Citation
Measurement of the Top Quark Mass in the All Hadronic Channel at the Tevatron

Material Information

Title:
Measurement of the Top Quark Mass in the All Hadronic Channel at the Tevatron
Creator:
Lungu, Gheorghe
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (181 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
Konigsberg, Jacobo
Committee Members:
Field, Richard D.
Mitselmakher, Gena
Ramond, Pierre
Nishida, Toshikazu
Graduation Date:
8/11/2007

Subjects

Subjects / Keywords:
Antiprotons ( jstor )
Average linear density ( jstor )
Calorimeters ( jstor )
Electrons ( jstor )
Mass ( jstor )
Muons ( jstor )
Protons ( jstor )
Quarks ( jstor )
Signals ( jstor )
Vertices ( jstor )
Physics -- Dissertations, Academic -- UF
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Physics thesis, Ph.D.

Notes

Abstract:
This study presents a measurement of the top quark mass in the all hadronic channel of the top quark pair production mechanism, using 1 fb & #8722;1 of pp collisions at ps=1.96 TeV collected at the Collider Detector at Fermilab (CDF). Few novel techniques have been used in this measurement. A template technique was used to simultaneously determine the mass of the top quark and the energy scale of the jets. Two sets of distributions have been parameterized as a function of the top quark mass and jet energy scale. One set of distributions is built from the event-by-event reconstructed top masses, determined using the Standard Model matrix element for the tt all hadronic process. This set is sensitive to changes in the value of the top quark mass. The other set of distributions is sensitive to changes in the scale of jet energies and is built from the invariant mass of pairs of light flavor jets, providing an in situ calibration of the jet energy scale. The energy scale of the measured jets in the final state is expressed in units of its uncertainty, & #190;c. The measured mass of the top quark is 171.1 & #177;3.7(stat.unc.) & #177;2.1(syst.unc.) GeV/c2 and to the date represents the most precise mass measurement in the all hadronic channel and third best overall. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2007.
Local:
Adviser: Konigsberg, Jacobo.
Statement of Responsibility:
by Gheorghe Lungu.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Lungu, Gheorghe. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
660822582 ( OCLC )
Classification:
LD1780 2007 ( lcc )

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Full Text






1-=- C-=a c-=-



car e :-- -- :-=





Figure D-2. Continued










many interesting discussions we had and for being the friends I needed during difficult

times.

At last, yet most importantly, I want to thank my wife, Corina, whom I dedicate

this work. Without her constant support, criticism and love I wouldn't have succeeded in

finding the balance needed to reach this goal. Also I thank my father and my sisters for

loving me, and my mother who will be ah-- 0-4 in my mind.






















































Figure D-1. Continued











































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Figure E-1. Continued










interaction was not understood until later. However, the CP conservation by the strong

force remains a mystery.

Another thing that puzzled the physicists was why the decay of the muon into an

electron and a photon was not observed. The solution adopted was the postulation

of two types of neutrinos, the electron-neutrino and the muon-neutrino, along with

the conservation of two new quantum numbers, the electron number and the muon

number. The muon-neutrino was eventually discovered in 1962 by Lederman, Schwarts

and Steinberger.

Through the work of Feynman in 1947, the physicists were able to calculate the

electromagnetic properties of the electron, positron and the photon using the Feynman

diagrams. This constitutes the birth of quantum electrodynamics, or QED.

The theory of weak interaction was first formulated by Fermi in 1933 and it was

assuming a four-fermion interaction acting at a single point. The Fermi coupling constant

GF=1.16639x10-s GeV-2 WaS giving the strength of the weak interaction. In 1956,

Feynman and Gell-Mann incorporated the phenomenon of parity violation into this theory.

The Fermi theory of weak interaction was able to explain the low-energy processes, but

was making unacceptable prediction for high-energy weak interactions. The solution

to this problem was to introduce a particle which mediates the weak interaction. This

particle was thought to be a spin 1 boson, with three charge states, W-, Wo, W+ and

was the result of work done by Schwinger, Bludman and Glashow in 1959. Later in 1967

Weinberg and Salam propose a theory that unifies the weak and the electromagnetic

forces. In this theory the neutral boson carrying the weak force is called Zo. In addition

to that a massive boson called the Higgs boson is predicted. The W and Z bosons will be

eventually discovered in 1983 at CERN in according to the predictions.

In 1964 the fundamental particles were: three quarks up (u), down (d) and strange

(s), and two pairs of leptons the electron (e) with its neutrino (ve), and the muon

(p-) with its neutrino (v,). Their corresponding antiparticles were also considered as

















































~ldf 231.3/11 6 ""
pO 1.105+ 0.002257 .1.25
1 .2


1.15


4415r1
0
1.115+ 0.002278


1.2


1


1-


09 150 160 170 180 190 200
Input Top Mass (GeV/cS


150 160 170 180 190 200
Input Top Mass (GeV/ci


Figure 9-5. Top mass pull width as a function of top mass for different treatment of the

correlation between the event top mass and the dijet mass. On the left is the

default case when the correlation is zero, while on the right is shown the

situation with the full correlation.










Figure 9-1 shows the event multiplicity single' I__- d events on the left, and for double

I__- d events on the right. Figure 9-2 shows the histograms of the three parameters

describing the gaussian fit for the single' I__- d events, while Figure 9-3 shows the

equivalent plots in the case of the double I__ d events. The uncertainties on the

background parameters as determined following the histogfram fluctuation are shown

in Table 9-1. Varying the background parameters within these uncertainties results in a

shift in top mass of 0.4 GeV.

9.7 Correlation Between Top Mass and Dijet Mass

We investigate here the effect of the correlation between the event top mass and

dijet mass has on the top mass pull widths and pull means. Our pseudo-experiments were

formed by randomly selecting the event top masses from the top mass templates and by

randomly selecting the dijet masses from the dijet mass templates. As a consequence the

correlation between two masses is reduced to zero. Figure 9-4 shows on the left the top

mass pull mean in the default case when the above correlation was reduced to zero, while

on the right is shown the situation with full correlation. Figure 9-5 shows the equivalent

comparison involving the top mass pull widths.

On average over different top mass samples, the pull mean is consistent within the

uncertainties between the two scenarios. However, the pull widths appear higher when

the correlation between the event top mass and the dijet mass is zero. We conclude that

there is no need for a systematic uncertainty, and we keep the default pull width as the

correcting factor on the statistical error on the top mass since it represents the more

conservative approach.

9.8 2D Calibration

We have varied the parameters of Equations 8-5 and 8-6 within their uncertainties as

listed in Table 8-2. We then re-calibrated the reconstructed values for the top mass. The

change in top mass is 0.2 GeV.










CHAPTER 3
EVENT RECONSTRUCTION

In this chapter we will describe how we can identify the particles produced in a pp

collision starting front the raw outputs of the different parts of the detector. First we

will see how information from silicon detectors and COT are used to reconstruct charged

particle trajectories. Then we will move to the reconstruction of jets of hadronic particles,

based on calorinteters. A section will be devoted to the correction of jet energies for

different error sources introduced by calorinteters and reconstruction algorithms. After a

brief description of the identification of leptons and photons, we will end with the different

methods used at CDF to identify a jet of particles originated front a b quark.

3.1 Tracks

Track reconstruction is performed using data from silicon tracking system and COT.

The reconstruction is based on the position of the hits left b charged particles on detector

components. Combining these hits one can reconstruct particle trajectories.

The whole tracking system is ininersed in a 1.4 T magnetic field. C'I Iaged particles

moving in a homogeneous magnetic field follow a helix trajectory. The helix axis is parallel

to the magnetic field. 1\easuring the radius of curvature of the helix, one can obtain the

transverse montentunt of the particle, while the longitudinal montentunt is related to the

helix pitch. To describe a helix five parameters are needed, three to paranieterize the circle

in r projection and two to paranieterize the trajectory in x. At CDF, as shown by

Equation :31, the helix of a charged particle is paranleterized.


S= (cot0, C, xo, D, 00) (:31)


The parameters used to describe the helix of a charged particle are: cot 8 is the

cotangent of the polar angle at nmininiun approach to the origin; C is the half curvature,

whose sign is given by the charge of the particle; xo is the position on x axis of the

nmininiun approach to the helix origin; D is the signed impact parameter (i.e., the distance












S= lisag 2tag JES 71

Both the single tag likelihood and the double tag likelihood are a product of four

terms as shown in Equation 7-2. The top template term, top, iS Shown in Equation 7-3.

The W template term, w, is shown in Equation 7-4. The constraint on total number of

events, Onev, is shown in Equation 7-5. The constraint on the it number of events, L,,, is

shown in Equation 7-6.

1,2tag = top .W .nev .n, (7-2)

Both top and W template terms have the same structure: a weighted sum of

the event signal probability at a given top mass and JES and the event background

probability. The fraction of it events, us/(us + ab), is the weight of the signal probability

and the fraction of background events, nb Es, + ab), is the weight of the background

probability. Together with M~ and JES, the parameters as and nb are free in the

likelihood fit.
et n, Ptop(m,, | M, JE S) + nb tl- )
us + nb
evt 1


Cw = r~v 11~U "et (7-4)
n, + nb
evt=1
The sum of signal and background events, as + ab, is constrained to the total number

of observed events in the data, NVor gs, via a Poisson probability with a mean equal to
Netot
even~lts *

Cnev = (eo enes/R 'b *p(NJnes/ (7-5)
(us + nb)

The number of signal events, us, is constrained to the expected number of it events,
ae sp, ia a Gaussnian of mean equa~l to nsp and width equal to o-Ps. The width of the

gaussian is simply the uncertainty on the expected number of it events.
The epecnpted nu~mbers of sigrnal evepnts, ns, are 13 Single' I__- d and 14 double

I__- d events, corresponding to a theoretical cross-section of 6.7'ji pb [55] and an










energy. Moreover, the sum of transverse moment of all tracks pointing to the 0.4 cone

should be less than 2 GeV/c. The line connecting the primary vertex to the shower max

position of the photon candidate determines the photon direction.

3.6 Bottom Quark Tagging

The hadrons produced by a b quark have two important properties: long lifetime

allowing it to travel before decaying and the possibility of semi-leptonic decay b luIs.

Typically, the lifetime is about 1.5 ps for a hadron with an energy of about 40 GeV, so

the distance it travels if few millimeters. From these properties it is possible to construct

algorithms to tag jets if they are produced by b quarks. At CDF there are used three such

algorithms: the SecVtx algorithm, the JetProbability (JP) algorithm and the Soft Lepton

T.--I ;::_ (SLT) algorithm.

3.6.1 SecVtx Algorithm

This algorithm [47] exploits the fact that the B hadron travels before it decays

and therefore the jet produced by it will contain a secondary vertex (Figure 3-6). The

algorithm starts from COT and silicon tracks inside a cone and as a first step, using as

discriminating variable their impact parameter, it removes tracks identified as Ks, A or y

daughters, or consistent with primary vertex or too far from it. Then a three dimensional

common vertex constrained fit is performed using two tracks: if X2 < 50 the two tracks are

used as seed to find other tracks that point toward the same secondary vertex. If at least

three tracks are found to be compatible with a secondary vertex, the jet containing them

is considered a b-tag if it passes the following cuts:

* |Le,| < 2.5 cm, where L,, is the decay length of the secondary vertex; this cut helps
rejecting conversions from the first 1 ., -r of SVXII;

~Lz

* if if is the invariant mass of the tracks, |mKs ii1T, I > 0.01 GeV and |mA i
0.006 GeV;

* Lv-(i./Pr) m




































c -=~nii a I 0~uii I- 0ruii
































Figure D-1. Continued









The inning in parton energy is defined such that each bin contains at least 3000

entries and it is wider than 5 GeV. This is done in each bin of pseudo-rapidity. Table 4-2

shows the definition of energy inning for the b-jets transfer functions, while Table 4-3 is

for the W-jets transfer functions.

In each bin the transfer function is represented by the distribution of the variable

1 Ejet/E,,rton. The shape of this distribution is fitted to the sum of two gaussians.

Appendix C holds the fitted shapes.

4.5 Transverse Momentum of the it System

The PT(p3 weight is written as dependent on the 4-vectors of the partons in the final

state, generically represented by P'in the argument of the function. This dependence is

difficult to parameterize. Therefore we will pick a more natural set of parameters to work

with. In the next section we will detail the change of variables needed to accommodate

this simplification. Until then we anticipate that the variables used for integration in
Equa~~tion 4-6 are 6 and ,6 representing the projections of the transverse momentum of

the it system along the x and y axes. The probability density related to the transverse

momentum of the it system weight is shown in Equation 4-31.


PT(p~ PT(p p) (4 31)


The parameters we actually use are the magnitude of the transverse momentum of the

it system, p), and the azimuthal angle, ~. The upper index means that these parameters

are determined using the 6 partons in the final state. We expect to have a flat dependence

on ## and therefore we can factorize the two dependence. The Equation 4-32 gives the
normalization relation.


dp d, PrX (p ~)= 1 = dpP~r (p~l )~ X d (4-32)

The transverse momentum spectrum of the it events, represented by PT(p ) in the

Equation 4-32, is obtained from a tt Monte Carlo sample with M~to = 178 GeV. The










integrated luminosity of 943 pb-l. These numbers have been determined using a tt Monte

Carlo sample with a cross-section equal to the theoretical value. The value of the top mass

used in the it Monte Carlo sample just mentioned is 175 GeV and it also corresponds to

the top mass value for which the theoretical cross-section has been calculated. Therefore

we read the expected number of signal events from Table 5-4.

The uncertainties on the numbers of signal events a,p are chosen to be the Poisson

errors. This is a conservative approach since the Poisson errors are larger than the

uncertainties derived based on the theoretical cross-section uncertainty.


L,, = exp ( >" (7-6)


The value of JES is constrained to the a priori determination of this parameter by

the CDF Jet Energy Resolution group, JESemp. This constraint is a gaussian centered on

JESemp and width equal to 1. The unit used is a, which represents the uncertainty on the

jet energy scale.

~~ ~( (JES JESemp2(77


7.2 Top Templates

7.2.1 Definition of the Template

As mentioned in section 7.1, we use the matrix element to build the top templates.

The event probability defined in section 4 is plotted as a function of the top pole mass in

the range 125 GeV and 225 GeV. In negative logarithmic scale this event probability will

be minimized for a certain value of top mass which we'll use to form the top templates.

The shape of these templates depends on the input top mass and JES for it events, but

not for background events.

7.2.2 Parameterization of the Templates

We form signal templates for the mass samples described in section 5 with 7 different

JES values: -3, -2, -1, 0, 1, 2, 3, after all our selection cuts have been applied. In total

there are 84 templates for signal used for parameterization. The function used to fit them




















-CH TopMass=175 sa
-HW TopMass=130 slas
HW TopMass=140
HW TopMass=150 sae
HW TopMass=160
SHW TopMass=170
HW TopMass=180
HW TopMass=190
-HW TopMass=200
HW TopMass=210
- ~HW TopMass=220
-HW TopMass=230
--= Pvt TooMass=178


APPENDIX B

TRANSVERSE MOMENTUM OF THE ft SYSTEM


PtTTbar


D I


PtT.ba


0 20 40 60 80 100


means


means


















30 35 40 45 50


0 5

rms


10 15 20 25


20 25


0 5 10 15


Figure B-1.


Transverse momentum of the it system for different generators and for

different top masses. Upper plot: shapes of the transverse momentum of the it

system for different generators (CompHep, Pythia and Herwig) and for
different top masses. Middle plot: the Means of the distributions in the upper

plot. Lower plot: the RMS of the distributions in the upper plot.





Figure E-2. Continued


zuu -
180 -

160 -
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120 -
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60 -
40 -
20 -

0 0 1 200 250 3







250 -


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0 1 0 200 250 UU It






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d dO dO 200 250 3UU 94


500 -


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500 -


400 400 -


300 300 -


200 200 -


100 100 -


00















PtTThar


18000 u 2i
Undelflow
16000 -C Overflow 197
Integral 4545e+05
14000 # \i~df 31 3e 92

12000C pO 5259e+05 i1445e+04
pl 3402 11018
10000t p2 2552e+04 i1083
p3 1658e+06 i2212e+04
8000 p4 -1183 i01924
p5 339219653
6000 p5 -1995e+06 i3403e+04
p7 -24 9110 05462
4000 p8 1514106078

2000-

0
Pt_ttbar [GeV]



Figure 4-4. Transverse momentum of the it events. The fit is a sum of 3 gaussians.


22 Indf 1.269 I 3
Prob 0.7365

p0 177.210.03468
pl 0.9892 10.001879


-y=x
- y =pO +(x -178)*pl


150 160 170 180 190 200
Input Top Mass [GeV]


Graph

F200


I<190


0180


170


160


150


X2 Indf 2.845 I 3
Prob 0.4162
pO 176.8 10.05232
pl 0.9866 10.002775


-y=x
| = O + x -178)*pl


150 160 170 180 190 200
Input Top Mass [GeV]



Figure 4-5. Reconstructed top mass versus input top mass at parton level. A) The

energies of the partons have been smeared by 5' B) The energies of the

partons have been smeared by 10'; C) The energies of the partons have been

smeared by 211' D) The energies of the partons have been smeared using the

transfer functions.













































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uu -

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Figure E-1. Continued










between the helix and the origin at minimum approach); 00 is the direction in r 4 of the

helix at the point of minimum approach.

If (.ro, Wo) is the center of the circle, then the impact parameter is calculated as in

E~quation? :32, where p = 2~is the radius of the circle and Q2 the charge of th~e particle.


D = Q ( r,~ x + YO2 p) (:32)


Having described the parameterization of a particle trajectory, we'll turn on the main

tracking algorithms developed for offline analysis, the Standalone and the Outside-In

algorithms.

Standalone tracking [:35] is a strategy to reconstruct tracks in the silicon detector. It

consists in findings triplets of aligned :3D hits, extrapolating them and adding matching

:3D hits on other 11s-c v ;. This technique is called standalone because it doesn't require any

input from outside: it performs tracking completely inside the silicon detector. First the

algorithm builds :3D hits from all possible couples of intersecting axial and stereo strips

on each lI ... Once a list of such hits is available, the algorithm searches for triplets of

aligned hits. This search is performed fixingf a 111-< v and doing a loop on all hits in the

inner and outer 11s-
and one in the outer 1.,-< c a straight line in the r x plane is drawn. Next step consists

in examining the 1 .,-cc in the middle: each of its hits is used to build a helix together with

the two hits of the inner and outer 111-c v ;. The triplets found so far are track candidates.

Once the list of candidates is complete, each of them is extrapolated to all silicon 11s-< rs

looking for new hits in the proximity of the intersection between candidate and 111-< v. If

there is more than one hit, the candidate is cloned and a different hit is attached to each

clone. Full helix fits are performed on all candidates. The best candidate in a clone group

is kept, the others rejected.

The Outside-In algorithm [:36] exploits information from both COT and silicon. The

first step is tracking in the COT, which starts translating the measured drift times in









APPENDIX D
SIGNAL TOP TE1\PLATES

I mn~uniin I I mnrunii I mn~uniaA





























Figure D-1. Top templates for it single' I__- d events for samples with different top
masses: from 150 GeV to 200 GeV. A) Case of JES = -3. B) Case of
JES = -2. C) Case of JES = -1. D) Case of JES = 0. E) Case of
JES = 1. F) Case of JES = 2. G) Case of JES = 3.









REFERENCES


[1] F. Abe et 74, 26:32 (1995).

[2] J.H. K~uhn, Lectures delivered at 2:3rd SLAC Suniner Institute, hep-ph/9707:321
(1997).

[:3] V.M. Ahazov et
[4] T. Affolder et Erratuni-ibid. D 67, 119901 (200:3).

[5] D. Acosta et
[6] D. Acosta et
[7] D. C'I I1:1 .I~orty, J. K~onigsherg and D.L. Rainwater, Ann. Rev. Nucl. Part. Sci. 53,
:301 (200:3).

[8] 31. Cacciari et 68, 114014 (200:3).

[9] B. Abbott et V.M. Ahazov et
[10] D. Acosta et
[11] S.L. Glashow, J. Iliopoulos and L. Alaiani, Phys. Rev. D 2, 1285 (1970).

[12] S. Eidelman et
[1:3] F. Abe et et (CDF Collaboration), Phys. Rev. D 62, 012004 (2000); V.M. Ahazov et Collaboration), Phys. Rev. Lett. 88, 15180:3 (2002).

[14] ALEPH, DELPHI, L:3 and OPAL Collaborations and The LEP Working Group for
Higgs Boson Searches, hep-ex/06120:34 (2006).

[15] P. Azzi et Group, hep-ex/0404010 (2004).

[16] ALEPH, DELPHI, L:3 and OPAL Collaborations and The LEP Working Group for
Higgs Boson Searches, Phys. Lett. B 565, 61 (200:3).










CHAPTER 10
CONCLUSION

We have applied the method described in the previous chapters to the data sample

corresponding to 943 ph l. In this sample, there are 48 single' I__- d and 24 double

I---- d events after all the cuts have been applied.

In the second column of Table 10-1, we show in the total number of events and the

expected number of signal events used as input in the 2D likelihood of Equation 7-1. Note

that in Equation 7-1 we need the uncertainty on the expected number of signal events and

this is also shown in Table 10-1. The numbers of background events are shown as well,

but they are not used as input values in the likelihood. In the third column we show the

number of events as they result from the minimization of the 2D likelihood.

Following the minimization of the 2D likelihood, we measured a top mass of 171.1 &

3.7 GeV, and a JES of 0.5 + 0.9 ec.. The value of the jet energy scale (JES) is therefore

consistent with the previous determination of JES at CDF.

The quoted uncertainty on the top mass represents the combination of the statistical

uncertainty with the systematic uncertainty due to JES uncertainty. In order to obtain

only the statistical uncertainty on the top mass, the minimization of the 2D likelihood is

modified such that the JES parameter is fixed to 0.5 ce. (the result from 2D fit). Following

this procedure the statistical uncertainty on the top mass is 2.8 GeV. Therefore the

systematic uncertainty due to JES is 2.4 GeV.

Figure 10-1 shows the distributions of event by event reconstructed top masses as

the black points for data and as the orange histogfram for the combination of signal and

background templates that best fitted the data. The blue histogram represents only the

background template. The sample with single I__ d events is shown in the left plot, while

the double' I__- d events are shown in the right plot.










[36] W. Yao, K(. Bloom, "Outside-In silicon tracking at CDF", CDF Note 5991.

[37] H. Stadie, W. Wagner, T. Muller, "VxPrim in Run II", CDF Note 6047.

[38] J.F. Arguin, B. Heinemann, A. Yagil, "The z-Vertex Algorithm in Run II", CDF
Note 0.25

[39] CDF collaboration, Jet Energy Group, "Jet Energy Corrections at CDF", CDF Note
7543.

[40] A.A. Bhatti, K(. Hatakeyama, "Relative jet energy corrections using missing Et
projection fraction and dijet I In 1al s! CDF Note 6854.

[41] B. Cooper, M. D'Onofrio, G. Flanagan, \!.i11ll sle interaction corrections", CDF
Note 7365.

[42] A. Bhatti, F. Canelli, "Absolute corrections and their systematic uncert 1!il I. -
CDF Note 5456.

[43] J.F. Arguin, B. Heinemann, "Underlying event corrections for Run II", CDF Note
6293.

[44] A. Bhatti, F. Canelli, L. Galtieri, B. Heinemann, "Out-of-Cone corrections and their
Systematic Uncert .sist s. CDF Note 7449.

[45] R. Wagner, "Electron Identification for Run II: algorithms", CDF Note 5456.

[46] J. Bellinger, "A guide to muon reconstruction and software for Run 2", CDF Note
5870.

[47] D. Glenzinski, "A detailed study of the SECVTX als.. )111 .1.. CDF Note 2925.

[48] D. Acosta, "Introduction to Run II jet probability heavy flavor .- -I__-:, CDF Note
6315.

[49] L. Cerrito, A. Taffard, "A soft muon' I---- 1- for Run II", CDF Note 6305.

[50] P. Azzi, A. Castro, A. Gresele, J. K~onigsberg, G. Lungu and A. Sukhanov, 1
kinematical selection for All-hadronic tt events in the Run II multijet <1 II I-, I CDF
Note 7717.

[51] P. Azzi, A. Castro, A. Gresele, J. K~onigsberg, G. Lungu and A. Sukhanov,
"B-' I__;l!_; efficiency and background estimate in the Run II multijet <1 It I-- I
CDF Note 7723.

[52] Roger Barlow, "Application of the Bootstrap resampling technique to Particle
Physics exp.~ Hin,! Il- MAN/HEP/99/4 April 14 2000.

[53] J.F. Arguin, P. Sinervo, "b-jets Energy Scale Uncertainty From Existing
Experimental Constraints", CDF Note 7252.










Figure 2-4 shows the initial instantaneous luminosity and total integrated luminosity as a

function of year. The initial instantaneous luminosity increased with running time due to

intprovenients such as using the Recycler to store antiprotons. Total integrated luminosity

is separated according to that delivered hv the Tevatron and that recorded to tape by the

CDF detector.

2.2.2 Silicon Tracking

The innermost component of CDF is a tracking system composed of silicon

micro-strip arrays. Its main function is to provide precise position measurements near

collision vertices, and it is essential for identification of secondary vertices.

Constructed in three separate components, LOO [28], SVXII [29] and ISL [:30], the

silicon tracking system covers detector |vy| < 2. LOO is a single 1... -r mounted directly on

the beam pipe, r = 1.6 cm, and is a single-sided array with a pitch of 50 ftn providing

solely axial measurements. SVXII is mounted outside of LOO, 2.4 < r < 10.7 cm, and is

composed of 5 concentric 1.,-< cms in 4 and :3 segments, or barrels, in x. Each lI.-c c is further

subdivided into 12 segments in ~, or wedges. Double-sided arrays provide axial (r 4)

measurements on one side and stereo (x) measurements on the other. The stereo position

of li n-c- c 1 and :3 is perpendicular to the x-axis, and that of lI .-cc 2 and 4 is is -1.2"

and +1.2", respectively. The SVXII detector spatial resolution for axial measurements

is 12 pn1. ISL surrounds SVXII, 20 < r < 29 cm, and is composed of three l o,-c rs of

double-sided arrays. As with SVXII, one side provides axial measurements and the other

stereo measurements at 1.2" relative to the x-axis. The ISL detector resolution for axial

measurements is 16 pni (Figure 2-5).

2.2.3 Central Outer Tracker

The Central Outer Tracker (COT) [:31] comprises the bulk of CDF's tracking volume,

located between 40 < r < 1:32 cm and detector |vy| < 1. The COT provides the best

measurements of charged particle montentunt, but does not measure position as precisely

as the silicon tracking system. It is a 96-1 .,-cc open-cell drift chamber subdivided into 8










the optimization can be found in [50]. Table 5-1 shows the number of events in the data

sample. Table 5-2 shows the number of events in a tt Monte Carlo sample with My =

170 GeV.

The SVX b-' I__-- used has a higher efficiency in the Monte Carlo than in the data.

Therefore we need to degrade the number of' I__- d events according to the appropriate

scale factor which is SF = 0.91. Taking this scale factor into account, and converting to

the luminosity of the data, we show in Table 5-3 the signal to background ratios, S/B,

for different top masses after the kinematical cuts for single and double I__ d events

separately. The conversion to the observed luminosity is done by using the theoretical it

cross section. The number of background events is the difference between the observed

number of events in the data shown in Table 5-1 and the signal expectation.

An additional cut is introduced to further cut down the background. This new

variable we cut on is the minimum of the event probability given in Equation 4-6 of

section 4. Figure 5-1 shows the distribution of the minimum of the negative log event

probability for a signal sample versus the background shape.

Note that the top mass value for which this event probability is minimized will be

used in the final top mass reconstruction, and the value of the probability in negative log

scale is used as a discriminating variable between it and background. We denote this value

as minLKL, and the cut definition is requiring this variable to be less than 10.

The value of this last cut has been obtained by minimizing the statistical uncertainty

on the top mass value as reconstructed in section 4, that is using only the matrix element

calculation. Table 5-4 shows the efficiency of this cut relative to the number of events

after' I__h;~! and after the kinematical cuts, for signal at different top masses and for

background. The table also shows the number of signal events corresponding to 943 pb-l

and the appropriate signal to background ratio.

