrum in the region .i,v- from jets.

Figure 2-8 shows a comparison of the event shape distributions between theorists'

predictions, PYTHIA without MPI, and Tune A. Clearly, the underlying event not only

shifts the means towards higher values, but also significantly distorts the over-all shape

of the distributions. Turning to the plot of the mean values as a function of leading jet

6 While a lower parton shower cutoff would produce more final state particles, those
particles would be more colinear with the initial outgoing parton, and therefore may lead
to smaller event shape values.


In comparison to electroweak theory, which has been tested and verified to a high

degree of precision1 understanding the dynamics of QCD has been significantly more

difficult. The complicated gauge structure and large coupling strength have limited the

precision of most high energy predictions to the level of a few percent. The situation

is further exacerbated by the fact that experimentally, the particles we observe in our

detectors are not the quarks and gluons participating in a hard scattering, but rather

hadrons produced by low energy processes which are not well understood. As a result,

studying QCD relies on the construction of observables based on final-state hadrons

capable of probing the underlying parton nature of the scattering. This dissertation

utilizes data from the CDF detector to study the distributions and mean values of two

event shape observables, the transverse thrust and thrust minor, sensitive to the dynamics

of QCD in hadronic collisions.

2.1 Motivation and Historical Perspective

Quite generally, event shapes describe the geometric properties of the energy flow

in QCD final states. They are similar to jet finding algorithms which can be used to

categorize events according to their topology. However, they prominently differ in that

event shapes encode information about the energy flow of an event in a continuous

fashion. That is, a single parameter can describe, for example, the transition between a

configuration with all particles flowing along a single axis and a configuration where the

energy is distributed uniformly over the 47r solid angle. Event shapes, therefore, provide

more detailed information about the final state geometry than a jet-finding algorithm

which would ahv--,- classify an event as having some finite number of jets even when the

1 The Higgs boson is the only aspect of the electroweak theory yet to be confirmed.

i 0.06
Global nhj
-e-- Pythia Parton (CTEQ5L)
I- 0.04 Pythia Hadron


a -1 -(Icos el
13 Isin el)
I I I I. I ,
100 150 200 250 300
EJet 1

Figure 2-7. The weighted difference of the mean values of thrust and thrust minor as a
function of the leading jet energy. Comparison is made between theoretical
predictions at (NLO+NLL) accuracy and PYTHIA without an UE.

Figure 3-7. Schematic of the SVX bulkhead design.

several track candidates associated to the original COT-only track. The best one in terms

of the number of hits and fit quality is ultimately selected.

In contrast to the inner silicon subdetectors, the 1l-_ iS of the ISL cover different

ranges in z. It's central l-v,-r located at a radius of 22 cm detects tracks with |T1\ < 1 and

is useful for extrapolating COT track into the SVX. The forward 1lv-.r-i at radii 30 and 28

cm provide measurement of tracks with 1 < |T]1 < 2, where coverage of the drift chamber

is incomplete. The ISL 1-.. r- are double-sided, providing axial and small-angle stereo

information. The ISL contains approximately 300,000 total channels.

3.2.3 Calorimetry

Calorimeters are particularly important in high energy physics because they can

detect neutral as well as charged particles. Generally, they differ from most other detectors

in that they actually change the nature of the particles being measured. As a result, in

a multi-purpose detector, calorimeters typically occupy the outer fringes of the detector.

Such is the case at CDF, where the calorimeter system lies on the outside edge of the

solenoid coil and surrounds the tracking systems, providing good central and forward

Table 3-2. Amount of material in the CDF II tracking volume as cited in the detector's
technical design report. The quoted thickness assumes normal incidence.
L- v-r Radius [mm] Material Xo]
BP 12.0 0.1
LOO 21.0 1.4
SC 32.0 0.5
SVX 1 42.0 2.0
SVX 2 69.0 2.0
SVX 3 100.0 2.0
SVX 4 129.0 2.0
SVX 5 157.0 2.0
ISL 1 210.0 1.4
ISL 2 290.0 1.4
COT 310.0-1400.0 1.3
Total: 12.0-1400.0 16.1

coverage (|rl| < 3.6); a fact that makes them important for the measurement of event


The CDF calorimeters are divided into two categories: electromagnetic and hadronic.

EM calorimeters are optimized to measure the energy of electrons and photons via

electromagnetic interactions, while hadronic calorimeters are designed to stop long-lived

mesons and baryons primarily by way of strong interactions with atomic nuclei. Both

categories of calorimeters are of a sampling variety, where 1lV. r- of absorbing material are

alternated with signal-producing scintillator 1lv -r-.

A particle exiting the tracking system will first encounter an absorber l-1 vr (lead) of

the EM calorimeter which will induce bremsstrahlung in energetic electrons and e+e- pairs

in photons. The resulting shower of secondary electrons and photons is then detected by

photo-multiplier tubes (PMTs) attached to successive 1l-.-iS of scintillator. The integrated

charge collected by the PMT then gives a measure of the deposited energy. The remaining

spray of outgoing particles then encounters the first absorber l-1 vr (iron) of the hadronic

calorimeter, which induces hadronic showers via a v ,i, I v of nuclear interactions. The

charged secondaries resulting from the hadronic interactions then produce a signal in the

corresponding scintillator 1~V. rs which is read out by another set of PMTs. It is worth

2008 Lester A. Pinera

5-2 Evolution of the mean values of the transverse thrust and thrust minor as a function
of the leading jet energy.Comparison is made between theoretical predictions
at (NLO+NLL) accuracy, PYTHIA Tune A at the hadron level as well as after
detector simulation, and Data. . . . . . . . 98

5-3 Plot of the weighted difference of the mean values of Thrust and Thrust Minor
as a function of the leading jet energy for CAESAR+NLO, PYTHIA Tune A at
the Hadron level and Data unfolded to the particle level. . . ..... 99

While the geometry of the detector favors the use of a cylindrical coordinate system,

there are times when it is more convenient to use spherical coordinates (r, 0, Q). In such

cases, the polar angle 0 is measured from the positive z direction with it's domain being

[0,7]. The azimuthal angle Q describes positions in the transverse plane with Q = 0

coinciding with the x axis. Particularly at hadron colliders, the polar angle 0 is often

replaced by the pseudo-rapidity, (TI), which is defined as

7 -lntan( ). (3-3)

In the relativisitic limit (pc > me2) when particle masses can be neglected,

pseudorapidity is equivalent to the Lorentz invariant quantity called rapidity y =

SIn(E P) = tanh-1 f. However, the pseudorapidity has the advantage that it can be

determined directly from measurement. From the definition of T] and the aforementioned

CDF conventions it follows that T = 0 when 0 = 900. Finally, pseudorapidity is often

combined with the azimuthal angle to define the angular separation between two objects:

R VA 7 +A<^2 (3-4)

3.2.2 Tracking and Vertexing Systems

The CDF detector has a cylindrical tracking system for the primary purpose of

precisely and efficiently measuring charged particle moment and trajectories. All

components are immersed in a 1.4 Tesla superconducting solenoid, 5 m in length and

3.2 m in diameter. The innermost tracking system is a silicon microstrip detector that

actually consists of three subdetectors. These are LV.-r 00 (LOO), which sits directly

around the beryllium beam pipe at a radius of 1.5 cm from the colliding beams, the

Silicon Vertex detector (SVX-II), composed of five concentric silicon l-v.-ri between radii

Table 4-1. The resolution of track Az parameter evaluated for different categories of tracks
based on the number of SVX and COT hits.
Algorithm crAz, cm
COT-only 1.20
Inside-Out (10) 0.60
Outside-In ro 1.80
Kalman Outside-In rf 1.80
Outside-In stereo 0.40
Kalman Outside-In stereo 0.40
Outside-In 3D 0.21
Kalman Outside-In 3D 0.21
SVX Only 0.78

Tracks coming from 7-conversions and Ko and A decays are removed using a

combination of cuts on impact parameter and the distance Rc,,m (see Fig 4-5). The impact

parameter is defined as the shortest distance in the r-Q plane between the interaction

point and the trajectory of the particle. It can be shown that for electrons and positrons

originating from 7-conversions

R.m, V ,' (4-1)

where pr is the transverse momentum of the charged particle in GeV/c, B is the magnetic

field in Tesla and Rcmv is measured in meters. Monte Carlo studies have shown that

placing the requirements Idol < 5 ado or Rcmv < 13 cm on tracks is more efficient

in removing this background than either of these cuts alone. Incidentally, the value

Rcmv 13 cm is motivated by the location of SVX port cards where a 1i i i i ly of

these secondary interactions occur in the MC simulations and data. The resolution of

the impact parameter, ado, varies for different types of tracks based on the number of

SVX and COT hits. Distributions of the impact parameter for tracks from different

reconstruction algorithms are shown in Fig. 4-6. The measured values of d0o are

summarized in Table 4-2.

To verify the effectiveness of the track quality cuts, we compare the inclusive particle

multiplicity and momentum distributions in Pythia Tune A Monte Carlo for charged







L 5 10 15 20 25 30

Figure 4-7.

Monte Carlo track multiplicity in jets before and after track quality cuts.
Particles are counted within a cone of opening angle Oc = 0.5 radians. The
label "CDF im, refers to MC after full detector simulation.

Pythia Tune A
CDFSim tracks
CDFSim tracks

charged hadrons
before cuts
after cuts

0 1 2 3 4 5 6

Figure 4-8. Inclusive momentum distribution of Monte Carlo tracks in jets before and
after track quality cuts. Particles are counted within a cone of opening angle
Oc = 0.5 radians.


0 Pythia Tune A charged hadrons
A CDFSim tracks before cuts
SCDFSim tracks after cuts

- AA


-- A


- -v A
J It A- 1. I .. I . I . I '^ -t A A -A 1

Q=50 GeV



_.-A- -AA -A-_A

-A- -A- A
_A __- __ __ ._ -__ a-

_- -A-

-.- -A-
_ -T-

II .
: -A-
I . I . I . I Jft ^A


In this chapter we present the experimental results of the measurement of event

shapes in pp collisions at /= 1.96 TeV. The results are compared to resumed

theoretical predictions that have been matched to fixed order results both of which are at

"next-to-leading; accuracy. Comparison to PYTHIA Monte Carlo with a tuned underlying

event are also presented.

The distributions of the transverse thrust and thrust minor, uncorrected for detector

effects, are presented in Figure 5-1 for the leading jet energies 100, 150, 200, and 300

GeV. The distributions in data are shifted by roughly a constant amount relative to the

distributions in PYTHIA Tune A after detector simulation; however, the over-all shape is

well reproduced by the MC. Both Data and PYTHIA Tune A show significant departures

in shape relative to the distributions provided by theorists, which do not incorporate an

underlying event.

The evolution of the mean values of these two observables is presented in Figure 5-2.

Here, again, the data have not been unfolded to the particle level. These plots highlight

the relatively small detector effects in the measurement of the transverse thrust and thrust

minor as well as the comparatively larger, but roughly constant offset between data and


Finally, Figure 5-3 shows the weighted difference between the mean values of the

transverse thrust and thrust minor as a function of the leading jet ET. This observable

ultimately allows for a direct comparison between data and the dedicated predictions

of theorists (labeled 'CAESAR + NLO') which do not incorporate an underlying event.

In this plot detector effects have been accounted for; to reflect this, the data is labeled

Unfolded". The figure shows good general agreement between theorists predictions,

Pythia Tune A, and data.

expanded cone. The expanded cone is not iterated for stability. This procedure of finding

stable cones is applied to every object in the seed list.

Additional seeds are added at the midpoint between all protojets whose separation

in TI 0 space is less than 2Rce,. A cone of radius R = Rce, is then drawn around the

midpoint seed and iterated until a stable configuration is found. If this configuration is not

in the list of protojets it is added to the list. After all midpoint seeds have been iterated

to stable cone configurations the list of protojets is complete.

In this procedure, there is the possibility of overlap between protojets. In order to

ensure that the same object is not included in more than one jet, overlapping protojets

are either split or merged. If the pr of the four-vector sum of shared objects between two

protojets is more than the fraction fmerge = 0.75 of the protojet with lower pr then the

two protojets are merged. If it is less, then the shared objects between the two protojets

are split and assigned to a closer cone in TI ( space.

3.3.2 Jet Corrections

As mentioned in the previous section, jets at the detector level are constructed from

i (uncorrected) calorimeter tower information. However, the measured jet energy

must be corrected to compensate for non-linearity and non-uniformity in the energy

response of the calorimeter. Moreover, in order to compare to pQCD predictions, which

do not take into account the presence of an underlying event, the energy deposited inside

the jet cone from sources other than the leading parton must be subtracted. Similarly,

hadronization or secondary interactions with detector material, may result in a situation

where energy associated with the leading parton spills outside the jet cone at the detector

level. These various effects and the corrections applied to the measured jet energies are

reviewed below. A more detailed description of the corrections can be found in [38].

The first step in correcting the jet energy is to remove any non-uniformity in qI from

the calorimeter response. This correction is particularly important in uninstrumented

The CDF-II detector, hereafter referred to as CDF, is actually comprised of a number

of different sub-detectors which are specialized to measure various properties of the

particles emitted in each collision. From the inside out, the primary components are:

the tracking system, magnetic solenoid, electromagnetic and hadronic calorimeters, and

the muon detectors. In addition, there is also a Time-of-Flight (TOF) system, which

expands CDF's particle identification capability in the low transverse moment region; and

Cerenkov Luminosity Counter (CLC) designed to measure the instantaneous luminosity at

CDF. Before beginning a more detailed description of the detector components relevant to

this dissertation, we review conventions and coordinate systems employ, ,1 at CDF.

3.2.1 The CDF Coordinate System

Because of its axial symmetry about the beam pipe, CDF uses a cylindrical

coordinate system (r, Q, z) with the origin at the center of the detector and the z axis

along the direction of the proton beam. In cases where a rectangular coordinate system

is simpler, the y axis points upward which by right-handededness defines the direction of

the x' axis. The plane perpendicular to the beam (i.e., the x-y plane) is referred to as the

transverse plane, while the projection of a particle's momentum vector onto this plane is

called the transverse momentum pr.

Projections of various quantities onto the transverse plane are commonly used in CDF

analyses for multiple reasons. In the relatively clean environment of e+e- colliders, the

point like leptons annihilate completely such that the initial momentum of the resulting

system along the longitudinal (z) direction is known. By contrast, the pp collisions in

the Tevatron are the result of interactions between the constituent quarks or gluons

which carry an indeterminate fraction of the particles' total momentum. As a result, the

center-of-mass frame of the parton collisions is boosted along the beam direction by an

unknown amount. However, because the transverse moment of the partons are negligible,

the center of mass can be considered at rest in this plane.

i |1jet I 0.7
ES : |[ < 3.5

Leading Jet ET> 100 GeV
Tune A Hadron
Tune A + CDF Sim

Ijt |Ir 0.7 Leading Jet ET > 200 GeV
Tune A Hadron
Tune A + CDF Sim
--- Data


I~t |r 0.7 Leading Jet ET > 300 GeV
Tune A Hadron
Tune A+ CDF Sim
-- Data

0.1 0.2 0.3

ISetl< 0.7
ES : |I < 3.5

Leading Jet ET> 100 GeV
Tune A Hadron
Tune A + CDF Sim

X = TMin

X = TMin

X = TMin

"'-a| Ietl< 0.7
1- 2 ES : || < 3.5

Leading Jet ET > 300 GeV
- Tune A Hadron
- Tune A + CDF Sim
- Data

v v

0.2 0.4 0.6
X = TMin

Figure 5-1.

Distributions of the transverse thrust and thrust minor for leading jet energies

100, 150, 200, and 300 GeV. Comparison is made between theoretical

predictions at (NLO+NLL) accuracy, PYTHIA Tune A at the hadron level as

well as after detector simulation, and Data.

5 Leading Jet ET > 100 GeV
Ca 5000-


no dz,do,Rconv, Cut
Tracks h| < 1.1
-5000I . I ,
0 1 2 3
X = OnT

Figure 4-11. Difference between Data and Monte Carlo in the distribution of tracks as a
function of the angle between the 2D track pr and the transverse thrust axis
nT over the entire central region |ITI < 1.1

At the level of the calorimeter, these additional particles from secondary interactions

appear as if they are simply part of the underlying event. In effect, they make events look

broader than they actually are. However, we anticipate this additional contribution to

cancel-out in the final observable constructed in Ch'! pter 2 (i.e., in the weighted difference

of the mean values of the transverse thrust and thrust minor).

4.5 Detector Effects

In general, the measurement of the event shapes may be distorted by the finite

position and energy resolution of the detector. In this section we attempt to understand,

at least qualitatively, how our detector instrumentation affects the observables measured.

Figure 4-14 shows the mean values of the transverse thrust and thrust minor as a function

of the leading jet energy for Pythia Tune A at the hadron level and at the calorimeter

level after full CDF detector simulation. The plot indicates the relatively small cumulative

effect of the detector on the observables. The corresponding plot of the weighted difference

Full Text








Inthecourseofwritingthisdissertation,ithasbecomeoverwhelminglyobvioustomethemultitudeofpeopletowhichIamindebted.Andunfortunately,asIsitdowntowritetheseacknowledgementsIampainfullyawareofrst,myownshortcomingsasawriter,andsecond,thelimitedspaceIhavetothanksomany.Andso,aswithmostendeavorsinmylife,Iundertakethewritingoftheseacknowledgementswithsomeanxiety.Firstandforemost,IwouldliketothankthecountlessscientiststhathavecontributedtotheCDFcollaborationandtotheoperationoftheTevatronaccelerator.WhenIstoptothinkaboutthecomplexityofcollidingsubatomicparticlesatsuchhighratesandthededicationrequiredtomaintainthedetectorsthatrecordthesecollisionsIamhumbled.Itliterallytakeshundredsofpeopleworkinginconcerttoachievesuchafeat.Thatafewbrilliantmindshadtheclarityofvisiontobelieveitcouldbedoneandthecouragetogatherthewherewithaltobuildsuchaninstrumentistrulyinspiring.Itwouldbeabrutishoversightnottospecicallythankheremyadvisor,ProfessorAndreyKorytov,whosuggestedeventshapesasathesistopic.Hispatience,optimism,andencouragementwereoftensourcesofgreatcomfort.Needlesstosay,hisguidanceoverthepastthreeyearsisinthepagesofthisdissertation.Iammostindebtedtomyfriendandoce-mateSergoJindarianiandhiswonderfulwifeOksana.WhetherdiscussingthenerpointsofjetfragmentationorourshareddreamofmanagingaPublixsupermarket,Sergo'sknowledgeandhumilityhavealwaysbroughtperspectivetomyownthoughts.Hisdailypresencehasbeensorelymissedthispastyear.ManythanksarealsoduetoCraigandNicoleGroupfortheirfriendshipandsupport.Craig'spositiveattitudeinthefaceofdiculttimeswasannoyingtosaytheleast,butmoreoftenthannot,justwhatIneededtogetthroughtheday.IcannotimaginehavingsurvivedmyyearsatFermilabwithoutallfourofyou.MazalTov!BeingapartoftheUniversityofFloridaHighEnergyExperimentalgroup,Ialsohadtheprivilegeofworkingdirectlywithanumberoftalentedscientists;particularly,Roberto 4