Comparing the signal-to-background ratios S/B between Table 5-3 and Table 5-4

there is an improvement of about a factor of 3 for samples with one I__ d heavy










The 2D likelihood is shown in Figure 10-2. The central point corresponds to the

nmininiun of the likelihood, while the contours represent the 1-signia, 2-signia, and :$-sigma

levels, respectively.

Using a tt 1\onte Carlo sample with a top mass equal to 170 GeV and the number of

signal and background events as resulted front the data fit, we formed pseudo-experintents

and determined the expected uncertainty on the top mass due to statistical effects and

JES. About 41 of the pseudo-experintents had such combined uncertainty on the top

mass lower than the measured value of :3.7 GeV. This can he seen in Figure 10-3, where

the histogram shows the results of the pseudo-experintents and the blue line represents

the measured uncertainty. In conclusion, the measured combined statistical and JES

uncertainties on the top mass agrees with the expectation.

The total uncertainty on the top mass in this analysis is 4.3 GeV. The previous best

mass measurement in this channel had an equivalent total uncertainty of 5.3 GeV [56]

which is 2 :' more. The source for this intprovenient is the uncertainty due to jet energy

scale (JES) on the top mass. In this analysis this uncertainty amounts to 2.4 GeV

compared to 4.5 GeV in the previous best result which is M' more. Some of this gain in

precision is lost due to the somewhat higher systematic uncertainties front other sources

and due to a slightly worse statistical uncertainty in this analysis compared with the

previous best mass result in this channel. A more careful estimation of the other sources of

systematic uncertainties on the top mass as well as a more efficient it event selection will

help further reduce the total uncertainty on the top mass.

Compared to mass measurements in other it decay channels, the mass measurement

front this analysis ranked third in the top mass world average [57] with a 11 weight.

The two better measurements were performed in the lepton+jets channel as it can he seen

in Figure 10-4. This measurement promotes the all hadronic channel as the second best

channel for the top quark mass analyses in Run II at the Tevatron.










In conclusion, it is for the first time in the it all hadronic channel to have a

simultaneous measurement of the top mass and of the jet energy scale. It is also the

first mass measurement in this channel that involved the use of the it matrix element

either in the event selection or in the mass measurement itself. All of the above were

successfully mixed together resulting in the best top mass measurement in the all hadronic

channel.


r


Table 10-1. Number of events for the it expectation and for the observed total for a
luminosity of 943 pb-l passing all the cuts. The input values for signal have
the uncertainties next to them in parenthesis. The background expectation
being the difference between total and signal is also shown. For the output
values, the numbers in the parenthesis are the uncertainties.
Number of Events Input Reconstructed
Total Observed(1tag) 48 47.8
Expected Signal (1tag) 13 + 3.6 13.2 + 3.7
Background (1tag) 35 34.6 + 7.2
Total Observed(2tags) 24 23.3
Expected Signal (2tags) 14 & 3.7 14.1 & 3.4
Background (2tags) 10 9.2 & 4.3


CDF Runil preliminary L=943pbl CDF Runil preliminary L=943pbl
16 Single Tags 1 --Double Tags
$1v Data
14 -- Dnal+Bakground M Signal+Bakground
5 2 Background I Background


Event Top Mass (GeV/cz)


Figure 10-1. Event reconstructed top mass for data (black points), signal+background
(orange) and only background events (blue). Single I__ d sample is on the
left, while the double' I__- d sample is on the right.
























xM103

600 _

500 -

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300-

200 -

100 -

00 50 100 150 200


hMW1c
Entries 6570
Mean 89.85
RMS 33.51
Underfow 0
Overfow 0
Integral 4.82e+06
X'Indf 4.569e+04126
Prob 0
pO 6.297e+06+i18356
pl 80.17+0.01
p2 7.005+0.01g
p3 1.568e+07+41300
p4 99.65+0.06
p5 29.81+ 0.03
p6 1.152e+07+i36575
p7 0.04026+i0.00000
pa 10.4+0.0
pg1.886+0.007


250 300 350


hMtN2c


7080
84.68
32.44
0
0
13e+05
946130
0
+5379
7+ 0.05
+gage
+9212
4+0.32
8 +0.18
+8169
0.0003
.4+ 0.2
+0.028


350


RMS
40000F Underfow
Overfow
35000 -Integral 2.7
X lndf 4(
30000:Prb
pO 6.582e+05
: pl 80.1i
25000 -p2 gagg5
p3 6.69e+05
20000t p4 94.6
p5 33.51
15000F l ) p6 5.412e+05
p7 0.0408+
10000~ p8 19
pg1.579
5000

00 50 100 150 200 250 300


Entries
Mean


Figure 7-4. Dijet mass templates for background events. Single tags in the

double tags in the right plot.


left plot, and


Table 7-4. Values of the parameters describing the dijet mass templates shapes in the case


of the background events.

Parameter Values (1Tag) Uncertainties (1Tag)

1 1.88e-01 9.52e-02

2 8.02e 01 4. 29e-02

3 7.01e 00 1.70e-02

4 4.68e-01 9.52e-02

5 9.97e 01 4. 29e-02

6 2.98e 01 1.70e-02

7 3.44e-01 9.52e-02

8 4.03e-02 4.29e-02

9 1.04e 01 1.70e-02

10 1.89e 00 9.52e-02


Values (2Tags)

3.53e-01

8.02e 01

9.13e 00

3.59e-01

9.46e 01

3.36e 01

2.90e-01

4.08e-02

1.04e 01

1.58e 00


Uncertainties (2Tags)

2.39e-01

1.12e-01

4.41e-02

2.39e-01

1.12e-01

4.41e-02

2.39e-01

1.12e-01

4.41e-02

2.39e-01















CDF RunlI preliminary L=943pb'


2 A In L=4.5
A In L=2

1C A In L=0.5







-2-

165 170 175 180
Top Mass (GeV/c2)


Figure 10-2. Contours for 1-sigma (red), the 2-sigma (green) and the 3-sigma (blue) levels
of the mass and JES reconstruction in the data.


Figure 10-3. Histogram shows the expected statistical uncertainty from 1\onte Carlo using
pseudo-experiments, while the line shows the measured one. About 41 of all
pseudo-experiments have a lower uncertainty.


CDF RunlI preliminary L=943pbl













































250 -


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0


Figure E-1. Continued














computer network to a storage facility using a robotic tape library. This data is then


processed with offline reconstruction software for use in analyses.


Fermilab's
ACCE L ER TOR CHAIN



fci~ ~\MAIN INJECTOR

.RECYCLER
TEVATRON



11 D:ERI Deetr TAGET HACL
Experiment ANTIPROTON

: (Colllder Deictp Infrmlb .7 :-
-p Iner~l BOOSTER


COCKCROFT-WALTON
PROTON




Dumps



Figure 2-1. Diagram of the Tevatron accelerator complex








CENTRAL DR IT CHAMBER
---~~C*O -- -- iAET IC
x, EM SHAMER
HADRONIC CALORIMETER
MUON DR IT CHAMBERS
--- INTILL TOR
ISL 3 LAER S

svX I (3 BARRELS)




z I-SOLENolD COlL
PRESHowER DETECTOR








Figure 2-2. Elevation view of the East hall of the CDF detector. The West half is nearly

symmetric.










I ml~liiiI II ml~liiiI II ml~liiiID







Fi ur D-2 Cotiue

















17 -
6 17e


JES =-1
oa JES=1
26 =3 8


JES =-1
JES=1
a JES=3


Figure 7-1.


Top templates for it events, single tags in the left plot, double tags in the right

plot. The upper plots show the parameterized curves, while the bottom plots

show the original histograms. The left column shows the templates variation

with top mass at JES = 0. The right column shows their variation with JES

at top mass lHop = 170 GeV.


minLKLmassV1


minLKLmassV1


minLKLmassV1

Mann 1851

ovdernow a
Integrol 4165 a
7ine J814*<4/22


minLKLmassV1
Emneso losi
Mean 1899
Rus 26os

Integral 4231.*04
findr a44/22
proa
po 1o'ii"oo
looeso372e"
112 2940+6417


35000

30000 _

25000 -

20000 -

15000-

10000-

5000-







Figure 7-2.


140 160 180 200 220
Scanned Top Mass (GeVlc 2)


0 140 160 180 200 220
Scanned Top Mass (GeVlc 2)


Top templates for background events. Single tags in the left plot, and double

tags in the right plot.


O
O
O



B rCIJ


,r


I


Figure 7-3.


Dijet mass templates for it events, single tags in the left plot, double tags in

the right plot. The upper plots show the parameterized curves, while the

bottom plots show the original histograms. The left column shows the

templates variation with top mass at JES = 0. The right column shows their

variation with JES at top mass lHop = 170 GeV.


-JES=-3
JES=-1
JES=1
JES=










hits positions: once all COT hit candidates in the event are known, the eight super-l} ... rs

are scanned looking for line segments. A line segment is defined as a triplet of aligned

hits which belong to consecutive l o,-;- s. A list of candidate segments is formed and

ordered by increasing slope of the segment with respect to the radial direction so that high

momentum tracks will be given precedence. Once segments are available, the tracking

algorithm tries to assemble them into tracks. At first, axial segments are joined in a 2D

track and then stereo segments and individual stereo hits are attached to each axial track.

Outside-In algorithm takes COT tracks and extrapolates them into the silicon detectors,

adding hits vi a progressive fit. As each lI .-cc of silicon is encountered (going from the

outside in), a road size is established based on the error matrix of the track: currently,

it is four standard deviations hig. Hits that are within the road are added to the track,

and the track parameters and error matrix are refit with this new information. A new

track candidate is generated for each hit in the road, and each of these new candidates are

then extrapolated to the next 1.,-c c in, where the process is repeated. At the end of this

process, there may be many track candidates associated with the original COT track. The

candidate that has hits in the largest number of silicon 1 .,-c rs is chosen as the real track:

if more than one candidate has the same number of hits, the X2 of the fit in the silicon is

used to choose the best track.

3.2 Vertex Reconstruction

The position of the interaction point of the pp collision (primary vertex) is of

fundamental importance for event reconstruction. At CDF two algorithms can he use

for primary vertex reconstruction.

One is called PrimVtx [37] and starts by using the beam line x-position (seed vertex)

measured during collisions. Then the following cuts (with respect to the seed vertex

position) are applied to the tracks: |Itrk Xertezr| < 1.0 cm, |do| < 1.0 cm, where do is track

impact parameter, and ( < 3.0, where o- is error on do.























C E C E~liiV C E~miI II ml~miV




I mn~uniin I mr~unia I mr~uniaB































Figure D-2. Continued










In Equation 3-10, R is the clustering cone radius, PT is the raw energy measured in

the cone and if the pseudo-rapidity of the jet: f,7, Af,, fabs, UE and 000 are respectively

relative, multiple interactions, absolute, underlying event and out-of-cone correction

factors .

3.4 Leptons Reconstruction

3.4.1 Electrons

Being a charged particle, an electron traversingf the detector first leaves a track in the

tracking system and then loses its energy in the electromagnetic calorinteter. So a good

electron candidate is made of a cluster in the electromagnetic calorinteter (central or plug)

and one or more associated tracks; if available, shower nmax cluster and preshower clusters

can help electron identification. The shower has to be narrow and well defined in shape,

both longitudinally and transversely. The ratio between hadronic and electromagnetic

energies has to be small and track montentunt has to match electromagnetic cluster

energy [45].

3.4.2 Muons

Muons can leave a track in the tracking system and in the nmuon system, with little

energy deposition in the calorinteter. Aluons are reconstructed using the information

coming front nuon chambers (CMET, CM~P, CM~X, BIfET) and nmuon scintillators

(CSP, CSX, BSU, TSU). The first provide measurements of drift time, which is then

converted to a drift distance (i.e., a distance front the wire to a location that the nmuon has

occupied in its flight, in the plane perpendicular to the chamber sense wire). Scintillators,

on the other hand, only produce timing information. The output of chambers and

scintillators produce nmuon hits. A nmuon track segment (a stub) is obtained by fitting

the nmuon hits. Finally, COT tracks are extrapolated to the nmuon chambers and matched

to nmuon stubs in the r plane [46].











TABLE OF CONTENTS


page

ACK(NOWLEDGMENTS ....._.__ .. .. 4

LIST OF TABLES ....._.. ... 9

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

ABSTRACT ......_ .._ ._ .. 14

CHAPTER

1 INTRODUCTION ..... ... 15

1.1 History of Particle Physics ......... .. .. 15
1.2 The Standard Model ......... . .. 21
1.3 Top Quark Physics ......... .. .. 2:3
1.4 Highlights of Mass Measurement . ..... .. :32

2 EXPERIMENTAL APPARATUS ....._ .. :38

2.1 Tevatron Overview ........ . .. :38
2.2 CDF Overview and Design ........ ... .. 40
2.2.1 Cl.,~ i. al:0,v Luminosity Counters ..... ... .. 41
2.2.2 Silicon Tracking ........ .. .. 42
2.2.3 Central Outer Tracker . .. .. .. 42
2.2.4 Calorinteters ........ ... .. 4:3
2.2.5 The bluon System ....... ... .. 44
2.2.6 The Ti1;__ 1- System ....... .. .. 44

:3 EVENT RECONSTRUCTION ........ .. 51

:3.1 Tracks ........ . .. 51
:3.2 Vertex Reconstruction ........ . .. 5:3
:3.3 Jets Reconstruction ........ .. .. .. 54
:3.3.1 Relative Energy Scale Correction .... .. .. 56
:3.3.2 Multiple Interactions Correction .... .... 57
:3.:3.3 Absolute Energy Scale Correction .... .. .. 57
:3.3.4 Underlying Event Correction . ... .. 58
:3.3.5 Out of Cone Correction ..... .. .. 58
:3.4 Leptons Reconstruction ........ .. 59
:3.4.1 Electrons ........ . .. 59
:3.4.2 Aluons ........ . .. 59
:3.4.3 Tau Leptons ........ .. .. 60
:3.4.4 Neutrinos ........ . .. 60
:3.5 Photon Reconstruction ........ .. .. 60
:3.6 Bottom Quark TI_-! .. it,-; ... .. .. .. 61










quark separates itself from all other quarks. For example, it is the most massive fermion

by a factor of nearly 40 (the bottom being the closest competitor).

Interestingly, even though the top quark is the most recent quark observed, its mass

is the best known of all quarks. This is because it has such a short lifetime that it decays

before any hadronization effects can occur. We should not be satisfied with this relative

success and a more accurate determination of M~to is Strongly motivated inside and

beyond the SM.

The top quark is the weak isospin partner of the b-quark in the Standard Model. As

such, it carries the following quantum numbers: an electric charge +2/3, an intrinsic spin

of 1/2 and a color charge associated with the strong force. Due to the relatively small data

sample collected in Run I of the Tevatron, none of these assignments have been measured

directly. However, strong indirect evidence exists. First, the precision electroweak data of

Z boson decay properties requires the existence of an isospin partner of the b-quark with

electric charge +2/3 and a large mass. Furthermore, the predicted rate of top quark pair

production, which is very sensitive to the spin and strong coupling of the top quark, is

in good agreement with the data [3] [4] [5] [6]. Therefore, current observations lead us to

believe that the particle observed at the Tevatron is indeed the top quark. However, direct

measurements are still desirable and will be attempted in the case of the electric charge

and spin using data from the Run II of the Tevatron or the LHC [7].

The other intrinsic properties of an elementary particle are its mass and lifetime. The

most precise knowledge of the mass comes from direct measurements. The current world

average containing only measurements performed during Run I at the Tevatron is 178

+ 4.3 GeV/c2. In quantum mechanics, the lifetime of a particle is related to its natural

width through the relationship -r = &/0. The branching ratio for the electroweak top

quark decay t Wb is far larger than any other decay mode and thus its full width can

be approximately calculated from the partial width F(t Wb). Assuming Myw = M1,. = 0,

the lowest order calculation of the partial width has the expression shown in Equation 1-1,










4.7 Checks of the Matrix Element Calculation

The event probability described in the section 4.6 depends on the top quark pole mass

and is expected to be minimized in negative log scale around the true masses in the event.

Multiplying all the event probabilities we obtain a likelihood function that depends on the

top pole mass. Equation 4-48 shows the expression of the likelihood.


L(Mtop) = (jMtp)8)
events

In negative log scale this likelihood is expected to have a minimum around the true

pole mass, and so the top mass reconstruction can be performed. This reconstruction

is the traditional matrix element top mass reconstruction. However, we only use this

reconstruction to check the matrix element calculation.

We use Monte Carlo samples generated at various input top masses. Only signal

events are used. For each sample, the reconstructed top mass done by using only the

matrix element calculation can be plotted against the input top mass. This can be done

at various levels of complexity. Ideally, we'd see a linear dependence with no bias and a

unitary slope.

The first check to do is at the parton level. We take the final state partons moment

from our Monte Carlo, smear their energies and use them as jets moment. Figure 4-5

shows a good linearity in the case of a 5' uniform smearing. There is a small bias of

about 0.8 GeV, but the slope is consistent with 1. As the smearing is increased the bias

becomes more evident, and slope degrades slightly. This can be also seen in Figure 4-5

for 101' smearing and for 211' smearing, respectively. In all of these situations a gaussian

centered on 0 and with width equal to the amount of smearing used has been emploi-x I as

a transfer function in the event probability computation.

The partons can also be smeared using the functions described in section 4.4, in

which case the same functions are used as transfer functions in the event probability

computation. This test makes the transition between the parton level to the jets level,












'~ ~'7 exp ( n (ment W S))

exx

to (mi az)
c03 \"ev "4 2
exp -(-2


NV(M, JES) from Equation 7-12 is given in


eve N(M~, JES)

x (mentW a~s)t9





The expression for normalization term

Equation 7-13.

1:


3k+1 JES + p3k+2 J~ES2) Mk~'


(713)


The dependence of the parameters asi from Equation 7-12 as a function of the top

mass M~ and jet energy scale JES is given by Equation 7-14.


as = p3i+6 + 3i+7 M~ + p3i+8 JES, i = 0, 9


(7-14)


The X2 per degree of freedom is 3551/2636 = 1.35 for the single' I__- d sample and

2972/2524 = 1.18 for the double' I__- d sample. The X2 has the same definition as in

Equation 7-11. In each sample, the values of the 36 parameters, p, are given in Table 7-3.

The shapes of few of the signal templates as well as the parameterized curves are shown in

Figure 7-3.

The background template shape is build in the same way as the signal templates. The

top contamination is removed in the same way as in the case of the top templates (see

section 7.2).

The background template is fitted to a normalized sum of two gaussians and a gamma

integfrand. For both the single' I__- d and the double' .,---- d samples, we show the values

of the parameters in Table 7-4.









CHAPTER 5
DATA SAMPLE AND EVENT SELECTION

5.1 Data and Monte Carlo Samples

The data events are the Run2 CDF multi-jet events selected with the TOP_M~ULTIJET

trigger, and it amounts to approximately 943 pb-l. This trigger selects about M' of the

it all hadronic events.

The Monte Carlo samples are the official CDF samples. We use 12 different samples

generated with the Herwigf package to parameterize the mass dependence of our templates.

The mass takes values from 150 GeV to 200 GeV in 5 GeV increments. There are also

samples with a top mass of 178 GeV used to determine various systematic uncertainties:

different choice of generator (in this case we used the Pythia package), different modeling

of the initial state radiation (ISR) and of the final state radiation (FSR), different choice

of proton parton distribution function (PDF). The background model described in

section 6 is validated with the help of two Monte Carlo samples generated with the Alpgfen

package: one with events having bb+4 light partons in the final state and another with

events having 6 light partons in the final state.

5.2 Event Selection

Before describing and listing the selection cuts, we need to mention the sample

composition. The multi-jet events contain beside our signal events, a multitude of

backgrounds:

* QCD multi-jets

* hadronic W,Z production

* single top production

* pair production in other channels

The QCD multi-jet production has the N----- -1 contribution, while the others can be

neglected since they involve electroweak couplings.









M~w and lMop. Indeed, the correction to the W boson mass Ar given in Equation 1-4

contains additional terms due to Higgs boson loops. These corrections depend only

logarithmically on M~H and have thus weaker dependence on M~H than on lMop. Still,

precise determination of lMop and M~w can be used to obtain meaningful constraints on

M~H aS illuStrated in Figure 1-5. Numerically, the constraints are [14] made explicit in

Equations 1-7 and 1-8.


M~H = 126+47 GeV/c2 (7

M~H < 280 GeV/c2 at 95' C.L., (1-8)


Only the top quark mass measurements from Run I have been used. Such constraints

on M~H can help direct future searches at the Tevatron and LHC and constitutes another

stringent test of the Standard Model when compared to limits from direct searches or

mass measurements from an eventual discovery.

Even though the Standard Model successfully describes experimental data up to a few

hundred GeV, it is believed that new physics must come into pIIl w at some greater energy

scale. At the very least, gravity effects are expected at the Planck scale (a 1019 GeV) that

the SM ignores in its current form.

The SM can thus be thought of as an effective theory with some unknown new

physics existing at higher energy scale. A link exists between the new physics and

the SM that manifests itself through radiative corrections to SM particles. The Higgs

boson sector is the most sensitive to loops of new physics. For example the Higgs boson

mass corrections from fermion loops shown in diagram (a) of Figure 1-6 are given by

Equation 1-9, where mf is the fermion mass and A is the "cut-off" scale used to regulate

the loop integral.

AM -i 2A +6f ln(A~ i /my + f ..., (1-9)

The parameter A can be interpreted as the scale for new physics that typically

corresponds to the scale of the Grand Unified Theory (GUT) near 1016 GeV. This is a






























X2 /ndf 0.5199 /6
Prob 0.9976
pO 0.05343 & 0.09964


X2 / ndf 36.54 / 6
Prob 2.168e-06
pO 1.058 &0.002828


-3 -2


0. 3 -2 -1 0


-
Input JES


2 3
Input JES


Figure 8-12. JES pull means versus

input top mass, for

input top mass equal
to 170 GeV.


Figure 8-13.


JES pull widths versus

input top mass, for

input top mass equal
to 170 GeV.


X2 / ndf 3.468 /11
Prob 0.983
pO 0.05026 10.02838


X2 / ndf 550.7 /111
Prob 0
pO 1.0441 0.0008059


150 160 170 180 190 200
Input Mass


150 160 170 180 190 200
Input Mass


Figure 8-15. Average of JES pull
widths versus input

top mass.


Figure 8-14. Average of JES pull
means versus input top
mass.


0.4 -
,0.3



0-











I- mn-==0iV I [--=-VI II n 0liiV










Figur D-2 Cotiue












I mnlKlmiiiVI I


id_
I mnrKuniiin I



I mnrKuniiin I



I mnrKuniiin I


I mnlKlmiiiVI I


Ikl
I mnrKuniia I



I mnrKuniia I


~LI
I mnrKuniia I


I mnlKlmiiiVI I



I mnrKuniia I



I mnrKuniia I



I mnrKuniia I



M


Figure D-2. Top templates for it double' I__- d events for samples with different top


masses: from 150 GeV to 200 GeV. A) Case of JES =
JES = -2. C) Case of JES = -1. D) Case of JES =
JES = 1. F) Case of JES = 2. G) Case of JES = 3.


-3. B) Case of
0. E) Case of





















80.5-


(D
CD
S80.4-

E


80.3-


Figure 1-5.


Constraint on the Higgfs hoson mass as a function of the top quark and W
hoson measured masses as of winter 2007. The full red curve shows the
constraints (0.1' C.L.) conting from studies at the Z hoson pole. The dashed
blue curve shows constraints (0.*' C.L.) front precise nicasurenient of M~w and


f


S
I \
I (
I
H\ I


(2) (b)



Figure 1-6. Loop contributions to the Higgs hoson propagator front (a) fernlionic and (b)
scalar particles.


175

mt [GeV]










background shapes one corrected for top of 160 GeV and the other corrected for top of 180

GeV. The change in the value of the reconstructed top mass is 0.9 GeV.

9.6 Background Statistics

Another effect we address here is the effect of the limited statistics of the sample

used to generate the background sample. To estimate this effect is enough to vary the

parameters describing the background shapes. First we notice that the dijet mass template

histograms for background are quite smooth, so only the event top mass template

histograms will be modified.

One has to reniember that the background model is based on about 2600 pretag data

events passing the kinentatical selection. Then using the nxistag matrix we artificially

increased the size of this sample by calling i.; 10 any distinct I__ d configuration.

Therefore any of the original 2600 events will generate a number of these artificial

.; .. 1 '. This number will be referred to as the multiplicity of the real event.

In order to find the uncertainties on the background parameters, we need to fluctuate

the content of the template histograms. Given the fact that entries of these histograms are

not real events, but artificial i... at ', we have to somehow fluctuate the number of real

events front each hin. The procedure is described below:

* assume the event multiplicity the same for all real events and equal to the average
multiplicity for the whole sample: 735 for single tags and 41 for double tags

* before the it contamination removal and based on the constants above, we scale down
the template histograms

* fluctuate the content of the scaled histograms using the Poisson probability

* after the Poisson fluctuation, scale back up the histogframs, remove the it contamination
and fit with a gaussian to obtain the new template function

* repeat the above steps 10,000 times, and histogfram the parameters of the new
templates

* extract the uncertainties on the background parameters front these last histograms


































S2007 Gheorghe Lungu





































0.7 0.8 0.9


APPENDIX A

PARTON DISTRIBUTION FUNCTION OF THE PROTON


pdfs _u


pdfs_u
ntes 9800
sen 0.2078
us .1ss


terl 2072


Oup
Odown
Ogluon
Oubar
Ot*3r
strange
charm
Obottom


sum
Fntrier 9800
Mean 0.00094
RMS 0.1239
Underfow 0

0.9954

Integral=0.995420








0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9


Figure A-1. Upper plot
section 4.3.

PDFs.


shows the PDF shapes used in the matrix element calculation of

Bottom plot shows a cross check of the normalization of these


1.5





0.5


00 0.1 0.2 0.3 0.4 0.5 0.6









The term aro is due to the running of a~. The term Ap is due to the one-loop

top quark correction to W-boson propagators shown in Figure 1-4, and is given by

Equation 1-6.


3 GF Mt2,
Ap = (1-6)
80K2~r
The uncertainty on the Fermi constant GF is completely negligible with respect to the

one on the top quark mass in the computation of Ap. The term aro and the Weinberg

angle in Equation 1-5 are known to a precision of 0."' The uncertainty on the top quark

mass is currently about an order of magnitude larger than the other uncertainties and

moreover it contributes quadratically to Ar. Thus the precision on Met, is currently the

limiting factor in the theoretical prediction of the W boson mass. The parameter Ap is

qualified as "universal" in the literature because it enters in the calculation of many other

electroweak observable like sinew and the ratio of the production of b-quark hadrons of all

types (usually denoted Rb), to name a few. Therefore, the top quark mass pha7i~ a central

role in the interplay between theoretical predictions and experimental observables that

aims to test consistency of the SM.

One consistency check is to compare the measured value of M~t, with the predicted

value from SM precision observables (excluding of course direct measurements of Meo).

The indirect constraints, inferred from the effect of top quark radiative corrections,

yields M~t, = 181'82 GeV/c2 [14]. The relatively small uncertainty is achieved because of

the large dependence of M~t, on many electroweak observables. This is in remarkable

agreement with the Run I world average of M~t, = 178 + 4.3 GeV/c2 [15], and is
considered a success of the SM.

A similar procedure can be used to constrain the Higgs boson mass (M~H), the last

particle in the SM that has yet to be observed. The only direct information on M~H is a

lower bound obtained from searches at LEP-II: M~H > 114 GeV/c2 at 95' confidence

level [16]. Indirect constraints on M~H can be obtained with precise measurements of










fundamental. Observing the pattern of the leptons many physicists started believing

in the existence of a fourth quark, called charm (c). In 1970 Glashow, Iliopoulos and

Alaiani proposed a mechanism through which the weak theory will allow flavor-conserving

Zo-mediated weak interactions. This mechanism was requiring the existence of a fourth

quark. Later in 197:3, at CERN, Perkins found evidence of weak interactions with no

charge exchange. The existence of charm was confirmed in 1974 by Richter and Ting who

found a charm-anticharm meson called J/W, and then reconfirmed in 1976 by Goldhaber

and Pierre who found a charm-antiup meson called DO.