Throughoutmylife,Ihavehadthegoodfortuneofbeingsurroundedbypositivepeoplewhohaveinspiredandmotivatedme.Itwouldbeimpudentnottothankthemherealso.Thesearepeoplewhowerenotdirectlyinvolvedinthisresearch,butwithoutwhomthisdissertationcouldnothavebeenwritten.First,IwouldliketothankmygreatfriendTonyCuadra,whotooka1500mileroadtripwithmewhenitmatteredmost{yourattemptstocoveryourgeniuswithrecklessabandonarenotfoolinganyone.ToJonLawrence,whomakesthebestpadthaithissideofBangkok,yourfriendshipandsupporthavehelpedmethroughsometoughtimes.ToShawnAllgeier,whostillwrestlesbearsnakedinthewoods,onedayyouwillwinandwhenyoudoIwillbetheretositonyou.ToAlexandraKingandhercousinBeckySue,thankyouformakingmelaughandpleasestopinbreeding.ToEdKazyanskaya,who'sgraduatecareerhasunfortunatelyparalleledmineintoomanyways,thankyouforunderstanding,andbelievemewhenIsaythebestisyettocome.ToSagarMungekar,who'sskewedmemoryhaslentitselftosomeofthefunniestwritingsIhaveeverread,thankyouforremindingmeofallthegreattimesI'vehad.AndtoRebeccaHyde,whohasknownmebetterthanmostanyone,thankyoufornotrunningawaysomanyyearsago.Becausesomuchinlifedependsonwhereyoustart,Ihavetotakethisopportunitytoalsothankmyfamily.Iamimmenselygratefulforhavingbeenbornintosuchalovingandcaringgroup.Tohavesuchaconcentrationofgood,decent,hard-workingpeopleinyourcampcannotbetheresultofchanceorcoincidence;andso,IbeginbythankingthegrandparentsIbarelyknew{RamonandRitaLlanes,whosevaluesareinthe13 5




page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 LISTOFSYMBOLS .................................... 14 ABSTRACT ........................................ 15 CHAPTER 1INTRODUCTION .................................. 16 1.1TheStandardModelofParticlePhysics ................... 17 1.2QuantumChromodynamics .......................... 20 1.3StructureofHadronicCollisions ........................ 22 2EVENTSHAPES ................................... 25 2.1MotivationandHistoricalPerspective ..................... 25 2.2EventShapeObservables ............................ 27 2.2.1TransverseThrust ............................ 27 2.2.2TransverseThrustMinor ........................ 27 2.3TheoreticalPredictions ............................. 29 2.3.1FixedOrderCalculations ........................ 30 2.3.2SoftQCDRadiation&Resummation ................. 31 2.3.3MatchingFixedOrder&ResummedResults ............. 34 2.4MonteCarloGenerators ............................ 34 2.4.1QCD2to2 ............................... 35 2.4.2PartonShowers ............................. 37 2.4.3Hadronization .............................. 37 2.4.4CDFSimulation ............................. 38 2.5TreatmentofUnderlyingEvent ........................ 38 2.6NLL+NLOvsPYTHIA ............................ 40 2.7PYTHIATuneA ................................ 41 3EXPERIMENTALAPPARATUS .......................... 48 3.1Accelerator ................................... 48 3.1.1ProtonSource .............................. 48 3.1.2MainInjector .............................. 50 3.1.3AntiprotonSource ............................ 50 3.1.4Tevatron ................................. 51 3.2TheCDFIIDetector .............................. 54 7


...................... 56 3.2.2TrackingandVertexingSystems .................... 57 3.2.3Calorimetry ............................... 62 3.2.4CerenkovLuminosityCounters ..................... 65 3.2.5TriggerSystemandDataAcquisition ................. 68 3.2.6GoodRunRequirements ........................ 71 3.3JetReconstruction ............................... 71 3.3.1JetClustering .............................. 72 3.3.2JetCorrections ............................. 73 4ANALYSISOFTHEDATA ............................. 77 4.1DataSamples .................................. 77 4.2EventSelection ................................. 78 4.3CalorimeterTowers ............................... 78 4.4Tracks:jj<1:1 ................................ 79 4.5DetectorEects ................................. 87 4.6SystematicUncertainty ............................. 91 4.6.1JetEnergyScale ............................. 93 4.6.2ContainmentintheDetector ...................... 93 4.6.3AcceleratorInducedBackgrounds ................... 95 5RESULTS ....................................... 96 6CONCLUSIONS ................................... 100 REFERENCES ....................................... 102 BIOGRAPHICALSKETCH ................................ 104 8


Table page 1-1SummaryofgaugebosonpropertiesoftheStandardModel. ........... 18 1-2Summaryofleptonproperties. ............................ 19 1-3Summaryofquarkproperties. ............................ 20 3-1SummaryofcurrentTevatronperformancecharacteristics. ............ 54 3-2AmountofmaterialintheCDFIItrackingvolumeascitedinthedetector'stechnicaldesignreport.Thequotedthicknessassumesnormalincidence. .... 63 3-3CalorimetersegmentationoftheCDFIIdetector. ................. 64 3-4SummaryofquantitiescharacterizingCDFIIcalorimetry.Thicknessesarelistedintermsofradiation(Xo)orinteraction()lengths.Thesymbolindicatesaconstantresolutiontermtobeaddedinquadraturetotheenergydependentterm. .......................................... 66 4-1TheresolutionoftrackzparameterevaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. .................... 82 4-2Theresolutionoftheimpactparameter,d0,evaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. ............... 84 9


Figure page 1-1Diagramofgluonemissionoaquarkwithmomentum~p. ............ 23 2-1Athree-jeteventapproachingthetwo-jetlimit. .................. 28 2-2Colinearbranchingofpartonswithinathree-jetevent. .............. 30 2-3Acartoondescriptionofthestagesofaneventsimulation. ............ 36 2-4RatioofthemeanvaluesofthePpTofparticlesbetweenPythiawithandwithoutmultiplepartoninteractionsasafunctionoftheleadingjetenergy. ....... 40 2-5Distributionsofthetransversethrustandthrustminorforleadingjetenergies100,150,200,and300GeV.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithoutanUE. ............. 42 2-6Evolutionofthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithoutanUE. ............. 43 2-7Theweighteddierenceofthemeanvaluesofthrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithoutanUE. ............. 44 2-8Distributionsofthetransversethrustandthrustminorforleadingjetenergies100,150,200,and300GeV.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithandwithoutanUE. ........ 45 2-9Evolutionofthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithandwithoutanUE. ........ 46 2-10Theweighteddierenceofthemeanvaluesoftransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithandwithoutanUE. .. 47 3-1AschematicpictureoftheacceleratorchainatFermilab. ............. 49 3-2ProtonandantiprotonbeamstructureattheTevatron.Eachbeamisdividedintothree\trains"whichareseparatedbyanabortgap. ............. 52 3-3TotalintegratedluminositydeliveredbytheTevatronsincethebeginningofRunII.Alsoshown,istheliveluminosity,labeled\Totape",whichexcludesintegratedluminosityduringdetectordead-times. ................. 53 3-4DiagramoftheCDFIIdetectorwithaquadrantremovedandazoomed-inviewoftheinnersubdetectors. .............................. 55 10


. 58 3-6Cross-sectionalviewsofCOTsuperlayersandindividualwiresinthreeCOTcells.Theanglebetweenwire-planeofthecentralcellandtheradialdirectionis35. ......................................... 59 3-7SchematicoftheSVXbulkheaddesign. ....................... 62 3-8SchematicpictureofonequadrantoftheCDFcalorimeter. ............ 64 3-9TheCerenkovLuminosityCounteratCDF.Thedetectormodulesarelocatedinthe\3-degreeholes"oftheeastandwestmodules. ............... 67 3-10FunctionalblockdiagramoftheCDFdataow. .................. 69 3-11Theratioofthetransversemomentaof\probe"and\trigger"jetsusingthe20GeVjetsample.Thecurvesareobtainedusingtwodierentmethods:themissingETprojectionfraction(red)andthedijetbalancetechnique(black).The\probe"triggerjetisrequiredtobeintheregion0:2

..................... 85 4-8InclusivemomentumdistributionofMonteCarlotracksinjetsbeforeandaftertrackqualitycuts.Particlesarecountedwithinaconeofopeninganglec=0:5radians. ........................................ 85 4-9DistributioninofMCchargedhadronsrelativetothetransversethrustaxis,comparedtothesamedistributionsinMCtracksafterfulldetectorsimulation. 86 4-10InclusivemomentumdistributionsofPythiaTuneAtracksfortheentirecentralregionjj<1:1 .................................... 86 4-11DierencebetweenDataandMonteCarlointhedistributionoftracksasafunctionoftheanglebetweenthe2DtrackpTandthetransversethrustaxisnTovertheentirecentralregionjj<1:1 ............................ 87 4-12RelativedierencebetweenDataandMonteCarlointhedistributionoftracksasafunctionoftheanglebetweenthe2DtrackpTandthetransversethrustaxisnTovertheentirecentralregionjj<1:1 ................... 88 4-13RelativedierencebetweenDataandMonteCarlointhedistributionoftowersasafunctionoftheanglebetweenthe2DtowerpTandthetransversethrustaxisnToverthecentralregionjj<1:1 ....................... 88 4-14TheeectofCDFdetectorsimulationonthetransverseThrust(top)andThrustMinor(bottom). ................................... 89 4-15TheeectofCDFdetectorsimulationonthenalobservableconstructed,theweighteddierenceinthemeanvaluesofthetransversethrustandthrustminor. 90 4-16Contributionofisolatedinstrumentaleectsonthetransversethrustandthrustminor. ......................................... 92 4-17Contributionofisolatedinstrumentaleectsontheweighteddierenceofthemeanvaluesofthetransversethrustandthrustminor. .............. 93 4-18EectoftowerETthresholdonthemeanvaluesofthethetransversethrustandthrustminorplottedagainsttheleadingjetenergy. .............. 94 4-19EectofthetowerETthresholdontheweighteddierenceinthemeanvaluesofthetransversethrustandthrustminor. ..................... 95 5-1Distributionsofthetransversethrustandthrustminorforleadingjetenergies100,150,200,and300GeV.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracy,PYTHIATuneAatthehadronlevelaswellasafterdetectorsimulation,andData. ............................ 97 12


............................ 98 5-3PlotoftheweighteddierenceofthemeanvaluesofThrustandThrustMinorasafunctionoftheleadingjetenergyforCAESAR+NLO,PYTHIATuneAattheHadronlevelandDataunfoldedtotheparticlelevel. ............. 99 13






1 2 ],thetheoryisnotwithoutitsownpeculiarities.Itincludespointlikeparticlesjustliketheelectron,buthundredsoftimesheavieraswellasparticleswithfractionalelectricchargeandinternalquantum 16


3 ]{whichistosaythatitisamarriageofquantummechanicsandspecialrelativity.Inthisview,interactionsaredescribedbythediscreteexchangeofbosons(i:e:,particlesofintegerspin).Theelectromagneticforceismediatedbymasslessphotons()whoseeectsareobservedfromsubatomictomacroscopicdistances.Theweakforceiscarriedbythreebosons(WandZ)whicharemassive,afactwhichultimatelylimitstherangeofitsinuencetosubatomicdistances.Furthermore,theWcarrieselectricchargeandthereforealsocouplestotheelectromagneticinteractions 17