A quantum field theory of strong interaction is formulated in 197:3 hv Fritzsch and

Gell-Mann. They introduce the gluon (g) as a massless quanta of the strong force. This

theory of quarks and gluons is similar in structure to QED, but since strong interaction

deals with color charge this theory is called quantum chromodynamics, or QCD. The

color charge was a concept introduced earlier in 196:3 by Greenberg, Han and Nambu.

The hadrons made of quarks were considered color neutral. In 197:3, Politzer, Gross and

Wilczek discover that at short distances the strong force was vanishing. This special

property was called.movi-nlll Ie freedom. In 1979, a strong evidence for a gluon radiated

by a quark is found at DESY, in Hamburg, Germany.

In 1976, another unexpected particle is discovered. This new particle seen by Perl at

SLAC was the tau lepton, denoted 7r, and it was the first particle of the third generation.

In 1977, the existence of a third generation was confirmed by Lederman at Fermilah by

discovering a new quark, called bottom (b). In 1989, the experiments at SLAC and CERN

strongly supported the hypothesis of only three generations of fundamental particles by

measuring the lifetime of Zo-hoson. Later in 1995 at Fermilah the remaining quark of the

third generation is discovered. This is called the top quark (t) and it has mass much larger

than the other quarks. Also at Fermilah the third generation is completed by the discovery

of the tau neutrino (v-) in 2000.












9.11 Summary of the Systematic Uncertainties

The total systematic uncertainty on the top mass combining all the effects listed

above is 2.1 GeV. Table 9-3 suninarizes all sources of systematic uncertainties with their

individual contribution as well as the combined effect.

EntrgdMt63 EntbgM~t12
45 Mean 7348 600 -Mean 4063
RMS 4969 RMS 388
40 Undemfow 0Undemfow0
35 ovemow o 500 -ovelfow
Integral 633 Integral 1120
30 400-
25
,, n,300-


0500 1000 1500 2000 2500 3000


050 100 150 200 250 300 350 400


Figure 9-1. Event multiplicity for background events. On the left is shown the plot for
single' I__- d events, while on the right the plot for double I__ d events is
shown.



Table 9-1. Uncertainties on the parameters of the top mass templates for background.

Parameter 1 tag 2 tags
Constant 10.2e-04 7.0e-04
Mean 2.59 :3.35

Sigma 272.1 711.9


Table 9-2. Residual jet energy scale uncertainty on the top mass.

Level Uncertainty (GeV/c2)
L1 0.2
L4 0.1
L5 0.5
L6 0.0
L7 0.5
L8 0.1
Total JES Residual 0.7










ACKENOWLED GMENTS

The first person I want to acknowledge is my advisor, Prof. Jacobo K~onigsberg,

for guiding and supporting me during my graduate student years in ner IlrJ rlis. His

dedication, his commitment to his work and his students, and his savviness in the

high-energy experimental field serve as an example to which I aspire as a physicist

and as a scientist.

Also I will be forever grateful to Dr. Valentin Necula in many aspects. He made

possible many things for me starting with lending me money to pI li the tests needed for

admission in the graduate school at the University of Florida. Moreover, he contributed

greatly to the success of this analysis, from the writing the C++ code for main tools

and ending with rich and enlightening discussions on the topic. His great skills and his

excellence represent a standard for me.

I would like to mention the great influence I received in my first years at the

University of Florida from Prof. K~evin Ingersent and Prof. Richard Woodard. With

or without their awareness, they helped me deepen my knowledge in theoretical physics.

Also I take this opportunity to thank the members of the committee supervising this

thesis: Dr. Toshikazu Nishida, Dr. Richard Field, Dr. Pierre Ramond and Dr. Guenakh

Mitselmakher. I will be inspired by their tremendous work and by their extraordinary

achievements in physics. Despite our rather brief interaction, I want to mention that my

experience during my Oral Examination helped redefine me as a physicist and as a person.

At CDF I drew much knowledge from interacting with many people such as Dr.

Roberto Rossin, Dr. Andrea Castro, Dr. Patrizia Azzi, Dr. Fabrizio Margfaroli, Dr.

Florencia Canelli, Dr. Daniel Whiteson, Dr. Nathan Goldschmidt, Dr. Unki Yang, Dr.

Erik Brubaker, Dr. Douglas Glenzinski, Dr. Alexandre Pronko, Dr. Mircea Coca, Dr.

Gavril Giurgiu. Special thanks to Dr. Dmitri Tsybychev, Dr. Alexander Sukhanov and

Dr. Song Ming Wang who helped me greatly getting up to the speed of the experimental

physics at CDF. Also I want to mention and thank Yuri Oksuzian and Lester Pinera for












P~jsn = ) j dzedzbfx) x b a b I 6 (2r32Edi (2x,)4 (4)(Efi, Ei,i)
4EEblV U a 2)3E tot (m)e(m) Ncombi
combi i= 1
|A|2 C E|2,,


x 6(2) 36)
i=1 i 2x (p )2

As mentioned previously, we will not use any constant that can be factored out in

the expression of the probability density. From now on we will omit all such constants

except for the number of combinations, Ncombi. Also in the- argument- of Prw ilu

just p6 but it should be understood ()2 2Which in turn should be understood

as a function of the 4-vectors of the final state partons.

We will move to spherical coordinates in the integration over the partons moment.

Due to the assumption that the angles of the partons are known as the measured angles

of the jets, made explicit by the delta functions, 6(2)(R04 04p), all the integrals after the

angles will be dropped together with the aforementioned delta functions. Also we use (4

instead of ((ji) in the argument of T.

One should notice that |E|2 1S divided out by the energy factors in the denominator

as seen in Equation 4-37.


P~j n)= j Va -, Itot(m)e(m) Ncombi ji p iF~ p)]
combi i= 1

x t -I' Py -t P (|Mag|R2 + | |17~,2 6(4)(Efi,, Ez,i) (4-37)
p6

To reduce the number of integrals we will work in the narrow width approximation for

the W-bosons. This translates in two more delta functions arising from the square of the

W-boson propagators as shown by Equation 4-38.


Pw =1 rw~l MW 6 2 -14 M ) (4-38)
(P& M)2+ W M~Wry










is a normalized product of a Breit-Wigfner function and an exponential. The parameters

of this function depend linearly on top mass and JES. The Equation 7-8 d~;-1i ph the fit

function and the dependence of its parameters on top mass and JES.


11

x (7-8)


The expression for normalization term NV(M, JES) from Equation 7-8 is given in

Equation 7-9.


N(MJES)= ( 3k 3+1 JES + p3k+2 JES2) Mk~ _79)


The dependence of the parameters asi from Equation 7-8 as a function of the top mass

M~ and jet energy scale JES is given by Equation 7-10.


asc = p1s i = (7-10)
p3i+13 + 3i+14 M~ + p3i+15 JES i = 2, 3

The X2 per degree of freedom is 1554/1384 = 1.12 for the single' I__- d sample

and 1469/1140 = 1.29 for the double' I__- d sample. The expression for X2 1S given ill

Equation 7-11.
p12 p7 Nl~bins hbin -fbin2
tm= 1 j= 1 bin=] hi <@ ))
(E2 p b ihns 1) 25

where hbin is the bin content of the template histogram and fbin is the value of the

function from Equation 7-8 at the center of the bin. The summation in Equation 7-11

is done for all templates and for all the bins for which Abin has more than 5 entries. The

denominator of Equation 7-11 is the number of degrees of freedom.

For each sample, the values of the 25 parameters, p, are given in Table 7-1. The

shapes of few of the signal templates as well as the parameterized curves are shown in

Figure 7-1.









[17] H. Haber and R. Hempfling, Phys. Rev. Lett. 66, 1815 (1991); Y. Okada, M.
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[31] T. Affolder et al. (CDF Collaboration), Nucl. Instrum. Meth. A 526 249-299 (2004).

[32] L. Balka et al. (CDF Collaboration), Nucl. Instrum. Meth. A 267 272-279 (1998); S.
Bertolucci et al. (CDF Collaboration), Nucl. Instrum. Meth. A 267 301-314 (1998).

[33] M. Albrow et al. (CDF Collaboration), Nucl. Instrum. Meth. A 480
524-545 (2002); R. Blair et al. (CDF Collaboration), Fermilab Report No.
FERMILAB-Pub-96-390-E, Section 9 (1996); G. Apollnari et al. (CDF
Collaboration), Nucl. Instrum. Meth. A 412 515-526 (1998).

[34] A. Artikov et al. (CDF Collaboration), Nucl. Instrum. Meth. A 538 358-371 (2005).

[35] P. Gatti, "Performance of the new tracking system at CDF II", CDF Note 5561.










leading six jets, and of the sub-leading four jets, aplanarity and centrality as defined in

section 5.

6.2.2 Validation in Control Region 2

We compare shapes between our background model for this region and a Monte Carlo

background. The background model for this region is formed by taking the pretag data

sample in this kinematical region and by using the mistag matrix to obtain the tag rates.

The Monte Carlo sample used has bb + 4 light partons in its final state.

One variable we can look at is the sum of the event probabilities as defined in

section 4 using the matrix element. The sum is between a top mass equal to 125 GeV up

to 225 GeV in steps of 1 GeV. Figure 6-3 shows the shapes of Monte Carlo background

and of the data-driven background.

Another interesting variable is the invariant mass of all the untl I_ d pairs of jets in

the event. Figure 6-4 shows this variable for the I__ d events before the minLKL cut,

while Figure 6-5 shows the case of' I__- d events after the minLKL cut.

6.2.3 Validation in the Signal Region

The top mass value for which the event probability is minimized represents another

interesting variable. Figure 6-6 shows this variable for events after the minLKL cut.

The event by event most probable top mass and the dijet mass variables are of

particular interest since they will be used in the reconstruction of the top mass and of the

JES variable to be described in section 7. All these comparisons show good agreement

between our data-driven background model and the Alpgfen bb + 4 light partons.

6.2.4 Effects on the Statistical Uncertainty

Using a top mass reconstruction technique based solely on the matrix element, we can

vary the background fraction of our mixture of signal and background events and observe

the effects on the statistical uncertainty of the top mass.

The goodness of the mass reconstruction is related to the parameters of the

reconstructed versus the input top mass. The statistical uncertainty is affected by the










Once collected into a beam, the antiproton are sent to the Debuncher, a triangular

synchrotron with a radius of 90 m, where their spread in energy is reduced using a

synchronized oscillating potential in the RF cavities. This potential is designed to

accelerate slower particles and decelerate faster particles. Uniform velocities of antiprotons

enables more efficient beam manipulation and increases instantaneous luminosity by

reducing bunch widths.

Thus prepared, the antiprotons are collected and stored until they are needed

for acceleration and collisions. One storage unit, the Accumulator, is a synchrotron

in the same tunnel as the Debuncher, labeled .1.1sI n-IIn~~ source" in Figure 2-1. The

Accumulator reduces the longitudinal momentum of the antiprotons using a synchronized

potential and stochastic cooling [24]. Stochastic cooling was developed at CERN in the

1970s and dampens unwanted momentum phase-space components of the particle beam

using a feedback loop. Essentially, the beam orbit is measured with a pickup and corrected

with a kicker.

The other antiproton storage unit is the Recycler, a synchrotron in the same ring as

the Main Injector. The Recycler was originally designed to collect antiprotons from the

Tevatron once collisions for a given store were finished, but attempts to use it for this

purpose have not been worthwhile. As an additional storage unit, the Recycler has allowed

increased instantaneous luminosity since 2004. The Recycler takes advantage of electron

c....11nlr in which a 4.3 MeV beam of electrons over 20 m is used to reduce longitudinal

momentum. When a store is ready to begin, antiprotons are transferred from either or

both the Accumulator and the Recycler to the Tevatron for final acceleration.

2.2 CDF Overview and Design

The Collider Detector at FNAL (CDF) is a general purpose charged and neutral

particle detector [25] [26]. It surrounds one of the beam crossing points described in

section 2.1. The detector observes particles or their decay remnants via charged tracks

bending in a 1.4 T solenoidal field, electromagnetic and hadronic showers in calorimeters,










Tracks surviving the cuts are ordered in decreasing pr and used in a fit to a common

vertex. Tracks with X2 TelatiVe tO the vertex greater than 10 are removed and the

remaining ones are fit again to a common point. This procedure is iterated until no

tracks have X2 > 10 relative to the vertex.

The second vertex finding algorithm developed at CDF is ZVertex~oll [38].

This algorithm starts from pre-tracking vertices (i.e., vertices obtained from tracks

passing minimal quality requirements). Among these, a lot of fake vertices are present:

ZVertex~oll cleans up these vertices requiring a certain number tracks with pT > 300 MeV

be associated to them. A track is associated to a vertex if it is within 1 cm from silicon

standalone vertex (or 5 cm from COT standalone vertex). Vertex position z is calculated

from tracks positions zo weighed by their error 6 according to Equation 3-3.


z = (3-3)


Vertices found by ZVertex~oll are classified by quality flags according to the number

of tracks with silicon/COT tracks associated to the vertex. Associated COT tracks have

shown to reduce the fake rate of vertices thus higher quality is given to vertices with COT

tracks associated:

* Quality 0: all vertices

* Quality 4: at least one track with COT hits

* Quality 7: at least one track with COT hits, at least 6 tracks with silicon hits

* Quality 12: at least 2 tracks with COT hits

* Quality 28: at least 4 tracks with COT hits

* Quality 60: at least 6 tracks with COT hits

3.3 Jets Reconstruction

Jets are reconstructed by applying a clustering algorithm to calorimeter data. This

algorithm determines the number of jets in an event, their energies and directions.










future prospects (e.g., black curve for Tevatron/LHC and red curve for the International

Linear Collider (ILC)) demonstrates very good discriminating power. The radiative

corrections from MSSM particles to the SM precision observables are discussed in more

detail in [19].

Other alternatives to replace the SM at energies near the TeV scale are theories

involving dynamical breaking of the electroweak symmetry [20]. These models, one

well-known example being Technicolor [21], do not include an elementary Higgs boson,

but rather give mass to the SM particles by introducing a new strong gauge interaction

that produce condensates of fermions that act as Higgs bosons. In some versions of

these models, denoted "topl In i the new gauge interaction acts only on the third

generation, and the fermion condensates are made of top quarks [22]. Such a model could

be discovered by looking for evidence of new particles in the it invariant mass at the

Tevatron or LHC.

1.4 Highlights of Mass Measurement

Now that the top quark was placed in the context of particle physics and of the

Standard Model, the most successful theory describing it, we stop to outline the remaining

of the study. In the following chapters a detailed analysis of the measurement of the mass

of the quark will be presented.

The experimental apparatus used to produce and collect the data is described in

broad details. This description is divided into a section dedicated to the accelerator of

particles, Tevatron, and another for detailing the particle detector, the Collider Detector

at Fermilab (CDF). M1 I.ny techniques are used for the identification of particles separately

for leptons, photons, quarks and gluons.

A more sophisticated tool involves the calculation of the matrix element for the

process us i tt bbundd used in the computation of a probability to observe such

process. This probability will be later used in the event selection and the in the mass




























































bbTFE_0_ bTFE 1 1
E'ntri son8 Entum 02

men oomo mea on. a.. B
300~~~,,. us 091 Rs 01
undemow 1I 300C undemow
"ealow o1 omow
25 -Iteoria so27 rI Inteoral Iml
xinar 3a26/34 250C -I Ix inr loeoiso
Pronl o2e22 I Pronl o42o
20 -consti 2713mas I consl 1307+2s3
emisl oose22ioooae 200C -I meani oloostooloo
slumal oosalifoooml I slumal oo11matooose

10-const2 2m82r8ozes cona2 1863+262
Meml2 oI991soa242 150C mean. 2 oo4374tooem
sigmn omo2rosi2o I slma2 oo282otooo41o

100 100-









-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2





EntiebTF_ 2 41

500os menoose
ans o1632
undemow
ouealow

400 Itoera 4168
,irnr 4564/2s
Prone oolme8
conni 2193+307

300- umsl o14oosiool11
slumal ominooo2e
conn2 2Bli29e

200 oslum2 oo232i00ooas



100mi -016~0









-2 -1.5 -1 -0.5 0 0.5 1 1.5 2






Figure C-2. Continue
















































147
















Graph

S 4 -

3-

O 2









-2-

-3-


150 160 170 180 190 200
output Mass


Figure 8-1. JES versus Top Mass plane. The
mass.


points represent the reconstructed JES and


X2 /ndf 4.116 /10
020 Prob 0.942
SpO 175.3 i0.2763
8190 pl 0.9674 10.01897 -







150 160 170 180 190 200
Input Top Mass [GeV]


Figure 8-2. Reconstructed top mass
versus input top mass,
for input JES equal to
0.


2 / ndf 0.6064 /5
Prob 0.9877
pO 0.0459310.0849
pl 0.98910.04234


//


-3 -2 -1 0 1 2 3
Input JES


Figure 8-3. Reconstructed JES
versus input JES, for
input top mass equal to
170 GeV.









corresponds to the measured mass Myw a 80.4 GeV/c2), given that Mt, > M~w + Ml,

This is an important characteristic of it events that is exploited in this analysis in the

reconstruction of the top quark mass and the W boson mass. The W boson will in

trn decay to two quarks about 2/3 of the time and a charged lepton associated with a

neutrino about 1/3 of the time.

The experimental signature of top quarks thus emerge. They are produced as it pairs,

each one decaying immediately to a real W boson and a b-quark, the latter hadronizing

to form a b-jet. The resulting W decay defines the it final state: There can be two

hadronic decays (all-hadronic channel), one leptonic and one hadronic decay (lepton + jets

channel), and two leptonic decays (dilepton channel), where the leptonic decays considered

are usually only to electrons and muons (with their associated neutrinos) due to the

experimental difficulty of identifying tau leptons. The approximate branching ratios for

each channel are given in Table 1-3.

The top quark pIIl us a central role in the predictions of many SM observables by

contributing to their radiative corrections. Good examples are the W and Z boson

propagators, in which loops involving top quarks are expected to strongly contribute, as

illustrated in Figure 1-4. These diagrams can exist for any type of quark or lepton, but

the very large value of M~t, makes the top quark contribution dominant. To illustrate the

effect of the top quark, we consider in Equation 1-4 the theoretical calculation of the W

boson mass [12].
xacl 1
z/Gysin28w 1 ar )
a~ is the fine structure constant, Ow is the Weinberg angle and Ar contains the

radiative corrections and is approximately given by Equation 1-5.









In Figure 3-3 the absolute jet energy scale corrections for jets cone size of 0.4 as a

function of the jet momentum (blue). The uncertainty for this correction is also shown as

a function of the jet momentum (black).

3.3.4 Underlying Event Correction

In a hadron-hadron collision, in addition to the hard interaction that produces the

jets in the final state, there is also activity in the detector originating from soft spectator

interactions. In some event, the spectator interaction may be hard enough to produce

soft jets. Energy from the underlying event can fall in the jet cones of the hard scattering

process thus biasing jet energy measurements. A correction factor for such effect has been

calculated using a sample of minimum bias events as for multiple interaction correction,

but selecting only those events with one vertex [43]. For each event, transverse energy

Er inside cones of different radii (0.4, 0.7 and 1.0) is measured in a region far away from

cracks (0.1 < |9|l < 0.7). The correction factor is extracted from the mean values of ET

distribution (Figure 3-4).

3.3.5 Out of Cone Correction

The jet clustering may not include all the energy from the initiating partons. Some

of the partons generated during fragmentation may fall outside the cone chosen for the

clustering algorithm. This energy must be added to the jet to get the parton level energy.

A correction factor is obtained using MC events [44]: hadron-level jets are matched to

partons if their distance in the rl plane is less than 0.1. Then the difference in energy

between hadron and parton jet is parameterized using the same method as for absolute

correction (Figure 3-5).

We have seen different corrections that account for different sources of jet energy

mis-measurement. Depending on the physics analysis, all of them or just a subset can be

applied. The corrections are applied to the raw measured jet momentum.


PT (R, PT, r) = (P}"(R)- f,(R, PT r)-M,~(R))- fabs(R PT)- UE(R)+ OOC(R, PT) (3-10)









shape of this distribution is normalized to unity and therefore we have in Equation 4-33
the value for #1.
dp r, (p ) = 1, O (4-33)


As mentionedl before wei needT tnpnpo ex rpres vrythingin terms of p6 andl p6 This can be

done just by changing the variables from the polar to the Cartesian coordinates as shown

in Equation 4-34.


dp d~ PT(p t) = 1= dpn6dp




T("'tp = (p6)2







Fiue 4-2 o riei quto 3 the shapepesio of the transverse momentum of tei vnsi hw itdt u


of ~p 3 gaussians.43




section 4.3,t 4.4 an 4.5~ offeredig detailsnc on the exreso ms b i uns of eea iprat piece





4 Ipeenteringd vlutono the probability density.UigEutos42,43an435wecnrten




Equation 4-36 the new expression for the probability density.










9.9 B-jet Energy Scale

We study the effect of the uncertainty on the modeling of heavy flavor jets due to

the uncertainty in the senli-leptonic branching ratio, the modeling of the heavy flavor

fragmentation and due to the color connection effects.

To determine this we reconstruct the top mass in a Monte Carlo sample where the

b-quarks could be geometrically matched to a jet, and the energy of such jets was modified

by 1 As it turns out in [53], 0.10' of the jet energy uncertainty on the b-jets is coming

front the effects listed above. Therefore the final shift on the top mass following our

1 shift in b-jets energies needs to be scaled down by a factor of 0.6. The systematic

uncertainty on the top mass due to the b-jet energy scale is 0.4 GeV.

9.10 Residual Jet Energy Scale

Fr-on the hi-dintensional fit for top mass and JES, we extract an uncertainty on the

top mass that includes a statistical component as well as a systematic uncertainty due

to the uncertainty on the JES parameter. However, the JES parameter is defined as the

sunt of six independent effects, and therefore the systematic uncertainty on the top mass

included in the 2D fit is only a leading order uncertainty due to our limited understanding

of the jet energy scale. Second order components of this uncertainty arise front the limited

understanding of the six individual contributions to JES. Additional details on this source

of uncertainty can he found in [54].

For this we have to study the effect on the top mass reconstruction front each of

these six sources: level 1, 4, 5, 6, 7 and 8. A Monte Carlo sample has been used where

the energies of the jets have been shifted up or down by the uncertainty at each level

separately, so a total of 12 samples have been obtained. We reconstruct the top mass in

each of them, without applying any constrain on the value of JES. In Table 9-2 we present

the average shift on the top mass at each level, and their sunt in quadrature. We conclude

front this that the residual jet energy uncertainty on top mass is 0.7 GeV.




















CDF Tracking Volume


,30






n = 2.0



*n =3.0
-30


5 10o 15
SVX II INTERMEDIATE
5 LAYERS SILICON LAYERS


Figure 2-3. Schematic of trackingf volume and plugf calorimeters of the upper east quadrant
of the CDF detector.
















Year2002 2003 2004 2005 2006 2007 Year2002 2003 2004 2005 2006 2007
Ms nth 4 7 10 1 4 7 101 4 7 1 47101 7 0 Ms nth 4 7 10 1 4 7 101 4 7 1 47101 7 0





150 12500



50 ls i~3500 eird
0 u


1000 1500 2000 2500 3000 3500 4000 4500 5000 1000 1500 2000 2500 3000 3500 4000 4500 5000
Store Number Store Number


Figure 2-4. Initial instantaneous luminosity (left) and total integrated luminosity (right)
as a function of year since the start of Run II.















































































Figure 3-5. Jet corrections due to out-of-cone effect for jets with cone size of 0.4 as a
function of the jet momentum (red). The uncertainty for this correction is also
shown as a function of the jet momentum (black).


20 40 60 80 100 120 140 160 180 200
Corrected jet PT (GeV)


t 0.14

0.12



C~0.08


U)0. 06
LI

- 0.04


Underlying Event Systematic Uncertainty
SCon 0




-oe0


Figure 3-4. Fractional
transverse


systematic uncertainty due to underlying event as a function of jet
momentum for different jet cone sizes.


**** Correction for Cone 0 4 jets
- Uncertaintyio


20 40 60 80 100 120 140 160 180 200
PT particle-jet (GeV)










mass is concentrated in a nucleus with the electrons orbiting around it. Several years later

in 1918, following a different scattering experiment with ac-particles, he will conclude that

the hydrogen nucleus is an elementary particle and it is present inside the nucleus of every

atom. This new particle was later called proton. While the proton was able to explain the

charge of the nucleus, it couldn't explain the mass of heavier atoms. Rutherford believed

that a neutral particle he called neutron exists, but this was confirmed experimentally only

in 1932 by ChI I [wick.

Rutherford's atom was not a satisfactory model. The electron going around the

nucleus would be accelerated centripetally and therefore should emit electromagnetic

radiation according to the classical theory of electromagnetism. The loss of energy through

radiation should make the electron collapse on the nucleus rendering Rutherford's atom

unstable. In 1913, Bohr will propose a different model for the atom in which the electrons

sit on orbits with discrete values of the orbital angular momentum. The electron can

move from one orbit to another by releasing or receiving a photon with an energy equal

to the energy difference between the orbits. This model will receive support from the

Franck-Hertz experiment where it was observed that the atoms can absorb only specific

amounts of photons.

Bohr's atom was still not explaining several experimental observations like the

splitting of the atomic spectral lines (Zeeman effect) or the splitting of a beam of electrons

when passing a magnetic field (Stern-Gerlach experiment). To explain this, in 1925,

Uhlenbeck and Goudsmit proposed that the electron spins on its axis as it orbits around

the nucleus. Soon Pauli introduced the exclusion principle stating that two particles can

occupy a state defined by the same quantum numbers explaining why the electrons were

spread overall several orbits.

In 1924, De Broglie extended the particle-wave duality from photons to any particle

such as the electron. The wavelike character of the electron was observed in 1927 in

a diffractive experiment hv Davisson and Germer. Based on this idea, Schrodinger











Tree level Feynman diagram for the process us i tt bbundd ......

Cross section for it production versus the top mass, from CompHep ...

Transverse momentum of the it events ......

Mass reconstruction using smeared parton energies ......

Mass reconstruction using jets matched to partons ......

Reconstructed top mass versus input top mass using realistic jets. ....

Minimum of the negative log event probability .......

Background validation in control region 1 for single I__ d events ....

Background validation in control region 1 for double I__ d events ...

Sum of event probabilities calculated for for background samples. ....


.... 86i

. .. 87

. 88

. 88

. 89

. 90

. 95

.... 100

.... 101

.... 101


6-4 Dijet invariant mass of the ulrnt I_ d jets for background before the cut on the
signal-like probability.


6-5 Dijet invariant mass of the ulrnt I_ d jets for background
on the signal-like probability ......

6-6 Event by event most probable top mass distributions for
after the signal-like probability cut .....

6-7 Effect of the background contamination in the top mass r
only the matrix element technique. .....

7-1 Top templates for it events. .....

7-2 Top templates for background events .....

7-3 Dijet mass templates for it events. .....

7-4 Dijet mass templates for background events .....

8-1 Raw reconstruction in the JES versus Top Mass plane .

8-2 Reconstructed top mass versus input top mass, for input

8-3 Reconstructed JES versus input JES, for input top mass

8-4 Slope of the mass calibration curve versus input JES. ..

8-5 Constant of the mass calibration curve versus input JES.

8-6 Slope of the JES calibration curve versus input JES. ..

8-7 Constant of the JES calibration curve versus input JES.


samples after the cut
.. 102


background samples
.. 103

reconstruction using
.. 103

. 111

. 111

. 111

.. 113

. 120

JES equal to 0. .. 120

equal to 170 GeV. .. 120

.. 121

.. 121

.. 121

. . 121










is also determined with the help of a Monte Carlo sample and we'll offer more details

in section 4.5. Therefore the new expression for the probability density is shown in

Equation 4-5.



1 dzdz a b
P~jIm= totmt(m>em 4 Xdb(,fX~EaEb Ug t, | i= (2xr)32Ei ,,,,




Even though a tt event in the all hadronic final state is fully reconstructed, there is

an ambiguity in assigning the jets to the partons. Therefore all the possible combinations

are considered and their contributions averaged. The number of possible assignments

depends on the topology of the event and this will be discussed in section 4.2. Until then

the Equation 4-6 gives the most general expression of the probability density.