SummaryofgaugebosonpropertiesoftheStandardModel. BosonSpinElectricchargeMass Photon()100W1180.398GeV/c2Z1091.1876GeV/c2Gluon(g)100 distances;however,thisisaconsequenceofthegaugestructureofthestronginteractions 1-1 .IntheStandardModelallmatterismadeupofspin1/2fermionswhichmustthereforeobeythePauliexclusionprinciple[ 4 ].Thesepoint-likeparticlesareclassiedaseitherleptonsorquarksandaregroupedintothreegenerationsofdoubletswithsuccessivelylargermasses.Particlesofthehighergenerationsareunstableandthereforedecaytolessmassiveparticlesofthelowergenerations.Thevisibleuniverseisprimarilycomposedofparticlesfromtherst,least-massivegroup.Curiously,theStandardModeloersnoexplanationastowhynatureisgroupedintothesegenerations.Theleptonsaresixinnumberandinteractexclusivelyviatheelectricandweakforces.Themuon()andtau()areidenticaltotheelectron(e)exceptforthefactthattheyarerespectively200and2500timesheavier.Inadditiontothesethreechargedleptons,therearethreecorrespondingneutralleptonsknownasneutrinos(e,,)whosemassesareallverysmall.Furthermore,theircross-sectionsforinteractingwithmatterarevanishinglysmallandsotheirdirectreconstructioninexperimentisdicult.ThepropertiesofleptonsaresummarizedinTable 1-2 .ThesecondclassoffermionicmatterintheStandardModelareknownasquarks.Theseparticlescomeinsixavours:up(u),down(d),strange(s),charm(c),bottom(b),andtop(t).Theyareuniqueinthattheyparticipateinalltheknownforcesandarethe 18


Summaryofleptonproperties. ParticleSpinChargeMass 1stGeneratione1/2-10.511MeV/c2e1/20<3106 3rdGeneration1/2-11777MeV/c21/20<18.2 onlymattereldstointeractviathestrongforce.Eachofthesixquarkscarriesoneofthreequantumnumbersmetaphoricallyknownascolourandusuallydenotedred,blue,andgreen 5 ].Ofthemesons,pionsarethemostcommon,buteventheirlifetimesareshort(<107s).ThepropertiesofquarksaresummarizedinTable 1-3 .TheonlyparticlepredictedbytheStandardModelyettobediscoveredistheHiggsboson(H).Itistheonlyscalarparticleinthetheoryandplaysakeyroleinexplainingtheoriginofmassforallotherelementaryparticles.ParticularlythedierencebetweenthemasslessphotonandtheveryheavyWandZbosons.TheHiggsmechanism[ 6 ]alsoprovidesameansofdynamicallygeneratingfermionmassesinagaugeinvariantway.ThesearchfortheStandardModelHiggsbosonremainsoneofthetopprioritiesattheTevatronandthefutureLargeHadronColliderexperiments. 19


Summaryofquarkproperties. ParticleSpinChargeMass 1stGenerationu1/22/31.5-4MeV/c2d1/2-1/34-8MeV/c2 7 ].However,intheirschematheexistenceofthe++particle,aspin3/2baryonbelievedtobeaboundstateofthreeuquarks,requiredtheintroductionofanadditionalquantumdegreeoffreedomknownas\colour"[ 8 ].Obviously,theintroductionofanadditionaldegreeoffreedomwouldleadtoaproliferationofstatesandsothecolourhypothesishadtobesupplementedwiththerequirementthatonlycoloursingletscouldexistinnature.Thefactthatthesesingletstateswerecomposedofeitherthreequarks(baryon)oraquarkanti-quarkpairs(meson)directlyleadtothemathematicalformulationofQCDasagaugetheorybasedonanSU(3)coloursymmetry.Formally,QCDisarenormalizablequantumeldtheory[ 3 ]constructedincloseanalogywithQuantumElectrodynamics(QED).Justasparticleswithelectricchargeinteractviatheexchangeofmasslessphotons,quarksinteractwitheachotherthroughtheexchangeofmasslessgluons.However,aprominentdierencebetweenthetwotheoriesisthatthegeneratorsoftheSU(3)gaugegroupdonotcommutewitheachother.Physically,thismeansthatthegluonsthemselvescarryacolourchargeandcaninteractwitheachother.Thegluon-gluoninteractionsofQCDhavenoanalogueinQEDandhaveverysignicantconsequencesforthetheory. 20


0ln(Q2=2QCD); where0=112nf=3,withnfbeingthenumberofquarkavors,andQCDistheenergyscaleatwhichthestrongcouplingdiverges.ThisphenomenaisknownasasymptoticfreedomandwasrstdiscoveredbyWilczek,Politzer,andGrossin1973[ 9 10 ].Conversely,atlowenergiesthestrengthofthecouplingappearstogrowwithout 21




Diagramofgluonemissionoaquarkwithmomentum~p. beejectedfromtheparticipatinghadronswithlargemomentatransversetothebeamdirection.Inthesecases,theprimaryinteractionoccursveryrapidlycomparedtotheinternaltime-scaleofthehadronwavefunctionandthemethodsofperturbativeQCDbecomeapplicable.Thisphaseofthehadroniccollisionisreferredtoasthehard-scatteringstageandistheoreticallycalculableatsomexed-orderinthestrongcoupling.Theejectedpartonsthenbeginradiatingsoftgluonswhichcaninturnsplitintoquarkanti-quarkpairsoremitfurthergluons.Considertheprobabilityofemittingagluonwithmomentumkandtransversemomentumk?relativetoahardscatteredquarkwithmomentump(seeFigure 1-1 ): 4[1+(1k p)2]dk kdk2? 23


11 ]. 24




12 ].However,itwasnotuntil1977thattheoristsrecognizedthatthis\maximumdirectedmomentum"representedacalculablequantityinperturbativeQCD.Itwasaroundthistimethateventshapestudiesbeganinearnestasasimple,quantitativewayofunderstandingthenatureofgluonbremsstrahlung.Infact,itwaseventshapeobservableswhichprovidedtherstindicationthatgluonswerevectorparticlesandnotscalars[ 13 ].Sincethen,eventshapeshaveenjoyedalongandimpressivehistoryate+eandDeepIneslaticScattering(DIS)experiments.Inthesetwoenvironmentstheyhaveprovidedaplethoraofmeasurementsofthestrongcoupling[ 14 ],aswellastestsofthecolourstructureofQCD[ 15 ],andvalidationofMonteCarlo(MC)eventgenerators[ 16 ].Moreover,they'veimprovedourunderstandingofthedynamicsofsoftpQCDandhaveevenprovidedinsightsintohadronizationthroughthestudyofpowercorrections[ 17 ],[ 18 ].Bycomparison,eventshapesathadroncollidershave,thusfar,receivedmuchlessattention.PrimarilybecausethepresenceoftheunderlyingeventcastssomedoubtastowhethertheseobservablescanevenbeusedtostudythedynamicsofpQCD,muchlessnon-perturbativecorrectionstothetheory.Thisdissertationrepresentstherstattempttomeasureglobaleventshapesatahadroncollider.Irrespectiveofwhetherdirectcomparisontotheoryispossible,themeasurementofeventshapesshouldprovideanadditionalmeansoftuningMCathadroncolliders. 26


wherethesumrunsoverallparticlesinthenalstateandthethrustaxis,~nT,isdenedastheunitvectorinthetransverseplanewhichmaximizesthisexpression.Foraperfectly\pencil-like"eventwithonly2outgoingparticles,T?=1.InthecaseofaperfectlyisotropiceventthetransversethrusttakesonthevalueT?=2 27


Athree-jeteventapproachingthetwo-jetlimit. Thethrustaxis~nTandthebeamdirection^ztogetherdenetheeventplaneinwhichtheprimaryhardscatteringoccurs.Thus,thethrustminorcanbeviewedasameasureoftheout-of-planetransversemomentum.Clearly,TMin=0forapencil-likeevent;whenthemomentumofbothparticlesisdirectedentirelyalongthethrustaxis.Foranisotropiceventthethrustminorassumesthevalue2 2-1 ,itbecomesclearthattheobservableshavedieringsensitivitiestotheopeningangle:1cos2 19 ]whosedenitionsincludesomedependenceonthelongitudinalcomponentofthenalstateparticles'momenta.However,preliminarystudiesshowedtheseobservablestobesensitivetodetectormismeasurement,particularlyintheforwardregions.Asaresult,wehavechosentofocusonthoseobservablesdenedexclusivelyinthetransverseplane. 28




Colinearbranchingofpartonswithinathree-jetevent. theobservableissmalltypicallycontainlargelogarithms{areectionoftheimportanceofsoftandcollinearemission.Asuccessfulpredictioninthisregionrequiresanall-orderresummedperturbativecalculation.Finally,thereisatleastonesignicantrestrictiononthetypeofobservablesthatarecalculablewithinperturbativeQCD(ineitherregime).Inordertoensurethecancellationofrealandvirtualdivergencesassociatedwithlow-energyradiation,observablesmusttobeinfraredandcollinear(IRC)safe;thatis,theobservablesmustbeinsensitivetotheemissionofasoftgluonorthebranchingofapartonintotwocollinearpartons(seeFig. 2-2 ).Thisrequirement,whichoriginallyemergedfromthediscussionsofStermanandWeinberg[ 20 ],hasprovenanecessaryconditionforguaranteeingniteperturbativepredictions.Moreover,thecriterionofIRCsafety,thoughposedontheoreticalgrounds,hasabasisinexperimentalreality{theresultsofameasurementshouldbeasinsensitiveaspossibletosmallchangesinadetector'sresolutionorgranularity.Bothoftheeventshapespresentedinthisdissertationaredenedtobeinfraredandcollinearsafe. =2 whereM(i!f)isthematrixelementconnectingstates`i'and`f'intheperturbedHamiltonian,andisthedensityofpossiblemomentumstatesinphasespaceforthe 30