1 d a z a b
P(j Im)=x
atot (m)e(m) Ncombi ddxf,)xb4EEblV i, r, | I (2xr)32Ei1

x |Mz~(m, p)|12(2xT)4 b(4) (Efi, Ei,i )TF(j13 |p P(pi3 (4-6)

4.2 Combinatorics

In general, there are 6! = 720 r-wsi~ to assign the observed jets to the six partons of

the final state in an all hadronic tt process. This number can be reduced by making few

observations and assumptions.

First, one has to notice that the matrix element is symmetric to t +-4 t. Let's write

down in Equation 4-7 the spin averaged matrix element squared for the process us i t.


4 M 288(p,g +' ps)m)v ~~T YL(~-m-y(j~ tl(
spons

Assuming that the masses of the up quarks are zero and omitting the constant and

the gluon propagator term, we can write Equation 4-8



spons









APPENDIX C
TRANSFER FUNCTIONS

A
























Figure C-1. Transfer functions for the W-boson decay partons. A) For partons with the
value for pseudo-rapidity |9| < 0.7. B) For partons with pseudo-rapidity
0.7 < |9| < 1.3. C) For partons with pseudo-rapidity 1.3 < |9|l < 2.































Graph



S3






-2





-2

-3

150 160 170 180 190 200
Corrected output Mass


Figure 8-16. JES versus Top Mass plane. The points represent the reconstructed JES and
mass after the 2D correction.










for which data is stored, CDF uses information from some detector components to make a

decision to save an event, called a tri ~-r. Data is stored in buffers until trim. r--i decisions

cause some of the events to be read out and stored on computer disk or the buffer to be

emptied. The trigger is divided into three levels of increasing sophistication in object

identification (Figure 2-9).

Data is stored in synchronous buffers awaiting an initial trigger decision. The first

trigger level returns a decision with a latency of 5.5 ps and a maximum accept rate of 50

kHz and will ak- -l-s occur in time to read out the event. Level one uses solely custom

hardware operating in three parallel streams. One stream, the extremely Fast Tracker

(XFT), reconstructs transverse COT tracks and extrapolates them to calorimeters and

muon chambers. Another stream detects possible electron, photon or jet candidates, along

with total and missing transverse energy. The final stream searches for tracks in muon

chambers. These streams are combined in the final level one decision.

After a level one accept, the event information is read out into .l-inchronous buffers.

Since events remain in these buffers until a level two decision is made, it is possible some

events passing level one will be lost when these buffers are full. The level two tr~i ;r

returns a decision with a latency of 25 ps and a maximum accept rate of 300 Hz. Level

two used custom hardware and modified commercial microprocessors to cluster energy

in calorimeters and reconstruct tracks in the silicon detector using the Silicon Vertex

Tracker (SVT). Calorimeter clusters estimate the total jet energy and help to identify

electrons and photons. The SVT measures the impact parameters of tracks, part of

locating displaced vertices.

The third trigger level runs on a commercial dual microprocessor farm and returns a

decision with a maximum accept rate of 150 Hz. The farm runs a version of CDF offline

reconstruction merging information from many detector systems to identify physical

objects in the event. Data passing level three tr~i ;r requirements is transferred via























































































Aplanarity


Figure 6-1.


Jet Eta
CDF Runil preliminary L=943pb'

0.2

0.1
U 5 'l'15 20
Number of Z's
CDF Runil preliminary L=943pb'
0.12
0.15 -
0. 8 -
0. 6 -

OU 100 O 0
SumEt3 (GeV/c2)
CDF Runil preliminary L=943pb'



O.02C -~

U 0.2 ~~040.6 0.8
Centrality


0 2 4 6
Jet Phi
CDF Runil preliminary L=943pb







0.0 0. .


slope of the calibration curve. The bias in the mass reconstruction is related to the


intercept of the calibration curve.


In the upper plot, Figure 6-7 shows how the slope decreases with the background


fraction, while the lower plot shows how the intercept changes with the background


fraction. The slope decrease indicates a decrease in the sensitivity, in other words an


increase in the statistical uncertainty on the top mass. For the calibration curves studied


in these plots the intercept should be 178 GeV, and it can he seen that as the background


fraction increases the intercept gets further from the 178 GeV value, that is the bias


mecreases.


The reason for the background fraction to have such a big effect on the mass


reconstruction using the matrix element technique of section 4 is because the background


is completely ignored in the matrix element calculation or in assessing a background event


probability. In this analysis we still won't calculate a background matrix element, but we


will use a background probability instead, which will be described in the next sections.

CDF Runil preliminary L=943pb' CDF Runil preliminary L=943pb'




"U 5 100 15 o 20 -O1


Jet Et (GeV/c2)
CDF Runil preliminary L=943pb


Background validation in control region 1 for single I__ d events. The red

points are the data points, while the black points are from the background
model.















C E C E~miV mlliI II n~miV


~W ~TI -E

I -0~uii I- -0 cn~mii -= a~mi







c =r=-ia c c ===iin IImnamii








Figure D-2. Continued









The Jacobian is obtained by solving a system of equations for pb and pg. The relations

entering the system of equations are shown in Equation 4-46.


(4-46)


We can then write in Equation 4-47 the expression of the probability density in its

final form which is used inside a C++ code.


P(jm) =/ x
ator (m) a(m) Nvcombi (12 2 Lo34 2p294
combi

x W((4|p) 6 t Pi (|Man|$ + |Mc~L|2 (47
fi= 1 F~p)]Dpn6

The integration is performed by simply giving values to the 4 integration variables

and then by adding up the integrand obtained at each step. The limits of the integration
are -60 GeVi 60 GeV~ for ,6 and 10 GeV 300 GeV for p24. The step of integration is

2 GeV. Given these limits, at each step of integration we have to check the physicality of

the components entering Equation 4-47. The probability density is evaluated for top mass

values going in 1 GeV increments from 125 GeV 225 GeV.

The dependence on mass of the it cross-section is obtained from values calculated by

CompHep Monte Carlo generator for the processes us i t, dd i t and gg i t. The

absolute values for these cross sections are not as important as their top mass dependence.

Figure 4-1 shows this dependence.
For the proton andl antiproton PDF, f ( ) f (p3i), we~ wVill use the~ CTE5LU dUistibutions

with the scale corresponding to 175 GeV. The shapes are given in Appendix A. The it

acceptance, e(m), depends on the top mass and will be described later when the event
selection is addressed.

The final expression of the probability density has been given and its implementation

has been detailed. The following section is dedicated to the checks we performed in order

to assure the proper functionality of the matrix element technique.
















































Figure C-2.


Transfer functions for the b-quark partons. A) For partons with the value for
pseudo-rapidity |vy| < 0.7. B) For partons with pseudo-rapidity 0.7 < |vy| < 1.3.
C) For partons with pseudo-rapidity 1.3 < |vy| < 2.










Equation 4-6, we will need to sum over all the possible spin configurations of the initial

state. We find two non-zero contributions corresponding to the situations when the

incoming partons have the same handedness. Therefore for the term I from Equation 4-12

is expressed in Equation 4-20.


IgR = ZEd (0, 1, i,0)
I = (p- o (s) =(4-20)
If, = ~E~(0,1,: -i, 0)

In principle, we need to average over all the possible spin configurations of the

final state. The Equations 4-18 and 4-19 represent the non-zero contributions. Using

Equations 4-18, 4-19 and 4-20, the product of the terms I, T, W1 and W2 is giVeH in

Equation 4-21.

I T W1 W2 = Ex ManR,LL (4-21)

Fr-om Equation 4-21, the term E proportional to the product of the energies of all

particles, incoming or outgoing, is shown in Equation 4-22.






May,LL ( f ) (7 .; o ) 0(h b naL ), m2 bRR,LL) 0 (4-23)


The terms ManR and MrsL, shown in Equation 4-23, are calculated in a C++ code

using Equation 4-15 and the matrix algebra. Therefore we can write down the expression

of the matrix element squared from Equation 4-6 in the form of Equation 4-24.

IM"-1 |A|=~2 -C ||
|Ad|2~~~~ 2622 -P P P (|Man|$ + |McL|2) (4-24)
spons
colors










7.50 in the wall, and 0.16 x 7.50 or 0.2-0.6 x 150 in the plug. The energy resolution of the

C1EM is o-(E)/E = 0.135/ Er(TGeV) 0.015. Figures 2-'7 shows a c~ross-sectional vie~w of

the plug calorimeter.

2.2.5 The Muon System

Whereas electrons create showers confined to the calorimeters, the mass of muons

makes them nearly minimum ionizing particles (jl\l's), and high momentum pass through

the calorimeters. The calorimeters (and in some cases additional steel shielding) block the

1 in .0 lRy of hadronic particles from reaching the outer detector. Drift chambers placed on

the outside of the detector identify charged tracks from muons and measure their position.

There are three muon detection systems: C \l U, C \lP' and CijlS [34]. CijlU and CijlP

cover detector |9|l < 0.6, with CijlP located outside CijlU, and CijlS covers detector 0.6



The C \LU chambers surround the central calorimeter in ~. They are composed of

4 concentric 1... ris of cells containing argon-ethane gas and high-voltage sense wires

parallel to the beam pipe (Figure 2-8). The CijlP chambers are separated from the C11lU

chambers by 60 cm of steel shielding. They are similar in construction to the C \!U

chambers, but the lIn-;-rs are successively offset by half of a cell. The C \! X chambers

are nearly identical to the C \LU chambers. They are arranged in four logical 1 ... rs

successively offset by half of a cell. Each logical 111-;-r consists of two partially overlapping

physical 1... ris of cells. On average, a particle will traverse six cells. Sense wires are

independent in the CijlP chambers, but are shared between 4 neighbors in CijlU and

C'j lS The single-hit r resolution is 0.25 mm. Measurements in z with a resolution

of 1.2 mm are also possible by using differences in arrival times and amplitudes of pulses

measured at either end of each wire in neighboring cells.

2.2.6 The Trigger System

Collisions occur every 396 ns (2.5 MHz), far too quickly even for CDF's custom

hardware to process and read out detector information. To reduce the number of collisions



















------ i -----


i

i

/I


00 R=29 cm


Port Cards











90crn


Layer 00)


SVX 11


64cm


Figure 2-5. Schematic with the r-< and the y-z views of the Run II CDF
system.


silicon tracking


I II


' I


+ Potential wires
*Sensewires
X Shaper wires
BareMylar
Gold on Mylar (Field Panel)


j6 58 60 62 64R
SL2


Layer # 1 2 3 4 5 6 7 8
Cells 188 192 240 288 336 384 432 480


Figure 2-6. East end-plate slots Sense and field planes are at the clock-wise edge of each
slot (left). Nominal cell layout (right).










super-111--c rs. Each super-11s-c r is further divided with gold covered Mylar field sheets into

cells containing 25 wires alternating between potential and sense wires, see Figure 2-6.

In half of the super-11s-c r~s, the wires are parallel to the beam line and provide axial

measurements, while in the other half, the wires are alternately at +2" and provide stereo

measurements. The innermost super-l} ... r provides a stereo measurement and subsequent

1 .,;-
comprised of 50'; argon and 50'; ethane (and lately, some oxygen was added to prevent

corrosion). This results in a maximum drift time of 100 ns, far shorter than the time

between hunch collisions. The single hit resolution of the COT is 140 pm, and the track

momentum resolution using muon cosmic ray,~s is o-,g,;~ M 0.001 (GeV/c)j-

2.2.4 Calorimeters

Calorimeters provide energy and position measurements of electron, photon and

hadron showers. They are divided into electromagnetic (EM) and hadronic (HA)

segments, with EM positioned closer to the interaction region than the HA. Both regions

are sampling calorimeters with alternating 11s-
generate photons in the scintillators which are collected and carried to PMTs with

wavelength shifting optical fibers. Lead is used as the absorber in EM segments and iron

in HA segments. The EM segment closest to the interaction region acts as a pre-shower

detector useful for photon and ~ro discrimination. A shower-maximum detector, placed at

about 6 radiation lengths in the EM calorimeter, measures the shower profile and obtains

a position measurement with a resolution on the order of a few mm.

Due to detector geometry, calorimeters are divided into a barrel shaped region

surrounding the solenoid, the central calorimeters (CPR, CES, CEM and CHA) [:32]; and

calorimeters capping the barrel, the plug calorimeters (PPR, PES, PEM and PHA) [:33]. A

wall hadronic calorimeter (WHA) fills the gap between the two. The central region covers

detector |vy| < 1, the wall 0.6 < |vy| < 1.3, and the plug 1.1 < |vy| < :3.6. Each of these

regions is further segmented in ty and 4 into towers covering 0.1 x 15" in the central, 0.1 x









Starting from the quantities in Equation 3-4, the jet transverse energy, transverse

momentum and pseudo-rapidity are calculated in Equations 3-5, 3-6 and 3-7.


PT = (3 5)


Er = PT, (3-6)


E pz

The jet 4-momenta measured in the calorimeter suffer from intrinsic limits of

both calorimeter and jet algorithm. Different particles produce different responses

in calorimeters and some of them can fall in uninstrumented regions of the detector.

Moreover, calorimeter response to particle energies is non-linear. The jet clustering

algorithm, on the other hand, doesn't take into account multiple interactions and

energy that can be radiated outside the fixed radius cone. For all these reasons, a set

of corrections has been developed in order to scale measured jet energy back to the energy

of the particle [39].

3.3.1 Relative Energy Scale Correction

Relative (or rl-dependent) jet energy corrections [40] are applied to raw jet energies

to correct for non-uniformities in calorimeter response along rl. Calorimeter response in

each rl bin is normalized to the response in the region with 0.2 < |9|l < 0.6, because this

region is far away from detector cracks and it is expected to have a stable response. The

correction factor is obtained using the dijet balancing method applied to dijet events.

This method starts selecting events with one out of two jets in the region 0.2 < |9|l <

0.6. This jet is defined as tr~i ;r jet. The other jet is defined as probe jet. If both jets

are in the region of 0.2 < |9|l < 0.6, tr~i -;r and probe jet are assigned randomly. The

transverse momentum of two jets in a 2 2 process should be equal and this property is

used to calculate first a pT balancing fraction Apr f as shown in Equation 3-8


,~~,prPTobe t riggerj (8










are fixed in the likelihood. However the JES is constrained via a gaussian centered on the

true JES and with a width of 1.

Figure 8-1 shows the reconstructed JES and the reconstructed top mass represented

by the points, versus the true JES and true top mass represented by the grid. Ideally the

points should match the grid crossings. Figure 8-2 shows reconstructed top mass versus

the true top mass for a true JES of 0. Ideally, this curve should have a slope of 1, and

an intercept of 175 consistent with no hias. Figure 8-3 shows reconstructed JES versus

the true JES for a true top mass of 170 GeV, and again, ideally, this curve should have

a slope of 1, and an intercept of 0 consistent with no hias. Figure 8-4 shows how the

slope of Figure 8-2 changes with the true JES, while Figure 8-5 shows how the intercept

of Figure 8-2 changes with the true JES. Figure 8-6 shows how the slope of Figure 8-3

changes with the true top mass, while Figure 8-7 shows how the intercept of Figure 8-3

changes with the true top mass. Figure 8-8 shows the mass pull means versus true top

mass, while Figure 8-9 shows the mass pull widths versus true top mass. In both plots

the true JES is 0. Based on these figures it results that the uncertainty on top mass has

to be inflated by 10.5' The average mass pull mean as a function of true JES is shown

in Figure 8-10, while the average mass pull width as a function of true JES is shown

in Figure 8-11. For a given true JES value, the average is over all the mass samples.

Figure 8-12 shows the JES pull means versus true JES, while Figure 8-13 shows the JES

pull widths versus true JES. In both plots the true top mass is 170 GeV. Based on these

plots it results that the uncertainty on the JES has to be inflated by 5.>' The average

JES pull mean as a function of true top mass is shown in Figure 8-14, while the average

JES pull width as a function of true top mass is shown in Figure 8-15. For a given true

top mass value, the average is over all the JES samples.

As it can he seen in Figure 8-1, there seems to be a slight hias in the reconstruction

of JES and top mass. We can extract the slope and the intercept of the dependence of

the reconstructed mass on the true mass. This can he done for different JES values.













































120 -


100 -

80 -


60 -

40 -


20 -


0 0 dO 200 250 3 00






220 -
200 -
180 -
160 -
140 -
120 -
100 -
80 -
60 -
40 -
20 -

0 0 150 200 250 3UU 00








0 -

350 -

300 -

250 -

200 -



O -

50 -

OC 0





400 -

350 -

300 -

250 -

200 -

150 .

100 .

50 -


OC 0


160 -

140 -

120 -

100 -

80 -

60 -

40 -

20 -

oC 0 dO 200 250 3 If 0








250 -


200 -


150 -


100 .


50 -


0 1 200 250 3UU If 0







300 -

250 -

200 -

150 -


100 -

50 -


OE E 0







450 -

400 -

350 -

300 -

250 -

200 _

150 -

100 .

50 -

0 E 0


180 -

160 -

140 -

120 -

100 -

80 -

60 -

40 -

20 -

0 dO 1 200 250 3UU ?0







250 .


200 -


150 -


100 -


50 -


0 1 1 200 250 3UU ?0







350 -

300 -

250 -

200 .

150 .

100 -

50 -

0






450 -

400 -

350 -

300 -

250 -

200 -

150 -

100 -

50 -

0


Figure E-2. Continued









CHAPTER 7
DESCRIPTION OF THE MASS MEASUREMENT METHOD

The N----- -r contribution to the uncertainty on the top quark mass is the jet energy

scale uncertainty. The jet energy scale and its uncertainty is measured independently at

CDF by the Jet Energy Resolution working group. It takes into account the differences

between the energy scale of the jets in our Monte Carlo samples and the scale observed

in the data. Its value depends on the transverse energy, pseudo-rapidity and the

electromagnetic fraction of the total energy of a jet. So the jet energy uncertainty is

different from jet to jet, but we will generically denote that with ac. The environment in

which this scale and uncertainty is determined is quite different than that of the it events,

and additional corrections might be needed at this level. We define a variable, JES, called

Jet Energy Scale, measured in units of ac. There is a correlation between the top mass

and the value of JES, and that's why we plan to measure them simultaneously to avoid

any double counting in the final uncertainty on the mass.

Our technique starts by modeling the data using a mixture of Monte Carlo signal

and Monte Carlo background events. The events will be represented by two variables:

dijet invariant mass and an event-by-event reconstructed top mass. The latter is obtained

using the matrix element technique described in section 4. For signal, the shapes obtained

in these two variables are parameterized as a function of top quark pole mass and JES.

For background no such parameterization is needed. Hence our model will depend on the

top mass and the JES. The measured values for the top quark mass and for the JES are

determined using a likelihood technique described in this section.

7.1 Likelihood Definitions

The likelihood function used to reconstruct the top mass, shown in Equation 7-1,

is product of 3 terms: the single tag likelihood used for single I__ d events, ~Lte,, the

double tag likelihood used for double I__ d events, 2tag and the JES constraint, JES,

whose expression is shown in Equation 7-7.











































350 -

300 -

250 -

200 -

150 -

100 -

50 -


0 50 0 1 200 250 UU ? 0






400 -

350 -

300 -

250 -

200 -

150 -

100 .

50 -

0 0 1 200 250 UU 7? 0





450

400 -

350 -

300 -

250 -

200 -

150 -

1



OC E 0





600 -


500 -


400 -


300 -


200 -

100 _


OC E 0


400 -

350 -

300 -

250 -

200 -

150 -

100 -

50 -

oC 50 100 150 200 250 3UU 3





500 -


400 -


300 -


200 -


100 -



0 1 200 250 3UU







500 -


400 -


300 -


200 -


100 -


0







500 -


400 -


300 -


200 -


100 -


0


400 -

350 -

300 -

250 -

200 -

150 -

100 -

50 -

01 50 100 150 200 250 3UU di 0





500 -


400 -


300 -


200 -


100 -



0 1 1 200 250 3UU ? 0






600 -

500 -

400 -


300 -

200 -


100 -

0







500 -


400 -


300 -


200 -


100 -


0


Figure E-2. Continued










All the discoveries described above led to the formulation of a theory that suninarizes

the current knowledge of the fundamental particles and the interactions between them.

This theory is called the Standard Model of particle physics and it will be described in

more detail in the next section.

1.2 The Standard Model

The Standard Model of particle physics is a theory which describes three of the four

known fundamental interactions between the elementary particles that make up all matter.

It is a quantum field theory which is consistent with both quantum niechanics and special

relativity. To date, almost all experimental tests of the three forces described by the

Standard Model have agreed with its predictions. However, the Standard Model falls short

of being a complete theory of fundamental interactions, primarily because of its lack of

inclusion of gravity, the fourth known fundamental interaction, but also because of the

large number of numerical parameters (such as masses and coupling constants) that must

he put "by hand" into the theory (rather than being derived front first principles).

The matter particles described by the Standard Model all have an intrinsic spin whose

value is determined to be 1/2, making them fernxions. For this reason, they follow the

Pauli exclusion principle in accordance with the spin-statistics theorem giving them their

material quality. Apart front their antiparticle partners, a total of twelve different types

of matter particles are known and accounted for by the Standard Model. Six of these

are classified as quarks (up, down, strange, charm, top and bottom), and the other six as

leptons (electron, nmuon, tau, and their corresponding neutrinos).

Each quark carries any one of three color charges red, green or blue, enabling them

to participate in strong interactions. The up-type quarks (up, charm, and top quarks)

carry an electric charge of +2/3, and the down-type quarks (down, strange, and bottom)

carry an electric charge of -1/3, enabling both types to participate in electromagnetic

interactions .



















72 / ndf 15.62 /4
pO 0.0058941 0.0007298
pl 0.35631 0.0006464


e 3.5
o

(u3.

E
o
"2.5

A

Lu .5
v
1

0.5


1 23 45 67 8
Nurnber of primary vertices


Figure 3-2. Average transverse energy as a function of the number of primary vertices in
the event: a correction factor is extracted from the slope of the fittingf line.


u 16

S15


S14



12


***--- CorrectionforCone04Jets
-Uncertainty to





-

-.~


50 100 150 200 250 300 350 400 450 500
PT jet (GeV)


Figure 3-3. Absolute jet energy scale corrections for jets with cone size of 0.4 as a function

of the jet momentum (blue). The uncertainty for this correction is also shown

as a function of the jet momentum (black).










flavor jets and about a factor of 6 for samples with two I__ d heavy flavor jets. This

improvement in the signal-to-background ratio will result in a better resolution in the top

mass reconstruction.

Table 5-1. Number of events in the multi-jet data after the clean-up cuts, kinematical cuts
and' I__;h! The integrated luminosity is L 943 pb-l
Cut Events Fr-action ( .)


Initial
|z| < 60cm
|z z,|1 < 5cm
Lepton Veto
fr/CE < 3
Netightets = 6
K~inematic Cuts
1 tag
> 2 ta f


12274958
3555054
3397341
3392551
3333451
380676
4172
782
148


100
28.9
27.7
27.6
27.2
3.1
0.034
6.37e-5
1.21e-5


Table 5-2. Number of events in the it Monte
Cut Events Fraction ( .)
Initial 233233 100
|z| < 60cm 128169 55.0
|z z,|1 < 5cm 128045 54.9
Tigfht Lepton Veto 113970 48.9
fr/CE < 3 88027 37.7
Neightjets = 6 29485 12.6
K~inematic Cuts 5999 2.6
1 tagf 2603 1.1
> 2 taf 1599 0.69


Carlo sample with M~top


170 GeV.























Table 5-4. Number of events, minLKL cut efficiency (e) relative to the kinentatical cuts
and the signal to background ratios for the it 1\onte Carlo samples with top
masses between 150 GeV and 200 GeV for a luminosity of 94:3 ph l. These
events pass all the cuts. The efficiency for background events is also shown.
M~,,, (GeV/c2) Single Tag S/B Double Tag S/B
150 18 0.25 1/2 14 0.32 :3/1
155 17 0.2:3 1/2 15 0.:33 4/1
160 16 0.21 1/2 14 0.31 :3/1
165 16 0.22 1/2 14 0.3 4/1
170 15 0.2 1/2 14 0.29 4/1
175 1:3 0.19 1/:3 14 0.29 :3/1
178 14 0.18 1/:3 14 0.28 4/1
180 12 0.18 1/:3 1:3 0.27 :3/1
185 11 0.16 1/:3 11 0.26 :3/1
190 9 0.15 1/4 11 0.25 :3/1
195 9 0.15 1/4 10 0.25 2/1
200 7 0.12 1/5 8 0.22 2/1
Background -0.05 --0.04
Data Events 48 -24











Table 1-1. Classification of the fundamental fermions
arranged in three generations.
Generation Flavor Mass (GeV/c2) !
U~p (u) 0.003
I Down (d) 0.006
e-Neutrino (ve) < 2 x10-6
Electron (e) 0.0005
('1. ) is (c)1.5
II Strange (s) 0.1
p--Neutrino (v,) < 2 x10-6
Muon (p) 0.1
Top (t) 171
III Bottom (b) 4.2
-rNeutrino (v,) < 2 x10-6
Tau (-r) 1.7


in Standard Model. They are


Weak Isospin
-

-

1

-

-


Table 1-2. Force carriers described in Standard Model.

Boson Force Mass (GeV/c2) l ie
Photon (y) EM 0 0
W* weak 80.4 +1
Zo weak 91.2 0
Gluon (g) strong 0 0


Figure 1-1. Leadingf order diagram for it production via quark-antiquark annihilation. In
this figure the incident quarks are the up-quarks.


O
I
O

I
p


Figure 1-2. Leading order diagrams for it production via gluon-gluon fusion.


I I P

s













Table 5-:3. Number of events and expected signal to background ratios for the it Monte
Carlo samples with top masses between 150 GeV and 200 GeV for a luminosity
of L 94:3 ph l. The number of data events is shown too. These events are
passing the kinentatical selection, but not the nxininiun likelihood cut.
M~t<, (GeV/c2) Single Tag S/B Double Tag S/B
150 7:3 1/10 45 1/2
155 72 1/10 46 1/2
160 74 1/10 45 1/2
165 74 1/10 48 1/2
170 74 1/10 49 1/2
175 71 1/10 47 1/2
178 75 1/9 50 1/2
180 69 1/10 47 1/2
185 67 1/11 44 1/2
190 61 1/12 4:3 1/2
195 59 1/12 :39 1/:3
200 56 1/1:3 :38 1/:3
Data Events 782 -148








minLKLminLKLb
0.14 -Ma s
0.12 -Uddo


0.08-
0.06-


Figure 5-1. Mininiun of the negative log event probability. In blue it's shown the curve for
it sample of M~t<> = 175 GeV, while in red it's shown the background shape.









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

MEASITREMENT OF THE TOP QUARK( MASS IN THE ALL
HADRONIC CHANNEL AT THE TEVATRON

By

Gheorghe Lungu

August 2007

C'I I!r: Jacoho K~onigfshergf
Major: Physics

This study presents a measurement of the top quark mass in the all hadronic channel

of the top quark pair production mechanism, using 1 fb- of p collisions at 2@=1.96 TeV

collected at the Collider Detector at Fermilah (CDF). Few novel techniques have been

used in this measurement. A template technique was used to simultaneously determine

the mass of the top quark and the energy scale of the jets. Two sets of distributions have

been parameterized as a function of the top quark mass and jet energy scale. One set of

distributions is built from the event-by-event reconstructed top masses, determined using

the Standard Model matrix element for the it all hadronic process. This set is sensitive

to changes in the value of the top quark mass. The other set of distributions is sensitive

to changes in the scale of jet energies and is built from the invariant mass of pairs of light

flavor jets, providing an in situ calibration of the jet energy scale. The energy scale of the

measured jets in the final state is expressed in units of its uncertainty, oy.. The measured

mass of the top quark is 171.1+3.7(stat.unc.)+2.1(syst.unc.) GeV/c2 and to the date

represents the most precise mass measurement in the all hadronic channel and third best

overall.





















CDF RunlI preliminary L=943pb ~

3C Bckg Data

--BB4P













0130 140 150 160 170 180 190 200 210 22U
Event Top Mass (GeV/c2)


08

06

01
02


02 01 06 08
Bb*BrOUnll~rd0110n
7
'82
180
178
176
171
172
170


CDF RunlI preliminary L=943pb 1


Figure 6-6. Event by event most probable top masses. These are the events after the

minLKL cut for Alpgfen bb + 4 light partons in blue, and for the background

model in red. The plot to the left shows the single' I__- d events, while the

plot to the right shows the double' I__- d events.


Figure 6-7.


Effect of the background contamination in the top mass reconstruction using

only the matrix element technique. The upper plot: slope of the calibration

curve versus the background fraction. The lower plot: intercept of the

calibration curve versus the background fraction. The calibration curves are

built using only the matrix element reconstruction technique described in

section 4.














































Grapl


~200 / ndf 3.627 / 3
Prob 0.3047
SpO 178.510.1308
pl0.939410.0071
,190-


8180-


170-


160- y=x
y= p + x -178)*pl

150-
150 160 170 180 190 200
Input Top Mass [GeV]



Figue 47. econstructed top mass versus input top mass using realistic jets.























C mnr~iia C Er~liiin C Er~liiin



c== c== c===


Figure D-2. Continued










Considering the high-energy limit, we have that the invariant mass of the W-boson

decay products is given by Equation 4-39. 01,2 is a geneTic HOtation for the polar, 01~,2

and the azimuthal, ~1,2, angles of the two decay products. Arl2a is the difference in

pseudo-rapidities of the two decay partons and a#12 = 1 2-.


P( = 2lp~snip28 ( 882COSha 012 COS 12~) = 2plp2 a(12 12) (4-39)


Making the change of variables P i pi, the Equation 4-38 can be written as a

delta function depending on the energy of one of the W-boson decay partons as shown in

Equation 4-40, where-- pO =VW MS/(2p2 12


Pw wtw 1- p) (4-40)


The mass of the W-boson is 80.4 GeV and its width is 2.1 GeV. Without these

new constants and using the expression from Equation 4-40 for both W-boson squared

propagators, we can write in Equation 4-41 the probability density.

P~~j mj C i~~~ dzedzb (a f( b) ip dPbR3 PT~p)
00mb -v i, |"Ttot (m) e(m) Ncombi p294 pT

x ((4|p) t b'" 4(Ef,,, E,?,) (4-41)
i= 1

When we calculated the matrix element in section 4.3 we assumed that the incoming

partons were traveling along the z-axis. This means their transverse momentum is zero.

Therefore the energy conservation is violated in the transverse coordinates since based

on Figure 4-2 we considered non-zero transverse momentum for the it system. However,

we expect this to be a small effect covered by the uncertainty on the parton distribution

functions of the proton and of the antiproton. Anyway, we need ignore the delta functions

requiring energy conservation along the x and y axes as shown in Equation 4-42.









BIOGRAPHICAL SKETCH

Gheorghe Lungu was born in Galati, Galati County, Romania, on December

16th 1977. After graduating from high school in 1996 he was accepted in the Physics

Department of the University of Bucharest. He graduated with a B.Sc. in physics in 2000,

entered the Physics Graduate Department at University of Florida in 2001 and moved to

Fermilab in 2003 for research within the CDF collaboration under the supervision of Prof.

Jacobo K~onigfsberg.

































CDEE mlliiI C mlEEECiI I CnlEEECiV I





























Figure D-1. Continued




Full Text

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TherstpersonIwanttoacknowledgeismyadvisor,Prof.JacoboKonigsberg,forguidingandsupportingmeduringmygraduatestudentyearsinmanyways.Hisdedication,hiscommitmenttohisworkandhisstudents,andhissavvinessinthehigh-energyexperimentaleldserveasanexampletowhichIaspireasaphysicistandasascientist.AlsoIwillbeforevergratefultoDr.ValentinNeculainmanyaspects.HemadepossiblemanythingsformestartingwithlendingmemoneytopaythetestsneededforadmissioninthegraduateschoolattheUniversityofFlorida.Moreover,hecontributedgreatlytothesuccessofthisanalysis,fromthewritingtheC++codeformaintoolsandendingwithrichandenlighteningdiscussionsonthetopic.Hisgreatskillsandhisexcellencerepresentastandardforme.IwouldliketomentionthegreatinuenceIreceivedinmyrstyearsattheUniversityofFloridafromProf.KevinIngersentandProf.RichardWoodard.Withorwithouttheirawareness,theyhelpedmedeepenmyknowledgeintheoreticalphysics.AlsoItakethisopportunitytothankthemembersofthecommitteesupervisingthisthesis:Dr.ToshikazuNishida,Dr.RichardField,Dr.PierreRamondandDr.GuenakhMitselmakher.Iwillbeinspiredbytheirtremendousworkandbytheirextraordinaryachievementsinphysics.Despiteourratherbriefinteraction,IwanttomentionthatmyexperienceduringmyOralExaminationhelpedredenemeasaphysicistandasaperson.AtCDFIdrewmuchknowledgefrominteractingwithmanypeoplesuchasDr.RobertoRossin,Dr.AndreaCastro,Dr.PatriziaAzzi,Dr.FabrizioMargaroli,Dr.FlorenciaCanelli,Dr.DanielWhiteson,Dr.NathanGoldschmidt,Dr.UnkiYang,Dr.ErikBrubaker,Dr.DouglasGlenzinski,Dr.AlexandrePronko,Dr.MirceaCoca,Dr.GavrilGiurgiu.SpecialthankstoDr.DmitriTsybychev,Dr.AlexanderSukhanovandDr.SongMingWangwhohelpedmegreatlygettinguptothespeedoftheexperimentalphysicsatCDF.AlsoIwanttomentionandthankYuriOksuzianandLesterPinerafor 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 ABSTRACT ........................................ 14 CHAPTER 1INTRODUCTION .................................. 15 1.1HistoryofParticlePhysics ........................... 15 1.2TheStandardModel .............................. 21 1.3TopQuarkPhysics ............................... 23 1.4HighlightsofMassMeasurement ........................ 32 2EXPERIMENTALAPPARATUS .......................... 38 2.1TevatronOverview ............................... 38 2.2CDFOverviewandDesign ........................... 40 2.2.1CherenkovLuminosityCounters .................... 41 2.2.2SiliconTracking ............................. 42 2.2.3CentralOuterTracker ......................... 42 2.2.4Calorimeters ............................... 43 2.2.5TheMuonSystem ............................ 44 2.2.6TheTriggerSystem ........................... 44 3EVENTRECONSTRUCTION ........................... 51 3.1Tracks ...................................... 51 3.2VertexReconstruction ............................. 53 3.3JetsReconstruction ............................... 54 3.3.1RelativeEnergyScaleCorrection ................... 56 3.3.2MultipleInteractionsCorrection .................... 57 3.3.3AbsoluteEnergyScaleCorrection ................... 57 3.3.4UnderlyingEventCorrection ...................... 58 3.3.5OutofConeCorrection ......................... 58 3.4LeptonsReconstruction ............................. 59 3.4.1Electrons ................................. 59 3.4.2Muons .................................. 59 3.4.3TauLeptons ............................... 60 3.4.4Neutrinos ................................ 60 3.5PhotonReconstruction ............................. 60 3.6BottomQuarkTagging ............................. 61 6

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............................ 61 3.6.2JetProbabilityAlgorithm ....................... 62 3.6.3SoftLeptonTagAlgorithm ....................... 62 4DESCRIPTIONOFTHEMATRIXELEMENTMACHINERY ......... 68 4.1ProbabilityDensityDenition ......................... 68 4.2Combinatorics .................................. 70 4.3CalculationoftheMatrixElement ...................... 71 4.4TransferFunctions ............................... 76 4.5TransverseMomentumofthettSystem .................... 78 4.6ImplementationandEvaluationoftheProbabilityDensity ......... 79 4.7ChecksoftheMatrixElementCalculation .................. 84 5DATASAMPLEANDEVENTSELECTION ................... 91 5.1DataandMonteCarloSamples ........................ 91 5.2EventSelection ................................. 91 6BACKGROUNDMODEL .............................. 97 6.1Denition .................................... 97 6.2ValidationoftheBackgroundModel ..................... 98 6.2.1ValidationinControlRegion1 ..................... 98 6.2.2ValidationinControlRegion2 ..................... 99 6.2.3ValidationintheSignalRegion .................... 99 6.2.4EectsontheStatisticalUncertainty ................. 99 7DESCRIPTIONOFTHEMASSMEASUREMENTMETHOD ......... 104 7.1LikelihoodDenitions ............................. 104 7.2TopTemplates ................................. 106 7.2.1DenitionoftheTemplate ....................... 106 7.2.2ParameterizationoftheTemplates ................... 106 7.3DijetMassTemplates .............................. 108 7.3.1DenitionoftheTemplate ....................... 108 7.3.2ParameterizationoftheTemplates ................... 108 8MODELVALIDATIONANDSENSITIVITYSTUDIES ............. 114 8.1Pseudo-experimentsSetup ........................... 114 8.2ValidationoftheModel ............................ 115 8.3ExpectedStatisticalUncertainty ........................ 118 9SYSTEMATICUNCERTAINTIES ......................... 127 9.1JetFragmentation ............................... 127 9.2InitialStateRadiation ............................. 127 9.3FinalStateRadiation .............................. 128 7

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......................... 128 9.5BackgroundShape ............................... 128 9.6BackgroundStatistics .............................. 129 9.7CorrelationBetweenTopMassandDijetMass ................ 130 9.82DCalibration ................................. 130 9.9B-jetEnergyScale ............................... 131 9.10ResidualJetEnergyScale ........................... 131 9.11SummaryoftheSystematicUncertainties ................... 132 10CONCLUSION .................................... 136 APPENDIX APARTONDISTRIBUTIONFUNCTIONOFTHEPROTON .......... 141 BTRANSVERSEMOMENTUMOFTHETTSYSTEM .............. 142 CTRANSFERFUNCTIONS ............................. 143 DSIGNALTOPTEMPLATES ............................ 149 ESIGNALDIJETMASSTEMPLATES ....................... 163 REFERENCES ....................................... 177 BIOGRAPHICALSKETCH ................................ 181 8

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Table page 1-1ClassicationofthefundamentalfermionsinStandardModel. .......... 34 1-2ForcecarriersdescribedinStandardModel. .................... 34 1-3Branchingratiosofthettdecaychannels. ..................... 35 4-1Denitionofthebinningofthepartonpseudo-rapidity .............. 85 4-2Denitionofthebinningofthepartonenergyforb-jets .............. 86 4-3DenitionofthebinningofthepartonenergyforW-jets ............. 87 5-1Numberofeventsinthemulti-jetdata ....................... 94 5-2Numberofeventsinthet tMonteCarlosample .................. 94 5-3Expectedsignaltobackgroundratiosforthet tMonteCarlosamples. ...... 95 5-4EciencyoftheminLKLcutforthet tMonteCarlosamples. .......... 96 7-1Valuesoftheparametersdescribingtheshapesofthetoptemplatesforthettsamples. ........................................ 110 7-2Valuesoftheparametersdescribingtheshapesofthetoptemplatesinthecaseofthebackgroundevents. .............................. 110 7-3Valuesoftheparametersdescribingthedijetmasstemplatesshapesforthettsamples. ........................................ 112 7-4Valuesoftheparametersdescribingthedijetmasstemplatesshapesinthecaseofthebackgroundevents. .............................. 113 8-1Valueofthecorrelationfactorbetweenanytwopseudo-experiments ....... 119 8-2LinearitycheckoftheMtopandJESreconstruction ................ 119 9-1Uncertaintiesontheparametersofthetopmasstemplatesforbackground. ... 132 9-2Residualjetenergyscaleuncertaintyonthetopmass. .............. 132 9-3Summaryofthesystematicsourcesofuncertaintyonthetopmass. ....... 133 10-1Expectedandobservednumberofeventsforthet tevents ............. 138 9

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Figure page 1-1Leadingorderdiagramforttproductionviaquark-antiquarkannihilation .... 34 1-2Leadingorderdiagramsforttproductionviagluon-gluonfusion. ......... 34 1-3Cross-sectionofttpairproductionasafunctionofcenter-of-massenergy .... 35 1-4Diagramsfortheself-energiesofW-bosonandZ-boson .............. 35 1-5ConstraintontheHiggsbosonmass ......................... 36 1-6LoopcontributionstotheHiggsbosonpropagator ................. 36 1-7ExperimentalconstraintsonMWandMtop. .................... 37 2-1DiagramoftheTevatronacceleratorcomplex ................... 46 2-2ElevationviewoftheEasthalloftheCDFdetector ................ 46 2-3Schematicoftrackingvolumeandplugcalorimeters ................ 47 2-4InitialinstantaneousluminosityandtotalintegratedluminosityinRunII .... 47 2-5SchematicviewoftheRunIICDFsilicontrackingsystem. ............ 48 2-6Eastend-plateslotsSenseandeldplanesinCOT ................ 48 2-7Crosssectionofupperpartofnewendplugcalorimeter. ............. 49 2-8Congurationofsteel,chambersandcountersfortheCMUdetector ....... 49 2-9ReadoutfunctionalblockdiagraminRunII. .................... 50 3-1Jetscorrectionfactorasafunctionof. ...................... 63 3-2Averagetransverseenergyasafunctionofthenumberofprimaryverticesintheevent ....................................... 64 3-3Absolutejetenergyscalecorrectionsforjetswithconesizeof0.4 ........ 64 3-4Fractionalsystematicuncertaintyduetounderlyingevent ............ 65 3-5Jetcorrectionsduetoout-of-coneeectforjets .................. 65 3-6Schematicviewofaneventcontainingajetwithasecondaryvertex. ...... 66 3-7Jetprobabilitydistributionforprompt,charmandbottomjets. ......... 66 3-8Signedimpactparameterdistribution ........................ 67 4-1TreelevelFeynmandiagramfortheprocessuu!tt 85 10

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86 4-3Crosssectionfort tproductionversusthetopmass,fromCompHep ....... 87 4-4Transversemomentumofthet tevents ....................... 88 4-5Massreconstructionusingsmearedpartonenergies ................ 88 4-6Massreconstructionusingjetsmatchedtopartons ................. 89 4-7Reconstructedtopmassversusinputtopmassusingrealisticjets. ........ 90 5-1Minimumofthenegativelogeventprobability ................... 95 6-1Backgroundvalidationincontrolregion1forsingletaggedevents ........ 100 6-2Backgroundvalidationincontrolregion1fordoubletaggedevents ........ 101 6-3Sumofeventprobabilitiescalculatedforforbackgroundsamples. ........ 101 6-4Dijetinvariantmassoftheuntaggedjetsforbackgroundbeforethecutonthesignal-likeprobability ................................. 102 6-5Dijetinvariantmassoftheuntaggedjetsforbackgroundsamplesafterthecutonthesignal-likeprobability ............................. 102 6-6Eventbyeventmostprobabletopmassdistributionsforbackgroundsamplesafterthesignal-likeprobabilitycut ......................... 103 6-7Eectofthebackgroundcontaminationinthetopmassreconstructionusingonlythematrixelementtechnique. ......................... 103 7-1Toptemplatesforttevents. ............................. 111 7-2Toptemplatesforbackgroundevents ........................ 111 7-3Dijetmasstemplatesforttevents. ......................... 111 7-4Dijetmasstemplatesforbackgroundevents .................... 113 8-1RawreconstructionintheJESversusTopMassplane ............... 120 8-2Reconstructedtopmassversusinputtopmass,forinputJESequalto0. .... 120 8-3ReconstructedJESversusinputJES,forinputtopmassequalto170GeV. ... 120 8-4SlopeofthemasscalibrationcurveversusinputJES. ............... 121 8-5ConstantofthemasscalibrationcurveversusinputJES. ............. 121 8-6SlopeoftheJEScalibrationcurveversusinputJES. ............... 121 8-7ConstantoftheJEScalibrationcurveversusinputJES. ............. 121 11

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........ 122 8-9Masspullwidthsversusinputtopmass,forinputJESequalto0. ........ 122 8-10AverageofmasspullmeansversusinputJES. ................... 122 8-11AverageofmasspullwidthsversusinputJES. ................... 122 8-12JESpullmeansversusinputtopmass,forinputtopmassequalto170GeV. .. 123 8-13JESpullwidthsversusinputtopmass,forinputtopmassequalto170GeV. .. 123 8-14AverageofJESpullmeansversusinputtopmass. ................. 123 8-15AverageofJESpullwidthsversusinputtopmass. ................ 123 8-16CorrectedreconstructionintheJESversusTopMassplane ............ 124 8-17SlopeoftheMtopcalibrationcurveversustrueJESafterthe2Dcorrection. ... 125 8-18InterceptoftheMtopcalibrationcurveversustrueJESafterthe2Dcorrection. 125 8-19SlopeoftheJEScalibrationcurveversustrueMtopafterthe2Dcorrection. ... 125 8-20InterceptoftheJEScalibrationcurveversustrueMtopafterthe2Dcorrection. 125 8-21Massreconstructionusingblindmasssamples ................... 125 8-22JESreconstructionusingblindJESsamples .................... 125 8-23Expecteduncertaintyontopmassversusinputtopmass ............. 126 8-24ExpecteduncertaintyonJESversusinputJES .................. 126 9-1Eventmultiplicityforbackgroundevents ...................... 132 9-2Parametersofthetopmasstemplateforsingletaggedbackgroundevents .... 133 9-3Parametersofthetopmasstemplatefordoubletaggedbackgroundevents ... 134 9-4TopmasspullmeanasafunctionofMtopconsideringthecorrelationbetweentheeventtopmassandthedijetmass ....................... 134 9-5TopmasspullwidthasafunctionofMtopconsideringthecorrelationbetweentheeventtopmassandthedijetmass. ....................... 135 10-1Eventreconstructedtopmassinthedata ...................... 138 10-2ContoursofthemassandJESreconstructioninthedata ............. 139 10-3ExpectedstatisticaluncertaintyfromMonteCarlo ................. 139 10-4MostprecisetopmassresultsatFermilab ..................... 140 12

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.... 141 B-1Transversemomentumofthettsystemfordierentgeneratorsandtopmasses. 142 C-1TransferfunctionsfortheW-bosondecaypartons ................. 143 C-2Transferfunctionsfortheb-quarkpartons ..................... 146 D-1Toptemplatesforttsingletaggedevents ...................... 149 D-2Toptemplatesforttdoubletaggedevents ..................... 156 E-1Dijetmasstemplatesforttsingletaggedevents .................. 163 E-2Dijetmasstemplatesforttdoubletaggedevents .................. 170 13

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1-1 ).Theforce-mediatingparticlesdescribedbytheStandardModelallhaveanintrinsicspinwhosevalueis1,makingthembosons(Table 1-2 ).Asaresult,theydonotfollowthePauliExclusionPrinciple.Thephotonsmediatethefamiliarelectromagneticforcebetweenelectricallychargedparticles(thesearethequarks,electrons,muons,tau,W-boson).Theyaremasslessandaredescribedbythetheoryofquantumelectrodynamics.TheWandZgaugebosonsmediatetheweaknuclearinteractionsbetweenparticlesofdierentavors(allquarksandleptons).Theyaremassive,withtheZ-bosonbeingmoremassivethantheW-boson.AninterestingfeatureoftheweakforceisthatinteractionsinvolvingtheWgaugebosonsactonexclusivelyleft-handedparticles.Theright-handedparticlesarecompletelyneutraltotheWbosons.Furthermore,theW-bosonscarryanelectricchargeof+1and-1makingthosesusceptibletoelectromagneticinteractions.TheelectricallyneutralZ-bosonactsonparticlesofbothchiralities,butpreferentiallyonleft-handedones.Theweaknuclearinteractionisuniqueinthatitistheonlyonethatselectivelyactsonparticlesofdierentchiralities;thephotonsofelectromagnetismandthegluonsofthestrongforceactonparticleswithoutsuchprejudice.Thesethreegaugebosonsalongwiththephotonsaregroupedtogetherwhichcollectivelymediatetheelectroweakinteractions. 22

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1 ].Thediscoveryofthetopquarkwasnotasurprise.Indeed,theexistenceofanisospinpartnerfortheb-quarkisstronglymotivatedbyargumentsoftheoreticalconsistencyoftheStandardModel,absenceofavorchangingneutralcurrentinBmesondecaysandstudiesofZbosondecays[ 2 ].However,thelargemassofthetopquark,nearly175GeV/c2,wasinitselfasurpriseatthetime.Inthisregard,thetop 23

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3 ][ 4 ][ 5 ][ 6 ].Therefore,currentobservationsleadustobelievethattheparticleobservedattheTevatronisindeedthetopquark.However,directmeasurementsarestilldesirableandwillbeattemptedinthecaseoftheelectricchargeandspinusingdatafromtheRunIIoftheTevatronortheLHC[ 7 ].Theotherintrinsicpropertiesofanelementaryparticleareitsmassandlifetime.Themostpreciseknowledgeofthemasscomesfromdirectmeasurements.ThecurrentworldaveragecontainingonlymeasurementsperformedduringRunIattheTevatronis1784.3GeV/c2.Inquantummechanics,thelifetimeofaparticleisrelatedtoitsnaturalwidththroughtherelationship=~=.Thebranchingratiofortheelectroweaktopquarkdecayt!Wbisfarlargerthananyotherdecaymodeandthusitsfullwidthcanbeapproximatelycalculatedfromthepartialwidth(t!Wb).AssumingMW=Mb=0,thelowestordercalculationofthepartialwidthhastheexpressionshowninEquation 1{1 24

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0(t!Wb)=GFM2topjVtbj2 tpairsattheTevatronviathestronginteraction.Atacenter-of-massenergyof1.96TeV,theprocessq q!t tandgg!t toccurapproximately85%and15%ofthetime,respectively.TheleadingorderdiagramsforthetwoprocessesareshowninFigure 1-1 andinFigure 1-2 .Calculationsofthetotalttcross-sections(tt)havebeenperformeduptothenext-to-leadingorder(NLO)inthecouplingconstantofthestrongforce(s).Thetheoreticalvalueatacenter-of-massenergyof1.96TeV[ 8 ]isshowninEquation 1{2 forMtop=175GeV/c2. 1-3 whereweshow(tt)asafunctionofthecenter-of-mass 25

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3 ][ 4 ]and1.96TeV(RunII)[ 5 ][ 6 ].Figure 1-3 illustratesonemotivationtomeasureaccuratelyMtop:theknowledgeofthetopquarkmassisnecessarytocompareaspreciselyaspossiblethetheoreticalpredictionsandmeasurementsofthettcross-section.Aneventualdiscrepancycouldbeasignofnewphysicsasdiscussedinmoredetailin[ 7 ].TheelectroweakproductionofsingletopquarksisalsopredictedbytheStandardModelbuthasnotbeenobservedtodate[ 9 ][ 10 ].Theproductioncross-sectionispredictedtobesmallerthanfortt(2.4pb)andtheexperimentalsignaturesuersfrommuchlargerbackgroundcontamination.Thetopquarkdecayismediatedbytheelectroweakinteraction.SinceavorchangingneutralcurrentsareforbiddenintheStandardModelduetotheGIMmechanism[ 11 ],thedecaysofthetopquarkinvolvingZorbosonsinthenalstate(e.g.,t!Zc)arehighlysuppressedandcanonlyoccurthroughhigherorderdiagrams.Therefore,thetopquarkdecayvertexmustincludeaWboson.Threepossiblenalstatesexist:t!Wb,t!Wsandt!Wd.AsillustratedinEquation 1{1 ,thepartialwidthofchargedcurrenttopdecaysisproportionaltothesquareofthecorrespondingCKMmatrixelement.AssumingaStandardModelwiththreefamilies,therelevantCKMmatrixelementshavetheconstraints[ 12 ]giveninEquation 1{3 0:004899.8%.Henceonlyt!Wbdecayshavebeenconsideredintheidenticationoftopquarks,thoughsearchesforotherdecaymodeshavebeenundertaken[ 13 ].WenotethattheWbosonfromthetopquarkdecayisreal(i.e.,itsmass 26

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1-3 .ThetopquarkplaysacentralroleinthepredictionsofmanySMobservablesbycontributingtotheirradiativecorrections.GoodexamplesaretheWandZbosonpropagators,inwhichloopsinvolvingtopquarksareexpectedtostronglycontribute,asillustratedinFigure 1-4 .Thesediagramscanexistforanytypeofquarkorlepton,buttheverylargevalueofMtopmakesthetopquarkcontributiondominant.Toillustratetheeectofthetopquark,weconsiderinEquation 1{4 thetheoreticalcalculationoftheWbosonmass[ 12 ]. 1r;(1{4)isthenestructureconstant,WistheWeinbergangleandrcontainstheradiativecorrectionsandisapproximatelygivenbyEquation 1{5 rr0 tan2W(1{5) 27

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1-4 ,andisgivenbyEquation 1{6 =3GFM2top 1{5 areknowntoaprecisionof0.2%.Theuncertaintyonthetopquarkmassiscurrentlyaboutanorderofmagnitudelargerthantheotheruncertaintiesandmoreoveritcontributesquadraticallytor.ThustheprecisiononMtopiscurrentlythelimitingfactorinthetheoreticalpredictionoftheWbosonmass.Theparameterisqualiedas\universal"intheliteraturebecauseitentersinthecalculationofmanyotherelectroweakobservablelikesinWandtheratiooftheproductionofb-quarkhadronsofalltypes(usuallydenotedRb),tonameafew.Therefore,thetopquarkmassplaysacentralroleintheinterplaybetweentheoreticalpredictionsandexperimentalobservablesthataimstotestconsistencyoftheSM.OneconsistencycheckistocomparethemeasuredvalueofMtopwiththepredictedvaluefromSMprecisionobservables(excludingofcoursedirectmeasurementsofMtop).Theindirectconstraints,inferredfromtheeectoftopquarkradiativecorrections,yieldsMtop=181+129GeV/c2[ 14 ].TherelativelysmalluncertaintyisachievedbecauseofthelargedependenceofMtoponmanyelectroweakobservables.ThisisinremarkableagreementwiththeRunIworldaverageofMtop=1784.3GeV/c2[ 15 ],andisconsideredasuccessoftheSM.AsimilarprocedurecanbeusedtoconstraintheHiggsbosonmass(MH),thelastparticleintheSMthathasyettobeobserved.TheonlydirectinformationonMHisalowerboundobtainedfromsearchesatLEP-II:MH>114GeV/c2at95%condencelevel[ 16 ].IndirectconstraintsonMHcanbeobtainedwithprecisemeasurementsof 28

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1{4 containsadditionaltermsduetoHiggsbosonloops.ThesecorrectionsdependonlylogarithmicallyonMHandhavethusweakerdependenceonMHthanonMtop.Still,precisedeterminationofMtopandMWcanbeusedtoobtainmeaningfulconstraintsonMHasillustratedinFigure 1-5 .Numerically,theconstraintsare[ 14 ]madeexplicitinEquations 1{7 and 1{8 OnlythetopquarkmassmeasurementsfromRunIhavebeenused.SuchconstraintsonMHcanhelpdirectfuturesearchesattheTevatronandLHCandconstitutesanotherstringenttestoftheStandardModelwhencomparedtolimitsfromdirectsearchesormassmeasurementsfromaneventualdiscovery.EventhoughtheStandardModelsuccessfullydescribesexperimentaldatauptoafewhundredGeV,itisbelievedthatnewphysicsmustcomeintoplayatsomegreaterenergyscale.Attheveryleast,gravityeectsareexpectedatthePlanckscale(1019GeV)thattheSMignoresinitscurrentform.TheSMcanthusbethoughtofasaneectivetheorywithsomeunknownnewphysicsexistingathigherenergyscale.AlinkexistsbetweenthenewphysicsandtheSMthatmanifestsitselfthroughradiativecorrectionstoSMparticles.TheHiggsbosonsectoristhemostsensitivetoloopsofnewphysics.ForexampletheHiggsbosonmasscorrectionsfromfermionloopsshownindiagram(a)ofFigure 1-6 aregivenbyEquation 1{9 ,wheremfisthefermionmassandisthe\cut-o"scaleusedtoregulatetheloopintegral. MH22+6m2fln(=mf)+:::;(1{9)TheparametercanbeinterpretedasthescalefornewphysicsthattypicallycorrespondstothescaleoftheGrandUniedTheory(GUT)near1016GeV.Thisisa 29