{z }/N {z }/Ns+Xj2loopMj| {z }/N+1s+::: Calculatingthetransitionrate,andhencethedierentialcrosssectiond/dy,requiresmultiplyingthistotalmatrixelementbyitscomplexconjugate.Thisresultcanbecalculatedanalytically,butgiventhecomplexgaugestructureofQCDandthemultitudeoftreelevelscatteringcongurationspossibleatahadroncollider,thenumberofFeynmandiagramsthatneedtobeaccountedforateventhelowestorderissignicant.Asaresult,xedordercalculationsaretypicallyperformednumericallybyMonteCarlointegrationprograms.Withregardtoageneraleventshapeobservablesy,xedordercalculationsdiverge(atallorders)inthelimity!0.ThexedorderresultsshowninthisdissertationaretheobtainedviatheMCprogramNLOJET. 31


21 ].Inthisdissertation,wedealwithobservableswhichexponentiateandsoNpLLshallrefertothelattermeaning.Insomesense,resummationismerelyareorganizationoftheperturbativeexpansion;however,understandingwhichtermswillappear,howtoresumthem,andhowtocombine 32


22 ].Thetheoreticalpredictionspresentedherearetheproductofthe\ComputerAutomatedExpertSemi-AnalyticalResummer"(CAESAR).Atpresent,atechnicalrestrictionoftheseautomatedresummations,andindeedofallfullyNLLanalyticalresummations,isthattheobservablemustbeglobal,thatis,itmustbesensitivetoemissionsinalldirectionsincludingarbitrarilyclosetothebeamline.Thisrequirementisindirectconictwiththeexperimentalrealitiesofthehadroncolliderenvironment{namelythelimiteddetectorcoverageintheforwardregion.However,forsucientlylargevaluesofthemaximumaccessiblepseudo-rapidity 23 ]thatwouldultimatelybesignicantonlyatverysmallvalues.Forexample,thefullglobalpredictionsforthetransversethrustandthrustminorshouldremainvalidforlny.maxwheremaxisthemaximumdetectorcoverage[ 19 ].Itshouldbenotedthattheoristsrstproposedanalternativedenitionforeventshapesathadroncolliderstospecicallydealwiththeissueoflimiteddetectorcoverage.Asoriginallyenvisioned,theeventshapesweretobedenedoverparticlesinsomereducedcentralregionandrendered\indirectly"globalbytheadditiononaneventbyeventbasisofa\recoil"term.Suchatermwouldbedenedoverparticlemomentainthesamecentralregionastherestoftheobservablebutwouldintroduceanindirectsensitivitytomomentaoutsidethatregion.Theproposedrecoiltermwasessentiallythevectorsumofthetransversemomentainthiscentralregion(whichbyconservation 33


24 ].Suchprogramssimulatetheproductionanddevelopmentofindividualhadroniceventsaccordingtoprobabilitydensities. 34


25 ]tosimulatemultihadroniceventsinourdetector.Thesimulationofeacheventproceedsinfourdistinctstages;aschematicofwhichisshowninFig. 2-3 26 ].However,tobeclear,theMonteCarlosimulationusedinthisdissertation(PYTHIA)calculatesthehardscatteringatleadingorder.Aspreviouslynotedthough,predictionsprovidedbytheoristsincorporateNLOresults. 35


Acartoondescriptionofthestagesofaneventsimulation. 36


27 ].Thisisasystemofdierentialequationsdevisedtodescribethesequenceofemissionsfromapartonasitevolvesfromahardscatteringdowntolowerenergyscales.Theyarebasedonasetof\splittingkernels",Pa!bc(s,z),whichdenetheprobabilityofapartonasplittingtoproducepartonsbandcwiththemomentumfractionzand(1z)respectively.Themodelincludesvariousfeaturestoincorporatecoherenceeects,thesimplestofwhichisangularorderingwhichrequiresthattheopeninganglebcofeachbranching(a!bc)belessthanthatofthepreviousbranchinthecascade.TheshowercontinuesuntilthevirtualityofthepartonsreachessomelowerlimitQo,whichisatunableparametersetbydefaultto1GeV.Thenalpartoncongurationisthenpassedtothenon-perturbativehadronizationstage.AmoredetaileddiscussionofpartonshowerphysicscanbefoundinRef.[ 13 ]. 28 ].Unliketheelectromagneticeldpatternsformedbydistributionsofchargeandcurrent,thecorrespondingeldsinQCDareexpectedtobeconnedinnarrowregionsstretchedbetweencolourcharges;thisisaresultofthegluon'sselfcoupling.Accordingtothestringmodel,theeldlineswilleventually`break'atseveralpointstoformnewqqordiquark-antidiquarkpairswhichleadtomesonandbaryonproduction.ThemodelhasmanytunableparameterswhichhavebeensetbydefaulttovaluesdeterminedbytheLEPexperiments.Finally,someofthehadronsproducedareexpectedtodecayveryclosetotheinteractionpoint.TheMCitselftreatsparticleswithlifetimeslessthan31010stobe 37


5 ]. 29 ],withsomemodicationsdirectedatmakingthesimulationworkfaster.OncethedetectorisbuiltinthelanguageofGEANT,almostanykindofparticlecanbetrackedthroughitwithallappropriatephysicsprocessestakingplacetomimicthephysicaldetectorresponse.Someinteractionsarehandledwithspecicparametrizedmodels,suchasGFLASHshowersimulationpackage[ 30 ],tunedtosingleparticleresponseandshowershapebasedonthetestbeamandcollisiondata.The\raw"data(digitizedphysicaldetectorresponse)afterdetectorsimulationisfedtothealgorithmthatimplementstheactualtriggerlogictodecideiftheeventshouldbeaccepted.Theeventspassingthetriggersimulationgothroughproductionstage,inwhichthecollectionofphysicsobjects(tracks,jets,muons,etc.)arecreatedfromtherawdata. 38


2{1 )andthrustminor(Eq. 2{2 ).Separatingthenalstateintohardandsoftcomponentsandrecognizingthatthethrustaxisisdeterminedalmostentirelybythehardcomponent,thetransversethrustandthrustminorcanbewrittenapproximatelyas: whereHARDandUErepresenttheanglebetweenthethrustaxisandthehardandsoftcomponentsrespectively.Thecontributionoftheunderlyingeventisexpectedtobeonaverageuniformoverthetransverseplane;therefore, Takingaweighteddierencebetweenthemeanvaluesofthethrustandthrustminorwearriveatanexpressionwhosenumeratorisindependentoftheunderlyingevent.hTMinihi0@XqHARD?jsinHARDj 39


RatioofthemeanvaluesofthePpTofparticlesbetweenPythiawithandwithoutmultiplepartoninteractionsasafunctionoftheleadingjetenergy. basedonMonteCarlogeneratedwithandwithoutMPItoproduceanexpressionentirelyindependentoftheUE. thenwecandeneanewquantity: ThefactorMCisplottedinFigure 2-4 asafunctionoftheleadingjetenergy.Finally,itistheevolutionofthisquantityasafunctionofleadingjetETthatwillallowforameaningfulcomparisonbetweenDataandtheorists'predictions. 2-5 showsacomparisonofthedistributionsofTransverseThrustandThrustMinorbetweendedicatedtheoreticalprediction,labeled\CAESAR+NLO",andPYTHIAatthepartonlevelandafterhadronization.Theseplotsrevealthatapartfromashiftawayfromthe2-jetlimitovernearlytheentirerangeofthevariables,theMonteCarlo 40


2-6 whichshowsthemeanvaluesoftheobservablesasafunctionoftheleadingjetET.Wenotethatthediscrepancybetweentheorists'predicationsandPYTHIAatthepartonleveldecreaseswithincreasingjetenergy.ThisdierenceislikelytheresultoftheamountofISRpresentintheMCwhichissettotheTuneAsetting(Parp[67]=4),butmayalsobetheresultoftherelativelylargepartonshowercuto(Qo=1GeV)intheMC 18 ].Finally,though,weseethatthesediscrepanciesvanishfromthenalobservableconstructed,C(hi;hTMini),(seeFig. 2-7 ). 31 ]whichutilizesmultiplepartoninteractionstoenhancetheactivityoftheunderlyingevent.Theparametersofthissimulationhavebeentunedtoreproducethechargedparticlemultiplicityandmomentumspectrumintheregionawayfromjets.Figure 2-8 showsacomparisonoftheeventshapedistributionsbetweentheorists'predictions,PYTHIAwithoutMPI,andTuneA.Clearly,theunderlyingeventnotonlyshiftsthemeanstowardshighervalues,butalsosignicantlydistortstheover-allshapeofthedistributions.Turningtotheplotofthemeanvaluesasafunctionofleadingjet 41


Distributionsofthetransversethrustandthrustminorforleadingjetenergies100,150,200,and300GeV.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithoutanUE. 42


Evolutionofthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithoutanUE. energy,Fig. 2-9 ,weobserveincomparingTuneAatthepartonandhadronlevels,thattheunderlyingeventappearstodampentheeectsofhadronizationonthedistributions.Insomesense,theadditionalparticlesfromtheunderlyingeventsaturatetheeventshapesdistributionstoapointwherethe\re-shuing"ofmomentathatoccursathadronizationhaslittleeectontheobservable.Finally,wenotethatinthenalobservableconstructed,C(hi;hTMini),thecontributionfromtheunderlyingeventcancels(asexpected)andgoodagreementisseenbetweentheorists'predictionsandPythiaTuneA. 43


Theweighteddierenceofthemeanvaluesofthrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithoutanUE. 44


Distributionsofthetransversethrustandthrustminorforleadingjetenergies100,150,200,and300GeV.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithandwithoutanUE. 45


Evolutionofthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithandwithoutanUE. 46


Theweighteddierenceofthemeanvaluesoftransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracyandPYTHIAwithandwithoutanUE. 47


3-1 48


AschematicpictureoftheacceleratorchainatFermilab. gastoproduceH.Theseionsarethenacceleratedbyapositivepotentialtoanenergyof750keV.Theythenenteralinearaccelerator(Linac)approximately150mlongwhereoscillatingelectriceldsacceleratethenegativehydrogenionsto400MeV.InordertokeepparticlesinphasewiththeRFeld,thebeamisnaturallyseparatedintodiscretepacketsintimeknownasbunches.AtthispointtheHionsarepassedthroughaseriesofgraphitefoilsthatstripthemoftheirelectronsleavingonlypositivelychargedprotons.TheprotonsaretheninjectedintotheBooster,anintermediateenergysynchrotronapproximately75metersinradius.Atthisstage,dipolemagnetssteerthebeamofprotonssothattheytravelinanearcircularorbitwhilequadrupolemagnetsfocusthebeamintheplaneperpendiculartoitsdirection.SeveralLinaccyclesareinjectedintotheBoostertoincreasetheprotonbeamintensity.Eachbunchwillmakenearly20,000orbitsaroundtheBoosterasRFcavitiesacceleratetheprotonsto8GeV. 49






ProtonandantiprotonbeamstructureattheTevatron.Eachbeamisdividedintothree\trains"whichareseparatedbyanabortgap. bunches.Eachtrainisfollowedbyanabortgapwhosepresenceismeanttoensureasaferemovalofthebeamshouldconditionsbecomeunstable.ThebeamcongurationisillustratedinFig. 3-2 .Finally,thebeamsarefocusedtointeractatcollisionpointswherethetwomajordetectorsarecentered,withabunchcrossingoccurringevery396ns.Thecriticalquantityfordeterminingtherateofcollisionsisthebeamluminosity,whichmaybeexpressedas, (3{1) wherefBisthebunchrevolutionfrequency,NBisthenumberofbunchesperbeam;Np(Np)isthenumberofprotons(antiprotons)perbunch,andpandparetheaveragecross-sectionalareasofthebunches.Indiscussionsofinstantaneousacceleratorperformancetheluminosityisoftengiveninunitsof[cm2s1].Foragivenphysicalprocesswithcross-section,theluminosity(L)willyieldthatinteractionatarateof 52


TotalintegratedluminositydeliveredbytheTevatronsincethebeginningofRunII.Alsoshown,istheliveluminosity,labeled\Totape",whichexcludesintegratedluminosityduringdetectordead-times. withsigmain[cm2]andRin[Hz].Thisquantitygivesrisetointegratedluminositywhichbettercharacterizestheamountofdatadeliveredovertime.Thecrosssectionforsomeprocessistypicallyquotedinunitscalled\barns"(1b=1028m2)andsointegratedluminosityismoreoftenquotedinunitsofinversecross-section.ThetotalintegratedluminositymeasuredatCDFsincethebeginningofRunIIisshowninFig. 3-3 .Theliveluminosity,whichexcludesintegratedluminosityduringalldetectordead-timesisalsoshown.RecentperformancehastheTevatronregularlyachievingpeakluminositiesof2.5-2.751032cm2s1.Theinstantaneousluminosityisatit'speakatthebeginningofastorewhenthebeamsinitiallybegincollidinganddecreasesapproximatelyexponentiallywith 53


SummaryofcurrentTevatronperformancecharacteristics. center-of-massenergy1.96TeVbunchcrossingseparation396nsnumberofprotonsperbunch240109numberofantiprotonsperbunch25109peakluminosity2901030cm2s1 3-1 .ThedesigngoalfortheTevatronistocollect8fb1bytheendof2009. 32 ],oneofthetwoprincipledetectorslocatedontheTevatronring.ThegenericnatureofCDF'sfullname,\ColliderDetectoratFermilab"reectsthefactthatitwastherstdetectorbuiltattheTevatronfortheppera.TheCDF-IInamereferstothepresentincarnationofthedetector,whichunderwentmajorupgradesinmanyofit'scomponentstocoincidewiththeTevatron'sincreasedcollissionrateandcenterofmassenergyduringRunII.Thedetectoriscapableofprecisionmeasurementsoftheenergy,momentum,andpositionofparticlesproducedinppcollisions.Ratherthanbeingdesignedforonespecicclassofhigh-energyphysicsmeasurement,CDFisdesignedtobeaversatile\multi-purpose"detectorcapableofstudyingmanyfundamentalprocesses.Thedetectorisaxiallysymmetricaboutthebeamlinecoveringalmostallsolidanglesexceptthoseclosestinangletothebeam.Itisabout10metershigh,extendsabout27metersfromendtoend,andweighsover5000tons.AdiagramoftheCDF-IIdetectorisshowninFig. 3-4 54


DiagramoftheCDFIIdetectorwithaquadrantremovedandazoomed-inviewoftheinnersubdetectors. 55




Intherelativisiticlimit(pcmc2)whenparticlemassescanbeneglected,pseudorapidityisequivalenttotheLorentzinvariantquantitycalledrapidityy=1 2ln(E+pz 57


Schematicr-zviewoftheCDFtrackingsystemandsurroundingsubdetectors. of2.5an10.6cm,andtheIntermediateSiliconLayers(ISL)consistingofonelayerat22cminthecentralregionandtwolayersat20and28cmintheforwardregions.ThesiliconlayersarethensurroundedbytheCentralOuterTracker(COT),a3.1mlongdriftchamberextendingfromaradiusof40to137cm.Figure 3-5 isaschematicofonequadrantoftheCDFtrackingsystemintherzplane.Thetotalsystemisreferredtoasthe\integrated"trackingsystem.Inadditiontoaccuratelydeterminingthemomentaofchargedparticles,thetrackingsystemalsoprovidesameansofdeterminingthelocationsofdecayandinteractionvertices.CentralOuterTrackerTheCOTistheanchoroftheCDFIItrackingsystem.Itprovidesprecisemeasurementsofthetransversemomentumofchargedparticlesinthecentralregionjj<1:0.Thedetectorisacylindricaldriftchamberwhosevolumebeginsat40cmfromthebeampipeandextendsradiallyto138cm.Thechamberspans310cminlengthalongthe^zdirectionandisimmersedina1.4Tmagneticeld.Furthermore,thedetectorislledwitha 58


Cross-sectionalviewsofCOTsuperlayersandindividualwiresinthreeCOTcells.Theanglebetweenwire-planeofthecentralcellandtheradialdirectionis35. \fast-gas"mixtureofargon,ethane,andisopropylalcoholwhichprovidesasmallenoughdrifttime(200ns)toallowhitread-outbetweenTevatronbunchcrossings.TheCOTconsistsof30,240sensewiresarrangedinto96layerswhicharegroupedradiallyintoeightsuperlayers,asdepictedinFig. 3-6 .Thesuperlayersaredividedazimuthallyintocells,eachwith12sensewiresheldatpotentialsbetween2.6-3.0kV.Inordertomaintainamaximumdriftdistanceof88cmbetweenwires,thenumberofcellspersuperlayerisrequiredtoscalewithradius.Thesensewiresineven-numberedsuperlayersarestrungparalleltothezdirection,therebyprovidingresolutioninthetransverseplane,whileodd-numberedsuperlayersusestereowiresstrungatsmallangles(2)withrespecttothezdirectionallowingforlongitudinalresolution.Particlesoriginatingfromthenominalinteractionpointatz=0whichhavejj<1:0traversealleightsuperlayerswhilethosewithjj<1:3willtraverseatleast4superlayers.TheorganizationofwireswithinacellisshowninFig. 3-6 .Eachcelliscomposedofhighvoltageeldpanels,potentialwires,andshaperwires{allofwhichworktosupportauniformelectrostaticeld.Achargedparticlepassingthroughthecellsionizesthegasin 59




3-7 .TheprimarygoaloftheSVXistodetectsecondaryverticesfromheavyavourdecays.ThesecondarygoalistomaximizetrackingperformancebycombiningtheCOTandSVXhitinformation.ThereforealignmentoftheSVXdetectoriscriticalfortrackreconstruction.TheprocessofcombinedCOTandSVXtrackreconstruction[ 33 ]startsintheCOT.AfteraCOT-onlytrackisreconstructed,itisextrapolatedthroughtheSVX.Becausethetrackparametersaremeasuredwithuncertainties,thetrackismorelikeatubeofsomeradius,determinedbytheerrorsontrackparameters.AteachSVXlayer,hitsthatarewithinacertainradiusareappendedtothetrackandthere-ttingisperformedtoobtainthenewsetofparametersforthetrack.Inthisprocesstheremaybe 61


SchematicoftheSVXbulkheaddesign. severaltrackcandidatesassociatedtotheoriginalCOT-onlytrack.Thebestoneintermsofthenumberofhitsandtqualityisultimatelyselected.Incontrasttotheinnersiliconsubdetectors,thelayersoftheISLcoverdierentrangesinz.It'scentrallayerlocatedataradiusof22cmdetectstrackswithjj<1andisusefulforextrapolatingCOTtrackintotheSVX.Theforwardlayersatradii30and28cmprovidemeasurementoftrackswith1

AmountofmaterialintheCDFIItrackingvolumeascitedinthedetector'stechnicaldesignreport.Thequotedthicknessassumesnormalincidence. Layer Radius[mm] Material[%Xo] BP 12:0 0:1L00 21:0 1.4SC 32:0 0.5SVX1 42:0 2.0SVX2 69:0 2.0SVX3 100:0 2.0SVX4 129:0 2.0SVX5 157:0 2.0ISL1 210:0 1.4ISL2 290:0 1.4COT 310:01400:0 1.3 Total: 12.0-1400.0 16.1 coverage(jj<3:6);afactthatmakesthemimportantforthemeasurementofeventshapes.TheCDFcalorimetersaredividedintotwocategories:electromagneticandhadronic.EMcalorimetersareoptimizedtomeasuretheenergyofelectronsandphotonsviaelectromagneticinteractions,whilehadroniccalorimetersaredesignedtostoplong-livedmesonsandbaryonsprimarilybywayofstronginteractionswithatomicnuclei.Bothcategoriesofcalorimetersareofasamplingvariety,wherelayersofabsorbingmaterialarealternatedwithsignal-producingscintillatorlayers.Aparticleexitingthetrackingsystemwillrstencounteranabsorberlayer(lead)oftheEMcalorimeterwhichwillinducebremsstrahlunginenergeticelectronsande+epairsinphotons.Theresultingshowerofsecondaryelectronsandphotonsisthendetectedbyphoto-multipliertubes(PMTs)attachedtosuccessivelayersofscintillator.TheintegratedchargecollectedbythePMTthengivesameasureofthedepositedenergy.Theremainingsprayofoutgoingparticlesthenencounterstherstabsorberlayer(iron)ofthehadroniccalorimeter,whichinduceshadronicshowersviaavarietyofnuclearinteractions.ThechargedsecondariesresultingfromthehadronicinteractionsthenproduceasignalinthecorrespondingscintillatorlayerswhichisreadoutbyanothersetofPMTs.Itisworth 63