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1{10 ,wherevisthevacuumexpectationvalueoftheHiggseldthatisknownfrompropertiesoftheweakinteractiontobeapproximately171GeV. 1{9 forfermionicparticles).Moreover, 30

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17 ]asshowninEquation 1{11 ,whereM~t1andM~t2arethemassesofthelightestandtheheavieststopquarks,respectively. M2hGFM4toplogM~t1M~t2 18 ].Usingthecurrentmeasurementsofprecisionobservables,itisalreadypossibletosetmeaningfulconstraintsonSUSY.Forexample,Figure 1-7 showsthecurrentmeasurementsofMtopandMWaswellastheregionallowedexclusivelyinsidetheMSSM(green),theSM(red)aswellasanoverlapregionbetweentheMSSMandSM(blue).Ascanbeseen,theadditionalradiativecorrectionsfromSUSYparticlesarelargeenoughsuchthattheoverlapregionbetweenSMandMSSMissmallintheMtopMWplane.Thecurrentexperimentalaccuraciesarenotgoodenoughtodistinguishbetweenthetwotheories,but 31

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19 ].OtheralternativestoreplacetheSMatenergiesneartheTeVscalearetheoriesinvolvingdynamicalbreakingoftheelectroweaksymmetry[ 20 ].Thesemodels,onewell-knownexamplebeingTechnicolor[ 21 ],donotincludeanelementaryHiggsboson,butrathergivemasstotheSMparticlesbyintroducinganewstronggaugeinteractionthatproducecondensatesoffermionsthatactasHiggsbosons.Insomeversionsofthesemodels,denoted\topcolor",thenewgaugeinteractionactsonlyonthethirdgeneration,andthefermioncondensatesaremadeoftopquarks[ 22 ].SuchamodelcouldbediscoveredbylookingforevidenceofnewparticlesinthettinvariantmassattheTevatronorLHC. 32

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ClassicationofthefundamentalfermionsinStandardModel.Theyarearrangedinthreegenerations. GenerationFlavorMass(GeV/c2)ChargeWeakIsospin Up(u)0.0032 31 2IDown(d)0.006-1 3-1 2e-Neutrino(e)<210601 2Electron(e)0.0005-1-1 2 31 2IIStrange(s)0.1-1 3-1 2-Neutrino()<210601 2Muon()0.1-1-1 2 31 2IIIBottom(b)4.2-1 3-1 2-Neutrino()<210601 2Tau()1.7-1-1 2 ForcecarriersdescribedinStandardModel. BosonForceMass(GeV/c2)Charge Photon()EM00Wweak80.41Z0weak91.20Gluon(g)strong00 Leadingorderdiagramforttproductionviaquark-antiquarkannihilation.Inthisguretheincidentquarksaretheup-quarks. Leadingorderdiagramsforttproductionviagluon-gluonfusion. 34

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Cross-sectionofttpairproductionasafunctionofcenter-of-massenergyforthetheorypredictionandCDFmeasurements. Table1-3. Branchingratiosofthettdecaychannels. ChannelBranchingRatio all-hadronic44%lepton+jets30%dilepton5%taulepton+X21% Diagramsfortheself-energiesofW-bosonandZ-bosonwherealoopinvolvingthetopquarkiscontributing. 35

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ConstraintontheHiggsbosonmassasafunctionofthetopquarkandWbosonmeasuredmassesasofwinter2007.Thefullredcurveshowstheconstraints(68%C.L.)comingfromstudiesattheZbosonpole.Thedashedbluecurveshowsconstraints(68%C.L.)fromprecisemeasurementofMWandMtop. LoopcontributionstotheHiggsbosonpropagatorfrom(a)fermionicand(b)scalarparticles. 36

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ExperimentalconstraintsonMWandMtop(outerblueellipse),theprojectedconstraintsattheendoftheTevatronandLHC(middleblackellipse)andattheILC(redinnerellipse).AlsoshownaretheallowedregionforMSSM(greenhatched),theSM(redcross-hatched)andtheoverlapregionbetweentheSMandMSSM(blueverticallines). 37

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psynchrotronacceleratorsupportsseveralexperiments,includingtwocolliderdetectors,oneofwhich,theColliderDetectoratFermilab(CDF),collecteddataforthisanalysis.Theacceleratoralsoprovidesprotonstoxedtargetexperiments.CDFisageneralpurposehardscatteringdetectorsupportingawidevarietyofphysicsanalyses.OneoftheprioritiesofFNALisaprecisemeasurementofthetopquarkmass.SeveralhundredpeoplesupporttheoperationoftheacceleratorandanotherseveralhundredareresponsibleforthecommissioningandoperationoftheCDFdetector.Acompetingcollaboration,D0,independentlymeasuressimilarphysicsquantities.Combinedresultsfromthesetwocollaborationshaveresultedinincreasinglyprecisemeasurementsofthetopquarkmassandotherinterestingphysicalphenomena.Thischapteroutlinesthebasicoperationandstructureoftheacceleratorandofthedetector. 2-1 schematicallydescribestheTevatroncomplex.ProtonscollidingintheTevatronstartoutashydrogengas.ThehydrogenisionizedbyaddinganelectronandthenfedtoaCockroft-Waltondirectcurrentelectrostaticaccelerator.ExitingtheCockroft-Waltonwith750keV,thehydrogenionsarefedintoaRFlinearaccelerator,theLinac,andrampedto400MeV.Thehydrogenionsthenstrikeastationarytargetofcarbonfoil,strippingthetwoelectronsfromtheionsandleavingbareprotons. 38

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23 ]asshowninEquation 2{1 (p+ 39

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2-1 .TheAccumulatorreducesthelongitudinalmomentumoftheantiprotonsusingasynchronizedpotentialandstochasticcooling[ 24 ].StochasticcoolingwasdevelopedatCERNinthe1970sanddampensunwantedmomentumphase-spacecomponentsoftheparticlebeamusingafeedbackloop.Essentially,thebeamorbitismeasuredwithapickupandcorrectedwithakicker.TheotherantiprotonstorageunitistheRecycler,asynchrotroninthesameringastheMainInjector.TheRecyclerwasoriginallydesignedtocollectantiprotonsfromtheTevatrononcecollisionsforagivenstorewerenished,butattemptstouseitforthispurposehavenotbeenworthwhile.Asanadditionalstorageunit,theRecyclerhasallowedincreasedinstantaneousluminositysince2004.TheRecyclertakesadvantageofelectroncooling,inwhicha4.3MeVbeamofelectronsover20misusedtoreducelongitudinalmomentum.Whenastoreisreadytobegin,antiprotonsaretransferredfromeitherorboththeAccumulatorandtheRecyclertotheTevatronfornalacceleration. 25 ][ 26 ].Itsurroundsoneofthebeamcrossingpointsdescribedinsection 2.1 .Thedetectorobservesparticlesortheirdecayremnantsviachargedtracksbendingina1.4Tsolenoidaleld,electromagneticandhadronicshowersincalorimeters, 40

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2-2 .CDFiscylindricalinconstruction,withthebeamlinedeningthez-axisorientedwiththedirectionofprotontravel,whichisalsothedirectionofthesolenoidaleldlines.Thex-axisisdenedaspointingawayfromtheTevatronring,andthey-axisisdenedaspointingdirectlyupward.Transversecomponentsaredenedtobeperpendiculartothebeamline,inotherwordsthepolarrdimensionasgiveninEquation 2{2 .AnotherusefulcoordinatevariableistherapidityshowninEquation 2{3 .Thepseudo-rapidity,,isthemasslesslimitofrapidityandisgiveninEquation 2{4 2lnE+pz 2ln(tan):(2{4)Pseudo-rapidityisalwaysdenedwithrespecttothedetectorcoordinatesunlessexplicitlyspecied.ManyofthecomponentsofCDFaresegmentedinpseudo-rapidity.Figure 2-3 showsthecoordinatesrelativetothetrackingvolumeandplugcalorimeter. 27 ]arepositionednearthebeamline,3.7
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2-4 showstheinitialinstantaneousluminosityandtotalintegratedluminosityasafunctionofyear.TheinitialinstantaneousluminosityincreasedwithrunningtimeduetoimprovementssuchasusingtheRecyclertostoreantiprotons.TotalintegratedluminosityisseparatedaccordingtothatdeliveredbytheTevatronandthatrecordedtotapebytheCDFdetector. 28 ],SVXII[ 29 ]andISL[ 30 ],thesilicontrackingsystemcoversdetectorjj<2.L00isasinglelayermounteddirectlyonthebeampipe,r=1.6cm,andisasingle-sidedarraywithapitchof50mprovidingsolelyaxialmeasurements.SVXIIismountedoutsideofL00,2.4
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2-6 .Inhalfofthesuper-layers,thewiresareparalleltothebeamlineandprovideaxialmeasurements,whileintheotherhalf,thewiresarealternatelyat2oandprovidestereomeasurements.Theinnermostsuper-layerprovidesastereomeasurementandsubsequentlayersalternatebetweenaxialandstereomeasurements.Thegasllingthechamberiscomprisedof50%argonand50%ethane(andlately,someoxygenwasaddedtopreventcorrosion).Thisresultsinamaximumdrifttimeof100ns,farshorterthanthetimebetweenbunchcollisions.ThesinglehitresolutionoftheCOTis140m,andthetrackmomentumresolutionusingmuoncosmicraysispT=p2T0.001(GeV/c)1. 32 ];andcalorimeterscappingthebarrel,theplugcalorimeters(PPR,PES,PEMandPHA)[ 33 ].Awallhadroniccalorimeter(WHA)llsthegapbetweenthetwo.Thecentralregioncoversdetectorjj<1,thewall0.6
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2-7 showsacross-sectionalviewoftheplugcalorimeter. 34 ].CMUandCMPcoverdetectorjj<0.6,withCMPlocatedoutsideCMU,andCMXcoversdetector0.6
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2-9 ).Dataisstoredinsynchronousbuersawaitinganinitialtriggerdecision.Thersttriggerlevelreturnsadecisionwithalatencyof5.5sandamaximumacceptrateof50kHzandwillalwaysoccurintimetoreadouttheevent.Leveloneusessolelycustomhardwareoperatinginthreeparallelstreams.Onestream,theextremelyFastTracker(XFT),reconstructstransverseCOTtracksandextrapolatesthemtocalorimetersandmuonchambers.Anotherstreamdetectspossibleelectron,photonorjetcandidates,alongwithtotalandmissingtransverseenergy.Thenalstreamsearchesfortracksinmuonchambers.Thesestreamsarecombinedinthenallevelonedecision.Afteraleveloneaccept,theeventinformationisreadoutintoasynchronousbuers.Sinceeventsremaininthesebuersuntilaleveltwodecisionismade,itispossiblesomeeventspassinglevelonewillbelostwhenthesebuersarefull.Theleveltwotriggerreturnsadecisionwithalatencyof25sandamaximumacceptrateof300Hz.LeveltwousedcustomhardwareandmodiedcommercialmicroprocessorstoclusterenergyincalorimetersandreconstructtracksinthesilicondetectorusingtheSiliconVertexTracker(SVT).Calorimeterclustersestimatethetotaljetenergyandhelptoidentifyelectronsandphotons.TheSVTmeasurestheimpactparametersoftracks,partoflocatingdisplacedvertices.Thethirdtriggerlevelrunsonacommercialdualmicroprocessorfarmandreturnsadecisionwithamaximumacceptrateof150Hz.ThefarmrunsaversionofCDFoinereconstructionmerginginformationfrommanydetectorsystemstoidentifyphysicalobjectsintheevent.Datapassinglevelthreetriggerrequirementsistransferredvia 45

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DiagramoftheTevatronacceleratorcomplex ElevationviewoftheEasthalloftheCDFdetector.TheWesthalfisnearlysymmetric. 46

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SchematicoftrackingvolumeandplugcalorimetersoftheuppereastquadrantoftheCDFdetector. Figure2-4. Initialinstantaneousluminosity(left)andtotalintegratedluminosity(right)asafunctionofyearsincethestartofRunII. 47

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Schematicwithther-andthey-zviewsoftheRunIICDFsilicontrackingsystem. Figure2-6. Eastend-plateslotsSenseandeldplanesareattheclock-wiseedgeofeachslot(left).Nominalcelllayout(right). 48

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Crosssectionofupperpartofnewendplugcalorimeter. Detailshowingthecongurationofsteel,chambersandcountersfortheCentralMuonUpgradewalls.Amuontrackisdrawntoestablishtheinteractionpoint.Counterreadoutislocatedatz=0.CounterslayersareosetfromthechambersandfromeachotherinxtoallowoverlappinglightguidesandPMTs,minimizingthespacerequired. 49

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ReadoutfunctionalblockdiagraminRunII. 50

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pcollisionstartingfromtherawoutputsofthedierentpartsofthedetector.FirstwewillseehowinformationfromsilicondetectorsandCOTareusedtoreconstructchargedparticletrajectories.Thenwewillmovetothereconstructionofjetsofhadronicparticles,basedoncalorimeters.Asectionwillbedevotedtothecorrectionofjetenergiesfordierenterrorsourcesintroducedbycalorimetersandreconstructionalgorithms.Afterabriefdescriptionoftheidenticationofleptonsandphotons,wewillendwiththedierentmethodsusedatCDFtoidentifyajetofparticlesoriginatedfromabquark. 3{1 ,thehelixofachargedparticleisparameterized. 51

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3{2 ,where=1 2CQistheradiusofthecircleandQthechargeoftheparticle. 35 ]isastrategytoreconstructtracksinthesilicondetector.Itconsistsinndingtripletsofaligned3Dhits,extrapolatingthemandaddingmatching3Dhitsonotherlayers.Thistechniqueiscalledstandalonebecauseitdoesn'trequireanyinputfromoutside:itperformstrackingcompletelyinsidethesilicondetector.Firstthealgorithmbuilds3Dhitsfromallpossiblecouplesofintersectingaxialandstereostripsoneachlayer.Oncealistofsuchhitsisavailable,thealgorithmsearchesfortripletsofalignedhits.Thissearchisperformedxingalayeranddoingalooponallhitsintheinnerandouterlayerswithrespecttothexedone.Foreachhitpair-oneintheinnerandoneintheouterlayer-astraightlineintherzplaneisdrawn.Nextstepconsistsinexaminingthelayerinthemiddle:eachofitshitsisusedtobuildahelixtogetherwiththetwohitsoftheinnerandouterlayers.Thetripletsfoundsofararetrackcandidates.Oncethelistofcandidatesiscomplete,eachofthemisextrapolatedtoallsiliconlayerslookingfornewhitsintheproximityoftheintersectionbetweencandidateandlayer.Ifthereismorethanonehit,thecandidateisclonedandadierenthitisattachedtoeachclone.Fullhelixtsareperformedonallcandidates.Thebestcandidateinaclonegroupiskept,theothersrejected.TheOutside-Inalgorithm[ 36 ]exploitsinformationfrombothCOTandsilicon.TherststepistrackingintheCOT,whichstartstranslatingthemeasureddrifttimesin 52

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pcollision(primaryvertex)isoffundamentalimportanceforeventreconstruction.AtCDFtwoalgorithmscanbeuseforprimaryvertexreconstruction.OneiscalledPrimVtx[ 37 ]andstartsbyusingthebeamlinez-position(seedvertex)measuredduringcollisions.Thenthefollowingcuts(withrespecttotheseedvertexposition)areappliedtothetracks:jztrkzvertexj<1.0cm,jd0j<1.0cm,whered0istrackimpactparameter,andd0 53

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38 ].Thisalgorithmstartsfrompre-trackingvertices(i.e.,verticesobtainedfromtrackspassingminimalqualityrequirements).Amongthese,alotoffakeverticesarepresent:ZVertexCollcleansuptheseverticesrequiringacertainnumbertrackswithpT>300MeVbeassociatedtothem.Atrackisassociatedtoavertexifitiswithin1cmfromsiliconstandalonevertex(or5cmfromCOTstandalonevertex).Vertexpositionziscalculatedfromtrackspositionsz0weighedbytheirerroraccordingtoEquation 3{3 54

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3{4 assumingthateachvectorcorrespondstoamasslessparticlethatdepositedallitsenergyinthetowerbarycenter. (3{4) 55

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3{4 ,thejettransverseenergy,transversemomentumandpseudo-rapidityarecalculatedinEquations 3{5 3{6 and 3{7 P(3{6) 39 ]. 40 ]areappliedtorawjetenergiestocorrectfornon-uniformitiesincalorimeterresponsealong.Calorimeterresponseineachbinisnormalizedtotheresponseintheregionwith0.2jj0.6,becausethisregionisfarawayfromdetectorcracksanditisexpectedtohaveastableresponse.Thecorrectionfactorisobtainedusingthedijetbalancingmethodappliedtodijetevents.Thismethodstartsselectingeventswithoneoutoftwojetsintheregion0.2jj0.6.Thisjetisdenedastriggerjet.Theotherjetisdenedasprobejet.Ifbothjetsareintheregionof0.2jj0.6,triggerandprobejetareassignedrandomly.Thetransversemomentumoftwojetsina2!2processshouldbeequalandthispropertyisusedtocalculaterstapTbalancingfractionpTfasshowninEquation 3{8 pTf=pT 56

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3{9 3-1 weshowthecorrectionfactorasafunctionoffordijetdata(black)andfordijetMonteCarlousingPythiaasgenerator(red). pinteractioncanoccur.Energyfromthesenonoverlappingminimumbiaseventsmayfallintothejetclusteringconeofthehardinteractioncausingthusamis-measurementofjetenergy.Acorrectionforthiseectisextractedusingasampleofminimumbiasevents[ 41 ]:foreachevent,transverseenergyETinsideconesofdierentradii(0.4,0.7and1.0)ismeasuredinaregionfarawayfromcracks(0.1jj0.7):then,thedistributionofaverageETasafunctionofthenumberofquality12verticesisttedwithastraightlineandtheslopeofthettinglinesaretakenascorrectionfactors(Figure 3-2 ). 42 ].Theproceduretoextractacalorimeter-to-hadroncorrectionfactorisbasedonthefollowingsteps:usefullysimulatedCDFsampleswhereparticleshavepTrangingfrom0to600GeV,clusterthecalorimetertowersandtheHEPGparticles,associatecalorimeter-leveljetswithhadron-leveljets,parameterizethemappingbetweencalorimeterandhadron-leveljetsasafunctionofhadron-leveljets,asacorrectionfactor,extracttheprobabilitiesofmeasuringajetwithpcalTgivenajetwithxedvalueofphadT. 57

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3-3 theabsolutejetenergyscalecorrectionsforjetsconesizeof0.4asafunctionofthejetmomentum(blue).Theuncertaintyforthiscorrectionisalsoshownasafunctionofthejetmomentum(black). 43 ].Foreachevent,transverseenergyETinsideconesofdierentradii(0.4,0.7and1.0)ismeasuredinaregionfarawayfromcracks(0.1jj0.7).ThecorrectionfactorisextractedfromthemeanvaluesofETdistribution(Figure 3-4 ). 44 ]:hadron-leveljetsarematchedtopartonsiftheirdistanceintheplaneislessthan0.1.Thenthedierenceinenergybetweenhadronandpartonjetisparameterizedusingthesamemethodasforabsolutecorrection(Figure 3-5 ).Wehaveseendierentcorrectionsthataccountfordierentsourcesofjetenergymis-measurement.Dependingonthephysicsanalysis,allofthemorjustasubsetcanbeapplied.Thecorrectionsareappliedtotherawmeasuredjetmomentum. 58

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3{10 ,Ristheclusteringconeradius,PTistherawenergymeasuredintheconeandthepseudo-rapidityofthejet:f;MI;fabs;UEandOOCarerespectivelyrelative,multipleinteractions,absolute,underlyingeventandout-of-conecorrectionfactors. 3.4.1ElectronsBeingachargedparticle,anelectrontraversingthedetectorrstleavesatrackinthetrackingsystemandthenlosesitsenergyintheelectromagneticcalorimeter.Soagoodelectroncandidateismadeofaclusterintheelectromagneticcalorimeter(centralorplug)andoneormoreassociatedtracks;ifavailable,showermaxclusterandpreshowerclusterscanhelpelectronidentication.Theshowerhastobenarrowandwelldenedinshape,bothlongitudinallyandtransversely.Theratiobetweenhadronicandelectromagneticenergieshastobesmallandtrackmomentumhastomatchelectromagneticclusterenergy[ 45 ]. 46 ]. 59

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3{11 ,Eiistheenergyoftheithtower,iisthepolarangleofthelinepointingfromtheinteractionpointtotheithtowerand~niisthetransverseunitvectorpointingfromtheinteractionpointtothecenterofthetower. 60

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47 ]exploitsthefactthattheBhadrontravelsbeforeitdecaysandthereforethejetproducedbyitwillcontainasecondaryvertex(Figure 3-6 ).ThealgorithmstartsfromCOTandsilicontracksinsideaconeandasarststep,usingasdiscriminatingvariabletheirimpactparameter,itremovestracksidentiedasKS;ordaughters,orconsistentwithprimaryvertexortoofarfromit.Thenathreedimensionalcommonvertexconstrainedtisperformedusingtwotracks:if2<50thetwotracksareusedasseedtondothertracksthatpointtowardthesamesecondaryvertex.Ifatleastthreetracksarefoundtobecompatiblewithasecondaryvertex,thejetcontainingthemisconsideredab-tagifitpassesthefollowingcuts:jLxyj<2.5cm,whereLxyisthedecaylengthofthesecondaryvertex;thiscuthelpsrejectingconversionsfromtherstlayerofSVXII;Lxy 61

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48 ].Theprobabilitydistributionisuniformlydistributedforajetarisingfromtheprimaryvertex,whileitshowsapeakatzeroforalong-livedjet(Figure 3-7 ).Theprobabilityisbasedontrackimpactparametersandontheiruncertainties.Alltracksassociatedtotheprimaryvertexhaveequalprobabilitytobeeitherpositivelyornegativelysignedasfarastheirimpactparameterisconcerned.Thewidthoftheimpactparameterdistributionfromthesetracksissolelyduetothetrackingdetectorresolutionandmultiplescattering.Along-livedparticlewillproducemoretrackswithpositiveimpactparameter(Figure 3-8 ).Tominimizethecontributionofmis-measuredtracks,thenalprobabilityiscomputedusingthesignedimpactparametersignicance(ratiooftheimpactparametertoitsmeasurederror)insteadoftheparameteritself.GivenatrackwithimpactparametersignicanceSd0,theprobabilitythatatrackfromalightquarkhasalargervalueofSd0iscalculated.Combiningprobabilitiesforalltracksinajet,oneobtainsthejetprobability.Byconstruction,thisprobabilityisatforjetscomingfromlightquarksorpeakedatzeroforthosecomingfromheavyquarks. 62

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49 ].First,thetaggabletracksarefound(i.e.,tracksthatcouldhavebeenleftbymuons).Totakeintoaccountthefactthatthemuonmightnothavehadenoughenergytoreachthemuonchambers,trackswhosemomentumislowerthan2.8GeVarerejected.Moreover,ithastopointtoavolumelimitedbythephysicaledgesofthemuonchambers,oradistanceof3MSinside/outsidethephysicaledges.HereMSisthestandarddeviationofthemaximumdeectionexpectedfrommultiplescatteringthroughthematerialofthedetector.Ifatrackistaggableandhasastubassociatedtoit,thealgorithmcomputesalikelihoodcomparingalltheavailableinformationaboutthemuoncandidatewiththeexpectedvalues.Besidesvariablesfrommuondetectors,forthelikelihoodonecanusealsosometrackqualityinformation,likethenumberofCOThits,thebeamline-correctedimpactparameterandthetrackz0position. Correctionfactorasafunctionoffordijetdata(black)andfordijetMonteCarlousingPythiaasgenerator(red).Thejetswerereconstructedwithaconeof0.4. 63

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Averagetransverseenergyasafunctionofthenumberofprimaryverticesintheevent:acorrectionfactorisextractedfromtheslopeofthettingline. Absolutejetenergyscalecorrectionsforjetswithconesizeof0.4asafunctionofthejetmomentum(blue).Theuncertaintyforthiscorrectionisalsoshownasafunctionofthejetmomentum(black). 64

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Fractionalsystematicuncertaintyduetounderlyingeventasafunctionofjettransversemomentumfordierentjetconesizes. Jetcorrectionsduetoout-of-coneeectforjetswithconesizeof0.4asafunctionofthejetmomentum(red).Theuncertaintyforthiscorrectionisalsoshownasafunctionofthejetmomentum(black). 65

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Schematicviewofaneventcontainingajetwithasecondaryvertex. Jetprobabilitydistributionforprompt,charmandbottomjets. 66

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Signedimpactparameterdistributionfortracksfromprimaryvertex(left)andfromsecondaryvertex(right). 67

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4{1 4EaEbjvavbjjM(m;j)j2(2)4(4)(EfinEini)6Yi=1d3~ji 4{1 ,jisagenericnotationbywhichweunderstandallsix4-momentadescribingthenalstate;za(zb)isthefractionoftheproton(anti-proton)momentumcarriedbythecollidingpartons;f(za)andf(zb)standforthepartondistributionfunctionsforprotonandforanti-protonrespectively;M(m;j)isthematrixelementcorrespondingtotheallhadronictt;Efinisagenericnotationforthe4-vectorofthenalstate,andsimilarlyfortheinitialstateweuseEini.Iftheelementarycross-sectionsfromagroupofeventsareaddedupweshouldobtainafractionoftotalttcross-section,tot(m),fortopmassmasshowninEquation 4{2 68

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4{3 4EaEbjvavbjjM(m;j)j2(2)4(4)(EfinEini) (2)32Ei(4{3)ThequantityP(jjm)Q6i=1d3~jiwillbetheprobabilityforaneventdenedbythesetofsixjets(i.e.,six4-momenta)tobetheresultofttproductionfollowedbyanallhadronicdecayfortopmassm.Sofarwedidn'tworryabouthowaccuratelywecandeterminethesix4-momenta.Inreality,thenalstatepartonswhichareobservedasjetsinthedetector,canbemis-measured.WecanaccountforthisusingourttMonteCarlosamplesanddetermineaprobabilityforapartonwith4-momentumptobeobservedasajetwith4-momentumj.ThisnewprobabilityiscalledTransferFunctionTF(~jj~p)andallthetechnicaldetailsonhowwedeterminethemwillbepresentedinsection 4.4 .Sincewedon'tknowwhatistheparton4-momentumthatgeneratedagivenjet4-momentumwehavetoconsiderallpossibilitiesandintegrateoverthemweighedbythetransferfunctions.TheEquation 4{3 canberewrittenasinEquation 4{4 4EaEbjvavbjZ6Yi=1d3~pi (4{4) ThepartoncongurationsintegratedoverinEquation 4{4 areweighedbythetransferfunctionssothatthosemorelikelytoproduceagiven6-jetseventareenhanced.Ideallythettphasespaceshouldbeenhancedaswellandnotdiminished.Inordertoenforcethislastaspectoftheintegration,weintroduceanadditionalweight,PT(~p),thatfollowstheshapeofthetransversemomentumofthettsystem.Thislastweight 69

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4.5 .ThereforethenewexpressionfortheprobabilitydensityisshowninEquation 4{5 4EaEbjvavbjZ6Yi=1d3~pi (4{5) Eventhoughatteventintheallhadronicnalstateisfullyreconstructed,thereisanambiguityinassigningthejetstothepartons.Thereforeallthepossiblecombinationsareconsideredandtheircontributionsaveraged.Thenumberofpossibleassignmentsdependsonthetopologyoftheeventandthiswillbediscussedinsection 4.2 .UntilthentheEquation 4{6 givesthemostgeneralexpressionoftheprobabilitydensity. 4EaEbjvavbjZ6Yi=1d3~pi (4{6) 4{7 thespinaveragedmatrixelementsquaredfortheprocessuu!tt. 1 4XspinsjMj2=g4s 4{8 1 4XspinsjMj2Tr[6pu6p 70

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4{9 1 4XspinsjMj232(pup 4{9 thet$ t=(b2;W2)g;ft=(b1;W2); t=(b2;W1)g.Itisobviousthatswappingtheb'sisequivalentwithswappingthetopquarks.Inconclusion,duetothet$ 4{10 summarizesthepossiblevaluesforNcombi. 71

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4{6 .Theinvariantamplitudefortheprocessuu!tt!bbuuddisgivenbelowasaproductofseveralfactorsasshowninEquation 4{11 4{11 aredetailedbytheEquation 4{12 (pu+p 72

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bWverticeswiththenumeratorsofthetopquarkandtheantitopquarkpropagators.ThetermsPtandP dandWd uvertices.ThetermsPW1andPW2arethedenominatorsoftheW+andWpropagators.WehaveusedtheFeynmangaugefortheWbosonpropagator.TheDiracgammamatricesaredenedintheDiracrepresentationasshowninEquation 4{13 ,where=(1;~)and 4{14 73

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4{15 2(1^p~)1 2(1+^p~)1CA;v(p)=p 2(1^p~)1 2(1+^p~)1CA(4{15)Thepresenceoftheoperator^p~willprojectthespinstatesalongthedirectionofmovementdenedby^p.Foraparticletravelinginthedirectiondenedbythepolarangleandbytheazimuthalangle,thespinstatesalongthisdirectionareshowninEquation 4{16 4{17 4{15 and 4{17 ,wecanrewriteinEquation 4{18 the4-vectorsW1andW2fromEquation 4{12 AlsothetensorintermTfromEquation 4{12 canberewrittenintheformgivenbyEquation 4{19 74

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4{6 ,wewillneedtosumoverallthepossiblespincongurationsoftheinitialstate.Wendtwonon-zerocontributionscorrespondingtothesituationswhentheincomingpartonshavethesamehandedness.ThereforeforthetermIfromEquation 4{12 isexpressedinEquation 4{20 u(0;1;i;0)ILL=p u(0;1;i;0)(4{20)Inprinciple,weneedtoaverageoverallthepossiblespincongurationsofthenalstate.TheEquations 4{18 and 4{19 representthenon-zerocontributions.UsingEquations 4{18 4{19 and 4{20 ,theproductofthetermsI,T,W1andW2isgiveninEquation 4{21 4{21 ,thetermEproportionaltotheproductoftheenergiesofallparticles,incomingoroutgoing,isshowninEquation 4{22 u(4{22) 4{23 ,arecalculatedinaC++codeusingEquation 4{15 andthematrixalgebra.ThereforewecanwritedowntheexpressionofthematrixelementsquaredfromEquation 4{6 intheformofEquation 4{24 26XspinscolorsjMj2=jAj2CjEj2 75

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4{24 aredetailedinEquation 4{25 93Xi;j;k;l=1aijakl36=234fPg=jPgj2=1 (pu+p (p2tm2)2+m22teP (p2 (P2W+M2W)2+M2W2WgPW2=jPW2j2=1 (P2WM2W)2+M2W2W 4{6 isinfactaproductofsixterms,oneforeachofthenalstatequarks:twofortheb-quarksandfourforthedecayproductsoftheW-boson.TheprobabilitydensityforthetransferfunctionsisgiveninEquation 4{26 4{27 toexpressthetransferfunctionsinamoregeneralway. 76

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4{28 4{29 givestheirnormalization. 4{26 againwiththefullexpressionenteringEquation 4{6 holdingtheprobabilitydensityforthettallhadronicprocess. tMonteCarlosamples.Moreexactly,ajetisassociatedtoapartonifitsdirectioniswithinaconeofR=0:4aroundthepartondirection.Wesaythatajetismatchedtothepartonifnootherjetshouldsatisfythisgeometricalrequirement.Wecallaneventasbeingamatchedeventifeachofthesixpartonsinthenalstatehasadierentjetmatchedtoit.Ofallthet tMonteCarloeventspassingthekinematicalselectiondenedlaterinsection 5 ,about50%arematchedevents.ThejetsformedbythedecaypartonsoftheW-bosonshaveadierentenergyspectrumthanthejetsoriginatingfromtheb-quarks.Thusweformdierentsetsoftransferfunctionsdependingontheavorofthepartonthejethasbeenmatchedto.Thetransferfunctionsaredescribedusingaparameterizationinbinsofthepartonenergiesandofthepartonpseudo-rapidities.Table 4-1 showsthedenitionofthebinninginpseudo-rapidity.Thesamedenitionholdsforb-jettransferfunctionandforW-jetstransferfunctions. 77

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4-2 showsthedenitionofenergybinningfortheb-jetstransferfunctions,whileTable 4-3 isfortheW-jetstransferfunctions.Ineachbinthetransferfunctionisrepresentedbythedistributionofthevariable1Ejet=Eparton.Theshapeofthisdistributionisttedtothesumoftwogaussians.Appendix C holdsthettedshapes. 4{6 arep6xandp6y,representingtheprojectionsofthetransversemomentumofthettsystemalongthexandyaxes.TheprobabilitydensityrelatedtothetransversemomentumofthettsystemweightisshowninEquation 4{31 4{32 givesthenormalizationrelation. 4{32 ,isobtainedfromattMonteCarlosamplewithMtop=178GeV.The 78

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4{33 thevaluefor6T. 2(4{33)Asmentionedbeforeweneedtoexpresseverythingintermsofp6xandp6y.ThiscanbedonejustbychangingthevariablesfromthepolartotheCartesiancoordinatesasshowninEquation 4{34 2=1=Zdp6xdp6yePTp6T=q q 2==Zdp6xdp6yPT(p6x;p6y) (4{34) WecannowwriteinEquation 4{35 thefullexpressionofthetransversemomentumofthettsystemweight. q 2(4{35)TheshapeofePT(p6T)hasaslightdependenceonthetopmass,butitturnsoutthatchoosingtheshapeobtainedwithMtop=178GeVdoesn'tintroduceasignicantbiasinthenalmassreconstruction.SeeAppendix B forthemassdependenceofthisshape.InFigure 4-2 theshapeofthetransversemomentumofthetteventsisshownttedtoasumof3gaussians. 4{6 .Thesections 4.3 4.4 and 4.5 oereddetailsontheexpressionsofseveralimportantpiecesenteringtheprobabilitydensity.UsingEquations 4{24 4{30 and 4{35 ,wecanwriteinEquation 4{36 thenewexpressionfortheprobabilitydensity. 79

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4EaEbjvavbjZ6Yi=1d3~pi Asmentionedpreviously,wewillnotuseanyconstantthatcanbefactoredoutintheexpressionoftheprobabilitydensity.Fromnowonwewillomitallsuchconstantsexceptforthenumberofcombinations,Ncombi.AlsointheargumentofePTwewillputjustp6T,butitshouldbeunderstoodq 4{37 (4{37) ToreducethenumberofintegralswewillworkinthenarrowwidthapproximationfortheW-bosons.ThistranslatesintwomoredeltafunctionsarisingfromthesquareoftheW-bosonpropagatorsasshownbyEquation 4{38 (P2WM2W)2+M2W2WWMW!(P2WM2W) MWW(4{38) 80

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4{39 .1;2isagenericnotationforthepolar,1;2,andtheazimuthal,1;2,anglesofthetwodecayproducts.12isthedierenceinpseudo-rapiditiesofthetwodecaypartonsand12=12. 4{38 canbewrittenasadeltafunctiondependingontheenergyofoneoftheW-bosondecaypartonsasshowninEquation 4{40 ,wherep01=M2W=(2p2!12). MWW1 2p2!12(1;2)(p1p01)(4{40)ThemassoftheW-bosonis80.4GeVanditswidthis2.1GeV.WithoutthesenewconstantsandusingtheexpressionfromEquation 4{40 forbothW-bosonsquaredpropagators,wecanwriteinEquation 4{41 theprobabilitydensity. (!12)2(!34)2(4)(EfinEini) (4{41) Whenwecalculatedthematrixelementinsection 4.3 weassumedthattheincomingpartonsweretravelingalongthez-axis.Thismeanstheirtransversemomentumiszero.ThereforetheenergyconservationisviolatedinthetransversecoordinatessincebasedonFigure 4-2 weconsiderednon-zerotransversemomentumforthettsystem.However,weexpectthistobeasmalleectcoveredbytheuncertaintyonthepartondistributionfunctionsoftheprotonandoftheantiproton.Anyway,weneedignorethedeltafunctionsrequiringenergyconservationalongthexandyaxesasshowninEquation 4{42 81

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InEquation 4{41 ,wemadethechangeofvariablesza!puandzb!p 4{43 theexpressionfortheenergy-conservingdeltafunction,wherep0u=P6i=1pi(1+cosi)=2andp0 2(pup0u)(p (4{43) Usingalloftheabove,theexpressionfortheprobabilitydensityisgivenbyEquation 4{44 inanalmostnalform. (!12)2(!34)2p2p46Yi=1gTF(ijpi)ePT(p6T) (4{44) Insection 4.5 ,weannouncedourpreferencetointegrateoverthexandycomponentsofthemomentumofthettsystem.Thatisaccomplishedbyalastchangeofvariablesfpb;p 4{45 82

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4{46 4{47 theexpressionoftheprobabilitydensityinitsnalformwhichisusedinsideaC++code. (!12)2(!34)2p2p46Yi=1gTF(ijpi)ePT(p6T) (4{47) Theintegrationisperformedbysimplygivingvaluestothe4integrationvariablesandthenbyaddinguptheintegrandobtainedateachstep.Thelimitsoftheintegrationare-60GeV!60GeVforp6x;yand10GeV!300GeVforp2;4.Thestepofintegrationis2GeV.Giventheselimits,ateachstepofintegrationwehavetocheckthephysicalityofthecomponentsenteringEquation 4{47 .Theprobabilitydensityisevaluatedfortopmassvaluesgoingin1GeVincrementsfrom125GeV!225GeV.Thedependenceonmassofthet tcross-sectionisobtainedfromvaluescalculatedbyCompHepMonteCarlogeneratorfortheprocessesu u!t t,d d!t tandgg!t t.Theabsolutevaluesforthesecrosssectionsarenotasimportantastheirtopmassdependence.Figure 4-1 showsthisdependence.FortheprotonandantiprotonPDF,f(p0u)f(p0 A .Thet tacceptance,(m),dependsonthetopmassandwillbedescribedlaterwhentheeventselectionisaddressed.Thenalexpressionoftheprobabilitydensityhasbeengivenanditsimplementationhasbeendetailed.Thefollowingsectionisdedicatedtothechecksweperformedinordertoassuretheproperfunctionalityofthematrixelementtechnique. 83

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4.6 dependsonthetopquarkpolemassandisexpectedtobeminimizedinnegativelogscalearoundthetruemassesintheevent.Multiplyingalltheeventprobabilitiesweobtainalikelihoodfunctionthatdependsonthetoppolemass.Equation 4{48 showstheexpressionofthelikelihood. 4-5 showsagoodlinearityinthecaseofa5%uniformsmearing.Thereisasmallbiasofabout0.8GeV,buttheslopeisconsistentwith1.Asthesmearingisincreasedthebiasbecomesmoreevident,andslopedegradesslightly.ThiscanbealsoseeninFigure 4-5 for10%smearingandfor20%smearing,respectively.Inallofthesesituationsagaussiancenteredon0andwithwidthequaltotheamountofsmearingusedhasbeenemployedasatransferfunctionintheeventprobabilitycomputation.Thepartonscanalsobesmearedusingthefunctionsdescribedinsection 4.4 ,inwhichcasethesamefunctionsareusedastransferfunctionsintheeventprobabilitycomputation.Thistestmakesthetransitionbetweenthepartonleveltothejetslevel, 84

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4-5 showsthelinearitycheckinthiscaseaswell.Thenextcheckismovingclosertorealitybyusinginthereconstructionthejetsthathavebeenmatchedtothepartons.Thisisalreadyacheckatthejetslevelandthefunctionsdenedinsection 4.4 havetobeused.Figure 4-6 showsthelinearitycheck.Thenalcheckisthemostrealisticwecangetusingonlysignalevents,andthatisweusealltheeventswehavewithdisregardtowhetherthejetshavebeenmatchedornottothepartons.Figure 4-7 showsthelinearitycheckinthiscase.Allthecheckswehavelistedaboveshowthegoodperformanceofourmatrixelementcalculation.Ingeneral,thetraditionalmatrixelementapproachisexpectedtoprovideabetterstatisticaluncertaintyonthetopmassthanthetemplateanalyses.Inthecaseofthepresentanalysis,thetraditionalmatrixelementmethoddoesbetteronlythereconstructionisperformedonsignalsamples.Whenthebackgroundismixedin,thetemplatemethodweusehasagreatersensitivity. TreelevelFeynmandiagramfortheprocessuu!tt Denitionofthebinningofthepartonpseudo-rapidityfortheparameterizationofthetransferfunctions. Binjj 85

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Denitionofthebinningofthepartonenergyfortheb-jetstransferfunctionsparameterization. Bin0jj<0:70:7jj<1:31:3jj2:0 110!5310!8310!1253!6483!111364!74111!1474!85585!97697!1147114!1 TreelevelFeynmandiagramfortheprocessuu!tt!bbuudd

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DenitionofthebinningofthepartonenergyfortheW-jetstransferfunctionsparameterization. Bin0jj<0:70:7jj<1:31:3jj2:0 110!3210!5010!98232!3850!6398!1338!4463!76444!4976!90549!5490!108654!59108!1759!64864!69969!751075!811181!891289!991399!11314113!1 Crosssectionfort tproductionasafunctionofthetopmass,asobtainedfromCompHep.Thelineisnotat. 87

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Transversemomentumofthet tevents.Thetisasumof3gaussians. A BFigure4-5. Reconstructedtopmassversusinputtopmassatpartonlevel.A)Theenergiesofthepartonshavebeensmearedby5%.B)Theenergiesofthepartonshavebeensmearedby10%.C)Theenergiesofthepartonshavebeensmearedby20%.D)Theenergiesofthepartonshavebeensmearedusingthetransferfunctions. 88

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DFigure4-5. Continued Reconstructedtopmassversusinputtopmassusingjetsthatwereuniquelymatchedtopartons. 89

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Reconstructedtopmassversusinputtopmassusingrealisticjets. 90

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MULTIJETtrigger,anditamountstoapproximately943pb1.Thistriggerselectsabout88%ofthettallhadronicevents.TheMonteCarlosamplesaretheocialCDFsamples.Weuse12dierentsamplesgeneratedwiththeHerwigpackagetoparameterizethemassdependenceofourtemplates.Themasstakesvaluesfrom150GeVto200GeVin5GeVincrements.Therearealsosampleswithatopmassof178GeVusedtodeterminevarioussystematicuncertainties:dierentchoiceofgenerator(inthiscaseweusedthePythiapackage),dierentmodelingoftheinitialstateradiation(ISR)andofthenalstateradiation(FSR),dierentchoiceofprotonpartondistributionfunction(PDF).Thebackgroundmodeldescribedinsection 6 isvalidatedwiththehelpoftwoMonteCarlosamplesgeneratedwiththeAlpgenpackage:onewitheventshavingb b+4lightpartonsinthenalstateandanotherwitheventshaving6lightpartonsinthenalstate. 91

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PET<3(GeV)1=2removeeventshavingmuonsorelectronsTheseclean-upcutsselectabout37%ofthet tMonteCarlosamplesoutofwhichabout84%areall-hadronicevents.Inthedataonly27%oftheeventspassthesecuts,mostoftheeventsfailingthegoodrunlistandthetriggercuts.Next,thekinematicalandtopologicalcutsareappliedinordertoenhancethet teventsoverthebackground:requireeventswithexactly6jetswithjj<2andET>15GeVAplanarity+0:005PET3>0:96centrality>0:78PET>280GeV1SVXtagswhereETissumofallthetransverseenergiesofallthesixjetsintheevent,3ETisthesumofallthesixjetsminusthetwomostenergeticones,CentralityisdenedinEquation 5{1 andtheAplanarityisdenedas3=2ofthesmallesteigenvalueofthesphericitymatrix^Sij.Thesphericitymatrix^SijisdenedinEquation 5{2 92

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50 ].Table 5-1 showsthenumberofeventsinthedatasample.Table 5-2 showsthenumberofeventsinat tMonteCarlosamplewithMtop=170GeV.TheSVXb-taggerusedhasahighereciencyintheMonteCarlothaninthedata.ThereforeweneedtodegradethenumberoftaggedeventsaccordingtotheappropriatescalefactorwhichisSF=0:91.Takingthisscalefactorintoaccount,andconvertingtotheluminosityofthedata,weshowinTable 5-3 thesignaltobackgroundratios,S=B,fordierenttopmassesafterthekinematicalcutsforsingleanddoubletaggedeventsseparately.Theconversiontotheobservedluminosityisdonebyusingthetheoreticalt tcrosssection.ThenumberofbackgroundeventsisthedierencebetweentheobservednumberofeventsinthedatashowninTable 5-1 andthesignalexpectation.Anadditionalcutisintroducedtofurthercutdownthebackground.ThisnewvariablewecutonistheminimumoftheeventprobabilitygiveninEquation 4{6 ofsection 4 .Figure 5-1 showsthedistributionoftheminimumofthenegativelogeventprobabilityforasignalsampleversusthebackgroundshape.Notethatthetopmassvalueforwhichthiseventprobabilityisminimizedwillbeusedinthenaltopmassreconstruction,andthevalueoftheprobabilityinnegativelogscaleisusedasadiscriminatingvariablebetweenttandbackground.WedenotethisvalueasminLKL,andthecutdenitionisrequiringthisvariabletobelessthan10.Thevalueofthislastcuthasbeenobtainedbyminimizingthestatisticaluncertaintyonthetopmassvalueasreconstructedinsection 4 ,thatisusingonlythematrixelementcalculation.Table 5-4 showstheeciencyofthiscutrelativetothenumberofeventsaftertaggingandafterthekinematicalcuts,forsignalatdierenttopmassesandforbackground.Thetablealsoshowsthenumberofsignaleventscorrespondingto943pb1andtheappropriatesignaltobackgroundratio.Comparingthesignal-to-backgroundratiosS=BbetweenTable 5-3 andTable 5-4 thereisanimprovementofaboutafactorof3forsampleswithonetaggedheavy 93

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Table5-1. Numberofeventsinthemulti-jetdataaftertheclean-upcuts,kinematicalcutsandtagging.TheintegratedluminosityisL=943pb1. CutEventsFraction(%) Initial12274958100jzj<60cm355505428.9jzzpj<5cm339734127.7LeptonVeto339255127.66ET=p PET<3333345127.2Ntightjets=63806763.1KinematicCuts41720.0341tag7826.37e-52tag1481.21e-5 Table5-2. Numberofeventsinthet tMonteCarlosamplewithMtop=170GeV. CutEventsFraction(%) Initial233233100jzj<60cm12816955.0jzzpj<5cm12804554.9TightLeptonVeto11397048.96ET=p PET<38802737.7Ntightjets=62948512.6KinematicCuts59992.61tag26031.12tag15990.69 94

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Numberofeventsandexpectedsignaltobackgroundratiosforthet tMonteCarlosampleswithtopmassesbetween150GeVand200GeVforaluminosityofL=943pb1.Thenumberofdataeventsisshowntoo.Theseeventsarepassingthekinematicalselection,butnottheminimumlikelihoodcut. Minimumofthenegativelogeventprobability.Inblueit'sshownthecurvefort tsampleofMtop=175GeV,whileinredit'sshownthebackgroundshape. 95

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Numberofevents,minLKLcuteciency()relativetothekinematicalcutsandthesignaltobackgroundratiosforthet tMonteCarlosampleswithtopmassesbetween150GeVand200GeVforaluminosityof943pb1.Theseeventspassallthecuts.Theeciencyforbackgroundeventsisalsoshown. 96

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teventsbasedontheStandardModel.TheshapeofthebackgroundeventscanbedeterminedwiththehelpofourMonteCarlosamples.However,duethesmallstatisticsofthissamples,wewillbeforcedtore-sampleheavilywhenwewillperformthesensitivitystudiesofourtechnique.Inordertoovercomethat,wewillformasampleofbackground-likeeventsusingdataeventsfromasamplequasi-dominatedbybackground.Thenwe'llmakesurethattheshapeofthisdata-drivenbackgroundmodelcorrespondstotheshapefromMonteCarlobackgroundevents.Toformthedata-drivenbackgroundevents,westartwithourpretagdataeventsbeforetheminimumlikelihoodcut,butafteralltheclean-upandkinematicalcuts.Inthissamplethesignaltobackgroundratioisabout1=25.Thenwestarttorandomlyb-tagthejetsoftheseeventsbyusingtheb-tagratesofthemistagmatrixdenedintheallhadroniccross-sectionanalysis[ 51 ].Eacheventcanendupinanyofthepossibletaggedcongurationsbyhavinganumberoftaggedjetsbetween0and6.Weiteratethisarticialb-taggingproceduremanytimeskeepingallthecongurationsthathaveatleastoneb-taggedjet.Somecongurationswillappearmultipletimesinthisprocess,andwewilluseitthatofteninourstudiesasifitwereadistinctconguration.The 97

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6-1 showsthecomparisonintheexclusivesingletaggedsample,whileFigure 6-2 showsthecomparisonintheinclusivedoubletaggedsample.Thevariableschosenforthiscomparisonarethetransverseenergies,pseudo-rapidityandthepolarangleofthejets,andthenumberofvertices,sumofthetransverseenergiesofthe 98

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5 b+4lightpartonsinitsnalstate.Onevariablewecanlookatisthesumoftheeventprobabilitiesasdenedinsection 4 usingthematrixelement.Thesumisbetweenatopmassequalto125GeVupto225GeVinstepsof1GeV.Figure 6-3 showstheshapesofMonteCarlobackgroundandofthedata-drivenbackground.Anotherinterestingvariableistheinvariantmassofalltheuntaggedpairsofjetsintheevent.Figure 6-4 showsthisvariableforthetaggedeventsbeforetheminLKLcut,whileFigure 6-5 showsthecaseoftaggedeventsaftertheminLKLcut. 6-6 showsthisvariableforeventsaftertheminLKLcut.TheeventbyeventmostprobabletopmassandthedijetmassvariablesareofparticularinterestsincetheywillbeusedinthereconstructionofthetopmassandoftheJESvariabletobedescribedinsection 7 .Allthesecomparisonsshowgoodagreementbetweenourdata-drivenbackgroundmodelandtheAlpgenb b+4lightpartons. 99

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6-7 showshowtheslopedecreaseswiththebackgroundfraction,whilethelowerplotshowshowtheinterceptchangeswiththebackgroundfraction.Theslopedecreaseindicatesadecreaseinthesensitivity,inotherwordsanincreaseinthestatisticaluncertaintyonthetopmass.Forthecalibrationcurvesstudiedintheseplotstheinterceptshouldbe178GeV,anditcanbeseenthatasthebackgroundfractionincreasestheinterceptgetsfurtherfromthe178GeVvalue,thatisthebiasincreases.Thereasonforthebackgroundfractiontohavesuchabigeectonthemassreconstructionusingthematrixelementtechniqueofsection 4 isbecausethebackgroundiscompletelyignoredinthematrixelementcalculationorinassessingabackgroundeventprobability.Inthisanalysiswestillwon'tcalculateabackgroundmatrixelement,butwewilluseabackgroundprobabilityinstead,whichwillbedescribedinthenextsections. Figure6-1. Backgroundvalidationincontrolregion1forsingletaggedevents.Theredpointsarethedatapoints,whiletheblackpointsarefromthebackgroundmodel. 100

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Backgroundvalidationincontrolregion1fordoubletaggedevents.Theredpointsarethedatapoints,whiletheblackpointsarefromthebackgroundmodel. Figure6-3. SumofeventprobabilitiescalculatedforMtop=125GeVuptoMtop=225GeVinstepsof1GeV.ThesearetheeventsbeforetheminLKLcutforAlpgenb b+4lightpartonsinblue,andforthebackgroundmodelinblack.Theplottotheleftshowsthesingletaggedevents(Kolmogorov-Smirnovprobabilityis1%),whiletheplottotherightshowsthedoubletaggedevents(Kolmogorov-Smirnovprobabilityis13%). 101

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Dijetinvariantmassoftheuntaggedjets.ThesearetheeventsbeforetheminLKLcutforAlpgenb b+4lightpartonsinblue,andforthebackgroundmodelinblack.Theplottotheleftshowsthesingletaggedevents(Kolmogorov-Smirnovprobabilityis25%),whiletheplottotherightshowsthedoubletaggedevents(Kolmogorov-Smirnovprobabilityis43%). Figure6-5. Dijetinvariantmassoftheuntaggedjets.ThesearetheeventsaftertheminLKLcutforAlpgenb b+4lightpartonsinblue,andforthebackgroundmodelinblack.Theplottotheleftshowsthesingletaggedevents(Kolmogorov-Smirnovprobabilityis90%),whiletheplottotherightshowsthedoubletaggedevents(Kolmogorov-Smirnovprobabilityis70%). 102

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Eventbyeventmostprobabletopmasses.ThesearetheeventsaftertheminLKLcutforAlpgenb b+4lightpartonsinblue,andforthebackgroundmodelinred.Theplottotheleftshowsthesingletaggedevents,whiletheplottotherightshowsthedoubletaggedevents. Eectofthebackgroundcontaminationinthetopmassreconstructionusingonlythematrixelementtechnique.Theupperplot:slopeofthecalibrationcurveversusthebackgroundfraction.Thelowerplot:interceptofthecalibrationcurveversusthebackgroundfraction.Thecalibrationcurvesarebuiltusingonlythematrixelementreconstructiontechniquedescribedinsection 4 103

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tevents,andadditionalcorrectionsmightbeneededatthislevel.Wedeneavariable,JES,calledJetEnergyScale,measuredinunitsofc.ThereisacorrelationbetweenthetopmassandthevalueofJES,andthat'swhyweplantomeasurethemsimultaneouslytoavoidanydoublecountinginthenaluncertaintyonthemass.OurtechniquestartsbymodelingthedatausingamixtureofMonteCarlosignalandMonteCarlobackgroundevents.Theeventswillberepresentedbytwovariables:dijetinvariantmassandanevent-by-eventreconstructedtopmass.Thelatterisobtainedusingthematrixelementtechniquedescribedinsection 4 .Forsignal,theshapesobtainedinthesetwovariablesareparameterizedasafunctionoftopquarkpolemassandJES.Forbackgroundnosuchparameterizationisneeded.HenceourmodelwilldependonthetopmassandtheJES.ThemeasuredvaluesforthetopquarkmassandfortheJESaredeterminedusingalikelihoodtechniquedescribedinthissection. 7{1 ,isproductof3terms:thesingletaglikelihoodusedforsingletaggedevents,L1tag,thedoubletaglikelihoodusedfordoubletaggedevents,L2tagandtheJESconstraint,LJES,whoseexpressionisshowninEquation 7{7 104

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7{2 .Thetoptemplateterm,Ltop,isshowninEquation 7{3 .TheWtemplateterm,LW,isshowninEquation 7{4 .Theconstraintontotalnumberofevents,Lnev,isshowninEquation 7{5 .Theconstraintonthet tnumberofevents,Lns,isshowninEquation 7{6 tevents,ns=(ns+nb),istheweightofthesignalprobabilityandthefractionofbackgroundevents,nb=(ns+nb),istheweightofthebackgroundprobability.TogetherwithMandJES,theparametersnsandnbarefreeinthelikelihoodt. (ns+nb)!(7{5)Thenumberofsignalevents,ns,isconstrainedtotheexpectednumberoft tevents,nexps,viaaGaussianofmeanequaltonexpsandwidthequaltonexps.Thewidthofthegaussianissimplytheuncertaintyontheexpectednumberoft tevents.Theexpectednumbersofsignalevents,nexps,are13singletaggedand14doubletaggedevents,correspondingtoatheoreticalcross-sectionof6:7+0:70:9pb[ 55 ]andan 105

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5-4 .TheuncertaintiesonthenumbersofsignaleventsnexpsarechosentobethePoissonerrors.ThisisaconservativeapproachsincethePoissonerrorsarelargerthantheuncertaintiesderivedbasedonthetheoreticalcross-sectionuncertainty. 7.2.1DenitionoftheTemplateAsmentionedinsection 7.1 ,weusethematrixelementtobuildthetoptemplates.Theeventprobabilitydenedinsection 4 isplottedasafunctionofthetoppolemassintherange125GeVand225GeV.Innegativelogarithmicscalethiseventprobabilitywillbeminimizedforacertainvalueoftopmasswhichwe'llusetoformthetoptemplates.TheshapeofthesetemplatesdependsontheinputtopmassandJESfort tevents,butnotforbackgroundevents. 5 with7dierentJESvalues:3;2;1;0;1;2;3,afterallourselectioncutshavebeenapplied.Intotalthereare84templatesforsignalusedforparameterization.Thefunctionusedtotthem 106