SchematicpictureofonequadrantoftheCDFcalorimeter. 15 7.5 7.5 15 CalorimetersegmentationoftheCDFIIdetector. notingthatbothtypesofshowers,butparticularlythehadronicvariety,aresubjecttostatisticaluctuationsthatultimatelyimpairtheenergyresolutionofthedetectors.AtCDF,thecalorimetersaresegmentedintotowerswhicharearrangedinaprojectivegeometrypointingtowardstheprimaryinteractionpoint(Fig. 3-8 ).Theentirecalorimeterismechanicallysubdividedintothreeregions:central,wallandplug.Thecomponentsaredenotedcentralelectromagnetic(CEM),centralhadronic(CHA),wallhadronic(WHA),plugelectromagnetic(PEM),andplughadronic(PHA).Thecentralcalorimetercoversthepseudorapidityregionjj<1:1,whiletheplugextendscoverageouttojj=3:6.TheWHAsystembridgesthegapbetweenthecentralandplughadroniccomponents.ThecalorimetersegmentationissummarizedinTable 3-3 64


3-4 summarizespropertiesoftheCDFcalorimetersystem. 65


CEMjj<1:119X013:5%=p CHAjj<1:14.575%=p Table3-4. SummaryofquantitiescharacterizingCDFIIcalorimetry.Thicknessesarelistedintermsofradiation(Xo)orinteraction()lengths.Thesymbolindicatesaconstantresolutiontermtobeaddedinquadraturetotheenergydependentterm. measurementfortheentireCDFcollaboration.Hence,myinvolvementintheup-keepofthisdetectoroverthepast3yearsmeritsitsinclusioninthisdissertation.TheCerenkovLuminosityCounter(CLC)wasaRunIIadditiontotheCDFdetectorintendedtoprovideprecisemeasurementsoftheinstantaneousandintegratedluminosity[ 34 ].Thedetectorconsistsoftwomodules(eastandwest)thatarelocatedinthefarforwardregion3:75

TheCerenkovLuminosityCounteratCDF.Thedetectormodulesarelocatedinthe\3-degreeholes"oftheeastandwestmodules. whereppisthetotalppcross-sectionatp TheprobabilityofhavinganemptybunchcrossingisthenP0()=e.Thus,measurementoftheprobabilityofhavinganemptycrossingisenoughtodeterminetheaveragenumberofinteractions,and,consequently,thevalueoftheinstantaneousluminosity.Thisprobabilityismeasuredbydividingthenumberofemptycrossings(correctedfordetectoracceptance)bythetotalnumberofbunchcrossingsinacertaintimeinterval.ForacrossingtobeconsideredemptythereshouldbenohitsineithertheEastorWestCLCmodules.Thedisadvantageofthismethodisthatatveryhigh 67


3-10 68


FunctionalblockdiagramoftheCDFdataow. Attherstlevel(L1)neweventsareloadedintoabueredpipelinewithadepthof42slots.WitheachTevatronclockcycle(132ns),theeventsaremoveduponeslot,implyingthatanaccept/rejectdecisionmustbereachedwithin5.5sforeachevent.Onlythemostrudimentarypatternmatchingandlteringalgorithmsareappliedtodatafromthecalorimeters,theCOT,andthemuonchambers.Thecalorimeterstream'sdecisionisbasedonthetotalenergydepositedintowersaswellasthemagnitudeofunbalanced 69


35 ]whichpartiallyreconstructstracksallowingforeventdecisionstobemadebasedontrackmultiplicityandtransversemomenta.ThemuonstreamcombineshitsinthemuonchamberswithXFTtrackstoidentifyeventswithmuoncandidates.Thesesimplecutsremoveasignicantmajorityofthebackground,reducingtheacceptedeventratetoabout30kHz.EventswhichmeettherequirementsoftheL1triggerarethenpassedtotheLevel-2trigger(L2).AtL2,aneventiswrittenintooneoffourbuerswithintheDAQelectronicsforeachdetectorcomponent.ThesebuersdierfromthedatapipelineusedinL1,inthataneventremainsinthebueruntilthedecisionismade;thatis,whileaneventisbeingprocessed,itcannotbeoverwrittenbyanothereventfromL1.IfaL1acceptoccurswhileallfourL2buersareoccupieddeadtimeisincurred.Inordertominimizethisdeadtime,thelatencyoftheL2decisionmustbelessthanapproximately80%oftheaveragetimebetweenL1accepts.Thiscreatesa20swindowtoacceptorrejectacandidateevent.DecisionsatL2combineinformationfromL1inadditiontodatafromothersubdetectorsliketheSVXandCESsubsystems.ThealgorithmsatL2cuttheacceptanceratedownto300Hz.AtLevel-3(L3)datafromtheentiredetectoriscombinedbytheEventBuildersystemforamorecomputationallyintensiveexaminationoftheevents.Thearrangedeventfragmentsaredistributedacrossafarmofalmost1000processorswhichallowsforapproximately1sperdecision.L3takesadvantageoffulldetectorinformationandbasesitsreject/acceptdecisionondetailedparticleidenticationandeventtopology.Thefulltriggersystemreducesthe2.5MHzeventratetoapproximately75Hz,whichamountsto20MB/sofdatadeliveredtostorageforeventualoineanalysis. 70




36 ],aconealgorithmthatcombinesobjectsbasedonrelativeseparationinspace;Midpoint,analgorithmsimilartoJetClu,butdenedtobeinfraredandcolinearsafe;andKT[ 37 ],analgorithmcombiningobjectsbasedontheirrelativetransversemomentaaswellastheirrelativeseparationinspace.Thisanalysisutilizesjetidenticationexclusivelyforthepurposeofeventselection.Asaresult,thejetalgorithmusedisnotexpectedtosignicantlyaectthenalresults.Thatbeingsaid,thisdissertationemploysCDF'simplementationoftheMidpointJetalgorithm. 72


38 ].Therststepincorrectingthejetenergyistoremoveanynon-uniformityinfromthecalorimeterresponse.Thiscorrectionisparticularlyimportantinuninstrumented 73



AveragetransverseenergydepositedinarandomconeofR=0:7inmin-biaseventsasafunctionofthenumberofprimaryverticesintheevent. inarandomconeinminimumbiasevents.TheseareeventswhoseonlyrequirementiscoincidencebetweeneastandwestmodulesoftheCLC.TheaveragetransverseenergyintheconeisparametrizedasafunctionofthenumberofprimaryverticesintheeventandisshowninFig. 3-12 .Thenextcorrectionisreferedtoasthe\absolute"correctionandismeanttoaccountforanynon-linearityandenergylossinthedetector.Quitegenerally,theresponseofacalorimetertowerdependsonthemomentum,position,incidentangle,andspeciesoftheincidentparticle.Moreover,theresponseoftheCDFcalorimeterisnon-linear,whichistosaythattheenergyrecordedbyatowerforaparticlewithmomentump1isdierentthanfortwoparticleswithmomentap2+p3=p1.WhiletheCDFdetectorsimulationhasbeencarefullytunedtoincludetheseeects,meaningfulcomparisontotheoryrequiresthatthemeasuredjetenergybeindependentofthese.Tothisend,MonteCarlowithfullCDFIIdetectorsimulationisusedtoreconstructjetsatthecalorimeterlevelandatthehadron 75






19 ].Inordertoensurethateventsselectedarenotcontaminatedbyhighenergycosmicrays,weapplyastandardCDFcutonthesignicanceofmissingtransverseenergy(6ET)intheevent.The6ETsignicanceisdenedas6ET/p 4-1 showstheanddistributionoftowersinDataandMC.Clearly,anexcessoftowersispresentinData;however,theshapesofthesedistributionsiswellreproducedbythesimulation. 78


Thedistributionofcalorimetertowersinandoverthefullrapidityrangeofthedetector.Thedistributionsarenormalizedtothenumberofeventsineachsample.ThelabelCDFSimreferstoPythiaTuneAMCafterfulldetectorsimulation. Thatis,theexcessisuniformlydistributedinspaceandwasfoundnottobetheresultof\hot"towers.Restrictingourselvestothecentralregion(jj<1:1)weobservethattheexcessappearsoverawiderangeoftransversemomentums(100MeV

Thetransversemomentumdistributionofcalorimetertowersinthecentralregionjj<1:1,normalizedtothenumberofeventsineachsample.ThelabelCDFSimreferstoPythiaTuneAMCafterfulldetectorsimulation. Figure4-3. Distributionoftowersoverthecentralregionjj<1:1asafunctionoftheanglebetweenthe2Dtower~pTandthetransversethrustaxis~nT


Distributionsofzfordierenttrackreconstructionalgorithms.Thedataisttoasumoftwo\Gaussians"todeterminethewidth,z,ofthedistributions,andislaterusedintrackselection. AfulldescriptionofCDFtrackreconstructioncanbefoundin[ 32 ][ 39 ].InordertoselectsignaltracksweapplythestandardCOTqualitycutrequiring2fit<6:0.Thiscutremovespoorlyreconstructedandspurioustracks.Furthermore,weconsideronlytrackswithpT>0:3GeV;belowthisthresholdchargedparticlesareexpectedtoloopinsidethemagneticeld.Additionally,toremovetrackswhichdonotoriginatefromtheprimaryinteractionweapplyacutonthezofeachtrack.Thisparameterisdenedasthedierencebetweenthezpositionofthetrackatthepointofclosestapproachtothebeam-lineandthezpositionoftheprimaryvertex.Wethenrequirethatjzj<5z,wheretheresolution,z,isdeterminedfordierenttypesoftracksbasedonthenumberofSVXandCOThits(Fig. 4-4 ).ThevaluesofzaresummarizedinTable 4-1 81


TheresolutionoftrackzparameterevaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. Algorithmz,cm COT-only1.20Inside-Out(IO)0.60Outside-Inr1.80KalmanOutside-Inr1.80Outside-Instereo0.40KalmanOutside-Instereo0.40Outside-In3D0.21KalmanOutside-In3D0.21SVXOnly0.78 Trackscomingfrom-conversionsandK0anddecaysareremovedusingacombinationofcutsonimpactparameterandthedistanceRconv(seeFig 4-5 ).Theimpactparameterisdenedastheshortestdistanceinther-planebetweentheinteractionpointandthetrajectoryoftheparticle.Itcanbeshownthatforelectronsandpositronsoriginatingfrom-conversions wherepTisthetransversemomentumofthechargedparticleinGeV/c,BisthemagneticeldinTeslaandRconvismeasuredinmeters.MonteCarlostudieshaveshownthatplacingtherequirementsjd0j<5d0orRconv<13cmontracksismoreecientinremovingthisbackgroundthaneitherofthesecutsalone.Incidentally,thevalueRconv=13cmismotivatedbythelocationofSVXportcardswhereamajorityofthesesecondaryinteractionsoccurintheMCsimulationsanddata.Theresolutionoftheimpactparameter,d0,variesfordierenttypesoftracksbasedonthenumberofSVXandCOThits.DistributionsoftheimpactparameterfortracksfromdierentreconstructionalgorithmsareshowninFig. 4-6 .Themeasuredvaluesofd0aresummarizedinTable 4-2 .Toverifytheeectivenessofthetrackqualitycuts,wecomparetheinclusiveparticlemultiplicityandmomentumdistributionsinPythiaTuneAMonteCarloforcharged 82


Illustrationofthedistance,Rconv,fromthebeamlinetothepointwheretheconversionoccurred.Here,d0istheimpactparameter. Figure4-6. Distributionoftheimpactparameterd0,fordierenttrackreconstructionalgorithms.Thedataisttothesumoftwo\Gaussians"todeterminethewidth,d0,andislaterusedinthetrackselection. 83


Theresolutionoftheimpactparameter,d0,evaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. Algorithmd0,mm COT-only0.110Inside-Out(IO)0.013Outside-Inr0.020KalmanOutside-Inr0.020Outside-Instereo0.014KalmanOutside-Instereo0.014Outside-In3D0.0095KalmanOutside-In3D0.0095SVXOnly0.020 hadronsandafterfulldetectorsimulationandreconstruction.TheresultsareshowninFigures 4-7 and 4-8 .Notethatthemomentuminthelaterplotisexpressedintermsoftheobservablewhichisdenedas=1=x=lnEjet 4-9 Curiously,ifwerelaxthecutsondz,d0,andRconvandcompareDataandPythiaTuneA,weobservethattherearemanymorerejectedtracksintheDatathanthereareinthesimulation(seeFig. 4-12 ).Furthermore,thisexcessisdistributeduniformly(Fig. 4-11 ),butisclearlymostprominentintheregionawayfromtheprimaryenergyow(nT=2)wheretherelativeoverageis30%(tracksaremeasuredwithpT>300MeV).Thesameplotforcalorimetertowersrevealsasimilarexcessof40%intheregionawayfromthetransversethrustaxis(towersaremeasuredwithET>100MeV).AdditionalstudiessuggestthatthisexcessistheresultofanunderestimationintheamountofdetectormaterialintheCDFsimulationpackage. 84


MonteCarlotrackmultiplicityinjetsbeforeandaftertrackqualitycuts.Particlesarecountedwithinaconeofopeninganglec=0:5radians.Thelabel\CDFSim"referstoMCafterfulldetectorsimulation. Figure4-8. InclusivemomentumdistributionofMonteCarlotracksinjetsbeforeandaftertrackqualitycuts.Particlesarecountedwithinaconeofopeninganglec=0:5radians. 85


DistributioninofMCchargedhadronsrelativetothetransversethrustaxis,comparedtothesamedistributionsinMCtracksafterfulldetectorsimulation. Figure4-10. InclusivemomentumdistributionsofPythiaTuneAtracksfortheentirecentralregionjj<1:1 86


DierencebetweenDataandMonteCarlointhedistributionoftracksasafunctionoftheanglebetweenthe2DtrackpTandthetransversethrustaxisnTovertheentirecentralregionjj<1:1 Atthelevelofthecalorimeter,theseadditionalparticlesfromsecondaryinteractionsappearasiftheyaresimplypartoftheunderlyingevent.Ineect,theymakeeventslookbroaderthantheyactuallyare.However,weanticipatethisadditionalcontributiontocancel-outinthenalobservableconstructedinChapter2(i:e:,intheweighteddierenceofthemeanvaluesofthetransversethrustandthrustminor). 4-14 showsthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetenergyforPythiaTuneAatthehadronlevelandatthecalorimeterlevelafterfullCDFdetectorsimulation.Theplotindicatestherelativelysmallcumulativeeectofthedetectorontheobservables.Thecorrespondingplotoftheweighteddierence 87


RelativedierencebetweenDataandMonteCarlointhedistributionoftracksasafunctionoftheanglebetweenthe2DtrackpTandthetransversethrustaxisnTovertheentirecentralregionjj<1:1 Figure4-13. RelativedierencebetweenDataandMonteCarlointhedistributionoftowersasafunctionoftheanglebetweenthe2DtowerpTandthetransversethrustaxisnToverthecentralregionjj<1:1 88


TheeectofCDFdetectorsimulationonthetransverseThrust(top)andThrustMinor(bottom). betweenthesetwovariables,Fig. 4-15 ,revealsthatonthescaleofthisnalobservableanoticeablesystematiceectispresentduetothesimulation.Possiblesourcesforthisshifthavebeenidentiedandinvestigatedasfollows: 89


TheeectofCDFdetectorsimulationonthenalobservableconstructed,theweighteddierenceinthemeanvaluesofthetransversethrustandthrustminor. broaderthanintheabsenceofamagneticeld.Toestimatethemagnitudeofthiseectonthenalobservable,MCparticlesatthehadronlevelwerepropogatedtotherstactivelayerofthecalorimeterundertheinuenceofa1.41TeslaB-eld.Thedirectionoftheparticleatthispointistakentobethelocationoftheparticlerelativetothezpositionoftheprimaryinteractionpoint. 90


4-16 andforthenalobservableinFigure 4-17 .Thegranularityofthecalorimeterappearsastheprimarysourceoftheinstrumentaleectobservedinthefulldetectorsimulation(i:e:,Fig. 4-15 ).Otherdetectoreectsincludethesharingofenergybetweentowersandtheenergyresponseofthecalorimeter.However,alloftheseeectsareincorporatedintothefullGEANTdetectorsimulation.Ultimately,thedierenceinthenalobservablebetweentheMCatthehadronlevelanddetectorlevelshallbequotedasacorrectionfactortothedata.Finally,theeventshapesaredenedtheoreticallyoverallparticlesinthenalstate,includingthosewitharbitrarilysmallmomenta.Inaneorttounderstandhowacutonthetransverseenergyaectstheobservables,wevarytheETthresholdontowersfrom100MeV(default)through200and300MeV.Figure 4-18 showstheresultofthisvariationonthemeanvaluesofthethrustandthrustminor.Clearlytheeventsappearnarroweraswecut-outmoretowers.However,Figure 4-19 showsthatfortheleadingjetenergiesstudiedinthisdissertation,thenalobservableisratherinsensitivetothecutontransversemomentum. 91


Contributionofisolatedinstrumentaleectsonthetransversethrustandthrustminor. 92


Contributionofisolatedinstrumentaleectsontheweighteddierenceofthemeanvaluesofthetransversethrustandthrustminor. ThedierencebetweenC(hi;hTMini)intheDatawithandwithoutthisscalefactoristhentakenasameasureofthesystematicuncertainty 93


EectoftowerETthresholdonthemeanvaluesofthethetransversethrustandthrustminorplottedagainsttheleadingjetenergy. 94


EectofthetowerETthresholdontheweighteddierenceinthemeanvaluesofthetransversethrustandthrustminor. thedetector.Asaresult,thefurtheracollisionoccursfromthenominalinteractionpointthegreaterthepossiblitythatparticlesfallbeyondthedetector'sconverage.Toevaluatetheuncertaintyduetothiseectwerequireatightercutonthezpositionoftheprimaryvertex.Thedierenceintheobservablebetweenthedefaultandthetightcutisthenassignedasasystematicuncertainty. 95


5-1 fortheleadingjetenergies100,150,200,and300GeV.ThedistributionsindataareshiftedbyroughlyaconstantamountrelativetothedistributionsinPYTHIATuneAafterdetectorsimulation;however,theover-allshapeiswellreproducedbytheMC.BothDataandPYTHIATuneAshowsignicantdeparturesinshaperelativetothedistributionsprovidedbytheorists,whichdonotincorporateanunderlyingevent.TheevolutionofthemeanvaluesofthesetwoobservablesispresentedinFigure 5-2 .Here,again,thedatahavenotbeenunfoldedtotheparticlelevel.Theseplotshighlighttherelativelysmalldetectoreectsinthemeasurementofthetransversethrustandthrustminoraswellasthecomparativelylarger,butroughlyconstantosetbetweendataandsimulation.Finally,Figure 5-3 showstheweighteddierencebetweenthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetET.Thisobservableultimatelyallowsforadirectcomparisonbetweendataandthededicatedpredictionsoftheorists(labeled`CAESAR+NLO')whichdonotincorporateanunderlyingevent.Inthisplotdetectoreectshavebeenaccountedfor;toreectthis,thedataislabeled\Unfolded".Thegureshowsgoodgeneralagreementbetweentheoristspredictions,PythiaTuneA,anddata. 96


Distributionsofthetransversethrustandthrustminorforleadingjetenergies100,150,200,and300GeV.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracy,PYTHIATuneAatthehadronlevelaswellasafterdetectorsimulation,andData. 97


Evolutionofthemeanvaluesofthetransversethrustandthrustminorasafunctionoftheleadingjetenergy.Comparisonismadebetweentheoreticalpredictionsat(NLO+NLL)accuracy,PYTHIATuneAatthehadronlevelaswellasafterdetectorsimulation,andData. 98


PlotoftheweighteddierenceofthemeanvaluesofThrustandThrustMinorasafunctionoftheleadingjetenergyforCAESAR+NLO,PYTHIATuneAattheHadronlevelandDataunfoldedtotheparticlelevel. 99

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LesterPinerawasborninColon,Cuba,onJanuary12,1979.HemovedtotheUnitedStatesin1980andprimarilygrewupinMiami,FL.HeattendedSouthwestMiamiSeniorHighschoolandgraduatedvaledictorianoftheClassof1997.HeearnedhisB.A.inphysicswithaconcentrationinmathfromCornellUniversityin2001.HebeganhisgraduateworkattheUniversityofFloridathatyearandjoinedtheHighEnergyExperimentalGrouptherein2004.HeearnedhisPh.D.in2008. 104