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7{8 displaysthetfunctionandthedependenceofitsparametersontopmassandJES. (mtopevt1)2+224 (7{8) TheexpressionfornormalizationtermN(M;JES)fromEquation 7{8 isgiveninEquation 7{9 7{8 asafunctionofthetopmassMandjetenergyscaleJESisgivenbyEquation 7{10 7{11 7{8 atthecenterofthebin.ThesummationinEquation 7{11 isdoneforalltemplatesandforallthebinsforwhichhbinhasmorethan5entries.ThedenominatorofEquation 7{11 isthenumberofdegreesoffreedom.Foreachsample,thevaluesofthe25parameters,p,aregiveninTable 7-1 .TheshapesoffewofthesignaltemplatesaswellastheparameterizedcurvesareshowninFigure 7-1 107

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7-2 .Figure 7-2 showstheshapesofthebackgroundtemplatesaswellastheparameterizedcurves,forsingleanddoubletaggedevents.InAppendix D ,allthetoptemplatescorrespondingtosignaleventsaredisplayed. 7.3.1DenitionoftheTemplateThedijetmasstemplatesareformedbyconsideringtheinvariantmassofallpossiblepairsofuntaggedjetsinthesample.TheshapeofthesetemplatesdependsontheinputtopmassandJESfort tevents,butnotforbackgroundevents. 7{12 showsthetfunctionandthedependenceofitsparametersontopmassandJES. 108

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TheexpressionfornormalizationtermN(M;JES)fromEquation 7{12 isgiveninEquation 7{13 7{12 asafunctionofthetopmassMandjetenergyscaleJESisgivenbyEquation 7{14 7{11 .Ineachsample,thevaluesofthe36parameters,p,aregiveninTable 7-3 .TheshapesoffewofthesignaltemplatesaswellastheparameterizedcurvesareshowninFigure 7-3 .Thebackgroundtemplateshapeisbuildinthesamewayasthesignaltemplates.Thetopcontaminationisremovedinthesamewayasinthecaseofthetoptemplates(seesection 7.2 ).Thebackgroundtemplateisttedtoanormalizedsumoftwogaussiansandagammaintegrand.Forboththesingletaggedandthedoubletaggedsamples,weshowthevaluesoftheparametersinTable 7-4 109

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7-4 showstheshapesofthebackgroundtemplatesaswellastheparameterizedcurves,forsingleanddoubletaggedevents.InAppendix E ,allthedijetmasstemplatescorrespondingtosignaleventsaredisplayed. Table7-1. Valuesoftheparametersdescribingtheshapesofthetoptemplatesforthettsamples. ParameterValues(1Tag)Uncertainties(1Tag)Values(2Tags)Uncertainties(2Tags) Table7-2. Valuesoftheparametersdescribingtheshapesofthetoptemplatesinthecaseofthebackgroundevents. ParameterValues(1Tag)Uncertainties(1Tag)Values(2Tags)Uncertainties(2Tags) 11.53e-023.09e-051.28e-029.08e-0521.59e+027.68e-021.63e+023.73e-0131.79e+037.17e+003.28e+036.42e+01 110

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Toptemplatesforttevents,singletagsintheleftplot,doubletagsintherightplot.Theupperplotsshowtheparameterizedcurves,whilethebottomplotsshowtheoriginalhistograms.TheleftcolumnshowsthetemplatesvariationwithtopmassatJES=0.TherightcolumnshowstheirvariationwithJESattopmassMtop=170GeV. Figure7-2. Toptemplatesforbackgroundevents.Singletagsintheleftplot,anddoubletagsintherightplot. Figure7-3. Dijetmasstemplatesforttevents,singletagsintheleftplot,doubletagsintherightplot.Theupperplotsshowtheparameterizedcurves,whilethebottomplotsshowtheoriginalhistograms.TheleftcolumnshowsthetemplatesvariationwithtopmassatJES=0.TherightcolumnshowstheirvariationwithJESattopmassMtop=170GeV. 111

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Valuesoftheparametersdescribingthedijetmasstemplatesshapesforthettsamples. ParameterValues(1Tag)Uncertainties(1Tag)Values(2Tags)Uncertainties(2Tags) 112

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Dijetmasstemplatesforbackgroundevents.Singletagsintheleftplot,anddoubletagsintherightplot. Table7-4. Valuesoftheparametersdescribingthedijetmasstemplatesshapesinthecaseofthebackgroundevents. ParameterValues(1Tag)Uncertainties(1Tag)Values(2Tags)Uncertainties(2Tags) 11.88e-019.52e-023.53e-012.39e-0128.02e+014.29e-028.02e+011.12e-0137.01e+001.70e-029.13e+004.41e-0244.68e-019.52e-023.59e-012.39e-0159.97e+014.29e-029.46e+011.12e-0162.98e+011.70e-023.36e+014.41e-0273.44e-019.52e-022.90e-012.39e-0184.03e-024.29e-024.08e-021.12e-0191.04e+011.70e-021.04e+014.41e-02101.89e+009.52e-021.58e+002.39e-01 113

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52 ],wefoundthatforanydistributionthestatisticaluncertaintyonthemeanshouldbeexpressedasinEquation 8{1 ,thewidthshouldbeexpressedasinEquation 8{2 andthestatisticaluncertaintyonthewidthshouldbeexpressedasinEquation 8{3 (NPE1)(1)+ 114

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8{1 8{2 and 8{3 ,NPEisthenumberofpseudo-experiments,rawistheuncorrectedwidthofadistribution,andistheaveragecorrelationbetweenanytwopseudo-experiments.Thevalueofthecorrelationfactorsdependsonthesizeofthenumberofeventsperpseudo-experimentandonthetotalnumberofeventsavailable.Sincethelasttwonumbersdependonthetopmass(seeTable 5-4 )thentheaveragecorrelationbetweenanytwopseudo-experimentswilldependonthetopmass.ThevaluesforthesecorrelationtermsaregiveninTable 8-1 .WhentheJESpriorisapplied,thevalueoftheJESeachpseudo-experimentisconstrainedtoisrandomlyselectedbasedonagaussiancenteredonthetrueJESofthesampleandofwidthequalto1.Thevariablesextractedfromeachpseudo-experimentarethevaluesofmass,Mout,andJES,JESout,thatminimizethelikelihoodsdenedinsection 7 ;thestatisticaluncertaintiesontheabovevariables,MoutandJESoutandthepullsasdenedbyEquation 8{4 7 .Neitherthetopmass,northeJES 115

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8-1 showsthereconstructedJESandthereconstructedtopmassrepresentedbythepoints,versusthetrueJESandtruetopmassrepresentedbythegrid.Ideallythepointsshouldmatchthegridcrossings.Figure 8-2 showsreconstructedtopmassversusthetruetopmassforatrueJESof0.Ideally,thiscurveshouldhaveaslopeof1,andaninterceptof175consistentwithnobias.Figure 8-3 showsreconstructedJESversusthetrueJESforatruetopmassof170GeV,andagain,ideally,thiscurveshouldhaveaslopeof1,andaninterceptof0consistentwithnobias.Figure 8-4 showshowtheslopeofFigure 8-2 changeswiththetrueJES,whileFigure 8-5 showshowtheinterceptofFigure 8-2 changeswiththetrueJES.Figure 8-6 showshowtheslopeofFigure 8-3 changeswiththetruetopmass,whileFigure 8-7 showshowtheinterceptofFigure 8-3 changeswiththetruetopmass.Figure 8-8 showsthemasspullmeansversustruetopmass,whileFigure 8-9 showsthemasspullwidthsversustruetopmass.InbothplotsthetrueJESis0.Basedontheseguresitresultsthattheuncertaintyontopmasshastobeinatedby10:5%.TheaveragemasspullmeanasafunctionoftrueJESisshowninFigure 8-10 ,whiletheaveragemasspullwidthasafunctionoftrueJESisshowninFigure 8-11 .ForagiventrueJESvalue,theaverageisoverallthemasssamples.Figure 8-12 showstheJESpullmeansversustrueJES,whileFigure 8-13 showstheJESpullwidthsversustrueJES.Inbothplotsthetruetopmassis170GeV.BasedontheseplotsitresultsthattheuncertaintyontheJEShastobeinatedby5:8%.TheaverageJESpullmeanasafunctionoftruetopmassisshowninFigure 8-14 ,whiletheaverageJESpullwidthasafunctionoftruetopmassisshowninFigure 8-15 .Foragiventruetopmassvalue,theaverageisoveralltheJESsamples.AsitcanbeseeninFigure 8-1 ,thereseemstobeaslightbiasinthereconstructionofJESandtopmass.Wecanextracttheslopeandtheinterceptofthedependenceofthereconstructedmassonthetruemass.ThiscanbedonefordierentJESvalues. 116

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8-4 and 8-5 showthedependencesontheJESoftheslopesand,respectively,oftheintercepts.Similarly,inthecaseofJESreconstructionweobtainFigures 8-6 and 8-7 .BasedonthetsfromFigures 8-4 and 8-5 ,wecanexpressanalyticallyhowthereconstructedmassdependsonthetruetopmassandonthetrueJES.ThisisshowninEquation 8{5 .UsingthetsfromFigures 8-6 and 8-7 ,wecanwritesimilarexpressionsforthereconstructedJES.ThisisshowninEquation 8{6 (8{5) TheparametersCm,Cj,Sm,andSjfromEquations 8{5 and 8{6 dependonthetruevaluesoftopmassandjetenergyscaleasshowninEquation 8{7 .ThevaluesoftheparametersoftheseequationscorrespondtothetparametersofFigures 8-4 8-5 8-6 and 8-7 .TheyarelistedinTable 8-2 8{5 and 8{6 asasystemofequationsandsolvethemforthetruetopmass,Mtrue,andthetrueJES,JEStrue.AfterthesecorrectionsareappliedthenewreconstructedvaluesforJESandtopmassareconsistentwiththetruevaluewithintheuncertainties,asitcanbeseeninFigures 8-16 8-17 8-18 8-19 and 8-20 117

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8-21 showstheresidualofthetopmassreconstructionusingsamplesforwhichtheinputtopmasswasunknowntous,andFigure 8-22 showstheJESresidualsforsampleswithunknowntrueJES.Thetopmassgroupconvenersprovidedthesamplesandtheyweretheonlyonesabletocalculatetheseresiduals.TheplotsindicatethatwithintheuncertaintiesthetopmassandJESreconstructionisunbiased. 8{5 and 8{6 ,weobtainanothersystemofequationstobesolvedfortherealuncertainties.SolvingEquations 8{8 and 8{9 willprovidethecorrectuncertaintiesontopmassandonJES. 8-23 showstheexpecteduncertaintyontopmassversusinputtopmass,usinganinputJESof0.Figure 8-24 showstheexpecteduncertaintyontheJESversusinputJESforaninputtopmassof170GeV.TheexpecteduncertaintiesshowninFigure 8-23 containboththepurestatisticaluncertaintyonthetopmassandtheuncertaintyduetoJES.Thisuncertaintydependsonthetopmassbecausetheexpectednumberoft teventsdependsonthetopmass.InordertodisentanglethestatisticalcontributionfromtheJEScomponentofthisuncertainty,weperformedadierentreconstructionofthetopmassbyxingtheJEStothetruevalueinthe2Dt.Followingthisreconstruction,theuncertaintyonthetopmassispurelyofstatisticalnature.Foratopmassof170GeVtheexpectedstatisticaluncertaintyis2.5GeV,whereasthecombinedstatisticalandJES-systematicuncertainty,asperFigure 8-23 ,is3.2GeV.ThatmeansthesystematicuncertaintyduetoJESontopmassis2.0GeV.Thissystematicuncertaintyshowsanimprovementof10%overthe1DJESsystematicuncertaintyontopmassof2.2GeV. 118

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Table8-1. Valueoftheaveragecorrelationfactorbetweenanytwopseudo-experiments.Thedependenceonthevalueofthetopmassisduetothettcross-sectiondependenceontopmass. Table8-2. ValuesoftheparametersdescribingthelineardependenceonthetrueJESandonthetrueMtop,oftheinterceptandslopeoftheMtopcalibrationcurveandoftheJEScalibrationcurverespectively. ParameterValueUncertainty 119

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JESversusTopMassplane.ThepointsrepresentthereconstructedJESandmass. Figure8-2. Reconstructedtopmassversusinputtopmass,forinputJESequalto0. Figure8-3. ReconstructedJESversusinputJES,forinputtopmassequalto170GeV. 120

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SlopeofthemasscalibrationcurveversusinputJES. Figure8-5. ConstantofthemasscalibrationcurveversusinputJES. Figure8-6. SlopeoftheJEScalibrationcurveversusinputJES. Figure8-7. ConstantoftheJEScalibrationcurveversusinputJES. 121

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Masspullmeansversusinputtopmass,forinputJESequalto0. Figure8-9. Masspullwidthsversusinputtopmass,forinputJESequalto0. Figure8-10. AverageofmasspullmeansversusinputJES. Figure8-11. AverageofmasspullwidthsversusinputJES. 122

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JESpullmeansversusinputtopmass,forinputtopmassequalto170GeV. Figure8-13. JESpullwidthsversusinputtopmass,forinputtopmassequalto170GeV. Figure8-14. AverageofJESpullmeansversusinputtopmass. Figure8-15. AverageofJESpullwidthsversusinputtopmass. 123

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JESversusTopMassplane.ThepointsrepresentthereconstructedJESandmassafterthe2Dcorrection. 124

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SlopeoftheMtopcalibrationcurveversustrueJESafterthe2Dcorrection. InterceptoftheMtopcalibrationcurveversustrueJESafterthe2Dcorrection. SlopeoftheJEScalibrationcurveversustrueMtopafterthe2Dcorrection. InterceptoftheJEScalibrationcurveversustrueMtopafterthe2Dcorrection. Figure8-21. Dierencebetweenthereconstructedmassandthetruemassforblindmasssamples. Figure8-22. DierencebetweenthereconstructedandthetrueJESforblindJESsamples. 125

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Expecteduncertaintyontopmassversusinputtopmass,forinputJESequalto0.ThisuncertaintyincludesthepurestatisticaluncertaintyandthesystematicuncertaintyduetoJES. Figure8-24. ExpecteduncertaintyonJESversusinputJES,forinputtopmassequalto170GeV. 126

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teventsisexclusivelybasedonthesimulationwhichdoesn'tdescribethephysicsofsucheventsveryprecisely.Themajorsourcesofuncertaintiesappearfromourunderstandingofjetfragmentation,ourmodelingoftheradiationotheinitialornalpartons,andourunderstandingoftheprotonandantiprotoninternalstructure.Apartfromthesegenericuncertainties,wealsoaddressotherissuesspecictothepresentmethodsuchastheshapeofthebackgroundtoptemplatesfollowingthet tdecontamination,thecorrelationbetweenthedijetmassesandthetopmassdeterminedforeachevent,andthelevelofimprecisioninthedeterminationofthebi-dimensionalcorrectionofthereconstructedtopmassandJES. 127

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tcontamination.Toremovethetopcontamination,weassumedatopmassof170GeV,andnowwehavetoestimateeectofthisassumption.Wehavemodifyourassumptiononthetopmassofthetopcontaminationby10GeV,thatiswegottwo 128

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tcontaminationremovalandbasedontheconstantsabove,wescaledownthetemplatehistogramsuctuatethecontentofthescaledhistogramsusingthePoissonprobabilityafterthePoissonuctuation,scalebackupthehistograms,removethet tcontaminationandtwithagaussiantoobtainthenewtemplatefunctionrepeattheabovesteps10,000times,andhistogramtheparametersofthenewtemplatesextracttheuncertaintiesonthebackgroundparametersfromtheselasthistograms 129

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9-1 showstheeventmultiplicitysingletaggedeventsontheleft,andfordoubletaggedeventsontheright.Figure 9-2 showsthehistogramsofthethreeparametersdescribingthegaussiantforthesingletaggedevents,whileFigure 9-3 showstheequivalentplotsinthecaseofthedoubletaggedevents.TheuncertaintiesonthebackgroundparametersasdeterminedfollowingthehistogramuctuationareshowninTable 9-1 .Varyingthebackgroundparameterswithintheseuncertaintiesresultsinashiftintopmassof0.4GeV. 9-4 showsontheleftthetopmasspullmeaninthedefaultcasewhentheabovecorrelationwasreducedtozero,whileontherightisshownthesituationwithfullcorrelation.Figure 9-5 showstheequivalentcomparisoninvolvingthetopmasspullwidths.Onaverageoverdierenttopmasssamples,thepullmeanisconsistentwithintheuncertaintiesbetweenthetwoscenarios.However,thepullwidthsappearhigherwhenthecorrelationbetweentheeventtopmassandthedijetmassiszero.Weconcludethatthereisnoneedforasystematicuncertainty,andwekeepthedefaultpullwidthasthecorrectingfactoronthestatisticalerroronthetopmasssinceitrepresentsthemoreconservativeapproach. 8{5 and 8{6 withintheiruncertaintiesaslistedinTable 8-2 .Wethenre-calibratedthereconstructedvaluesforthetopmass.Thechangeintopmassis0.2GeV. 130

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53 ],0:6%ofthejetenergyuncertaintyontheb-jetsiscomingfromtheeectslistedabove.Thereforethenalshiftonthetopmassfollowingour1%shiftinb-jetsenergiesneedstobescaleddownbyafactorof0:6.Thesystematicuncertaintyonthetopmassduetotheb-jetenergyscaleis0.4GeV. 54 ].Forthiswehavetostudytheeectonthetopmassreconstructionfromeachofthesesixsources:level1,4,5,6,7and8.AMonteCarlosamplehasbeenusedwheretheenergiesofthejetshavebeenshiftedupordownbytheuncertaintyateachlevelseparately,soatotalof12sampleshavebeenobtained.Wereconstructthetopmassineachofthem,withoutapplyinganyconstrainonthevalueofJES.InTable 9-2 wepresenttheaverageshiftonthetopmassateachlevel,andtheirsuminquadrature.Weconcludefromthisthattheresidualjetenergyuncertaintyontopmassis0.7GeV. 131

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9-3 summarizesallsourcesofsystematicuncertaintieswiththeirindividualcontributionaswellasthecombinedeect. Figure9-1. Eventmultiplicityforbackgroundevents.Ontheleftisshowntheplotforsingletaggedevents,whileontherighttheplotfordoubletaggedeventsisshown. Table9-1. Uncertaintiesontheparametersofthetopmasstemplatesforbackground. Parameter1tag2tags Constant10.2e-047.0e-04Mean2.593.35Sigma272.1711.9 Table9-2. Residualjetenergyscaleuncertaintyonthetopmass. LevelUncertainty(GeV/c2) L10.2L40.1L50.5L60.0L70.5L80.1TotalJESResidual0.7 132

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Histogramsoftheparametersofthegaussiantofthebackgroundeventtopmasstemplateforsingletaggedevents.Upperleftplotshowstheconstantofthegaussian,upperrightshowsthemeanofthegaussian,lowerleftshowsthewidthofthegaussian,andlowerrightplotshowsthenormalizationofthegaussian. Table9-3. Summaryofthesystematicsourcesofuncertaintyonthetopmass. SourceUncertainty(GeV/c2) InitialStateRadiation0.3FinalStateRadiation1.2PDFchoice0.5Pythiavs.Herwig1.0MethodCalibration0.2BackgroundShape0.9BackgroundStatistics0.4SampleComposition0.1HeavyFlavorJES0.4ResidualJES0.7Total2.1 133

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Histogramsoftheparametersofthegaussiantofthebackgroundeventtopmasstemplatefordoubletaggedevents.Upperleftplotshowstheconstantofthegaussian,upperrightshowsthemeanofthegaussian,lowerleftshowsthewidthofthegaussian,andlowerrightplotshowsthenormalizationofthegaussian. Figure9-4. Topmasspullmeanasafunctionoftopmassfordierenttreatmentofthecorrelationbetweentheeventtopmassandthedijetmass.Ontheleftisthedefaultcasewhenthecorrelationiszero,whileontherightisshownthesituationwiththefullcorrelation. 134

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Topmasspullwidthasafunctionoftopmassfordierenttreatmentofthecorrelationbetweentheeventtopmassandthedijetmass.Ontheleftisthedefaultcasewhenthecorrelationiszero,whileontherightisshownthesituationwiththefullcorrelation. 135

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10-1 ,weshowinthetotalnumberofeventsandtheexpectednumberofsignaleventsusedasinputinthe2DlikelihoodofEquation 7{1 .NotethatinEquation 7{1 weneedtheuncertaintyontheexpectednumberofsignaleventsandthisisalsoshowninTable 10-1 .Thenumbersofbackgroundeventsareshownaswell,buttheyarenotusedasinputvaluesinthelikelihood.Inthethirdcolumnweshowthenumberofeventsastheyresultfromtheminimizationofthe2Dlikelihood.Followingtheminimizationofthe2Dlikelihood,wemeasuredatopmassof171.13.7GeV,andaJESof0.50.9c.Thevalueofthejetenergyscale(JES)isthereforeconsistentwiththepreviousdeterminationofJESatCDF.ThequoteduncertaintyonthetopmassrepresentsthecombinationofthestatisticaluncertaintywiththesystematicuncertaintyduetoJESuncertainty.Inordertoobtainonlythestatisticaluncertaintyonthetopmass,theminimizationofthe2DlikelihoodismodiedsuchthattheJESparameterisxedto0.5c(theresultfrom2Dt).Followingthisprocedurethestatisticaluncertaintyonthetopmassis2.8GeV.ThereforethesystematicuncertaintyduetoJESis2.4GeV.Figure 10-1 showsthedistributionsofeventbyeventreconstructedtopmassesastheblackpointsfordataandastheorangehistogramforthecombinationofsignalandbackgroundtemplatesthatbestttedthedata.Thebluehistogramrepresentsonlythebackgroundtemplate.Thesamplewithsingletaggedeventsisshownintheleftplot,whilethedoubletaggedeventsareshownintherightplot. 136

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10-2 .Thecentralpointcorrespondstotheminimumofthelikelihood,whilethecontoursrepresentthe1-sigma,2-sigma,and3-sigmalevels,respectively.UsingattMonteCarlosamplewithatopmassequalto170GeVandthenumberofsignalandbackgroundeventsasresultedfromthedatat,weformedpseudo-experimentsanddeterminedtheexpecteduncertaintyonthetopmassduetostatisticaleectsandJES.About41%ofthepseudo-experimentshadsuchcombineduncertaintyonthetopmasslowerthanthemeasuredvalueof3.7GeV.ThiscanbeseeninFigure 10-3 ,wherethehistogramshowstheresultsofthepseudo-experimentsandthebluelinerepresentsthemeasureduncertainty.Inconclusion,themeasuredcombinedstatisticalandJESuncertaintiesonthetopmassagreeswiththeexpectation.Thetotaluncertaintyonthetopmassinthisanalysisis4.3GeV.Thepreviousbestmassmeasurementinthischannelhadanequivalenttotaluncertaintyof5.3GeV[ 56 ]whichis23%more.Thesourceforthisimprovementistheuncertaintyduetojetenergyscale(JES)onthetopmass.Inthisanalysisthisuncertaintyamountsto2.4GeVcomparedto4.5GeVinthepreviousbestresultwhichis88%more.Someofthisgaininprecisionislostduetothesomewhathighersystematicuncertaintiesfromothersourcesandduetoaslightlyworsestatisticaluncertaintyinthisanalysiscomparedwiththepreviousbestmassresultinthischannel.Amorecarefulestimationoftheothersourcesofsystematicuncertaintiesonthetopmassaswellasamoreecienttteventselectionwillhelpfurtherreducethetotaluncertaintyonthetopmass.Comparedtomassmeasurementsinotherttdecaychannels,themassmeasurementfromthisanalysisrankedthirdinthetopmassworldaverage[ 57 ]witha11%weight.Thetwobettermeasurementswereperformedinthelepton+jetschannelasitcanbeseeninFigure 10-4 .ThismeasurementpromotestheallhadronicchannelasthesecondbestchannelforthetopquarkmassanalysesinRunIIattheTevatron. 137

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Table10-1. Numberofeventsforthet texpectationandfortheobservedtotalforaluminosityof943pb1passingallthecuts.Theinputvaluesforsignalhavetheuncertaintiesnexttotheminparenthesis.Thebackgroundexpectationbeingthedierencebetweentotalandsignalisalsoshown.Fortheoutputvalues,thenumbersintheparenthesisaretheuncertainties. NumberofEventsInputReconstructed TotalObserved(1tag)4847.8ExpectedSignal(1tag)133.613.23.7Background(1tag)3534.67.2TotalObserved(2tags)2423.3ExpectedSignal(2tags)143.714.13.4Background(2tags)109.24.3 Figure10-1. Eventreconstructedtopmassfordata(blackpoints),signal+background(orange)andonlybackgroundevents(blue).Singletaggedsampleisontheleft,whilethedoubletaggedsampleisontheright. 138

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Contoursfor1-sigma(red),the2-sigma(green)andthe3-sigma(blue)levelsofthemassandJESreconstructioninthedata. Figure10-3. HistogramshowstheexpectedstatisticaluncertaintyfromMonteCarlousingpseudo-experiments,whilethelineshowsthemeasuredone.About41%ofallpseudo-experimentshavealoweruncertainty. 139

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MostpreciseresultsfromeachchannelfromtheD0andCDFexperimentatFermilabbyMarch2007.Takingcorrelateduncertaintiesproperlyintoaccounttheresultingpreliminaryworldaveragemassofthetopquarkis170.91.1(stat)1.5(syst)GeV/c2whichcorrespondstoatotaluncertaintyof1.8GeV/c2.Thetopquarkmassisnowknownwithaprecisionof1.1%. 140

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UpperplotshowsthePDFshapesusedinthematrixelementcalculationofsection 4.3 .BottomplotshowsacrosscheckofthenormalizationofthesePDFs. 141

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Transversemomentumofthettsystemfordierentgeneratorsandfordierenttopmasses.Upperplot:shapesofthetransversemomentumofthettsystemfordierentgenerators(CompHep,PythiaandHerwig)andfordierenttopmasses.Middleplot:theMeansofthedistributionsintheupperplot.Lowerplot:theRMSofthedistributionsintheupperplot. 142

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AFigureC-1. TransferfunctionsfortheW-bosondecaypartons.A)Forpartonswiththevalueforpseudo-rapidityjj<0:7.B)Forpartonswithpseudo-rapidity0:7jj<1:3.C)Forpartonswithpseudo-rapidity1:3jj2. 143

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Transferfunctionsfortheb-quarkpartons.A)Forpartonswiththevalueforpseudo-rapidityjj<0:7.B)Forpartonswithpseudo-rapidity0:7jj<1:3.C)Forpartonswithpseudo-rapidity1:3jj2. 146

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AFigureD-1. Toptemplatesforttsingletaggedeventsforsampleswithdierenttopmasses:from150GeVto200GeV.A)CaseofJES=3.B)CaseofJES=2.C)CaseofJES=1.D)CaseofJES=0.E)CaseofJES=1.F)CaseofJES=2.G)CaseofJES=3. 149

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Toptemplatesforttdoubletaggedeventsforsampleswithdierenttopmasses:from150GeVto200GeV.A)CaseofJES=3.B)CaseofJES=2.C)CaseofJES=1.D)CaseofJES=0.E)CaseofJES=1.F)CaseofJES=2.G)CaseofJES=3. 156

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AFigureE-1. Dijetmasstemplatesforttsingletaggedeventsforsampleswithdierenttopmasses:from150GeVto200GeV.A)CaseofJES=3.B)CaseofJES=2.C)CaseofJES=1.D)CaseofJES=0.E)CaseofJES=1.F)CaseofJES=2.G)CaseofJES=3. 163

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Dijetmasstemplatesforttdoubletaggedeventsforsampleswithdierenttopmasses:from150GeVto200GeV.A)CaseofJES=3.B)CaseofJES=2.C)CaseofJES=1.D)CaseofJES=0.E)CaseofJES=1.F)CaseofJES=2.G)CaseofJES=3. 170

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W.Yao,K.Bloom,\Outside-InsilicontrackingatCDF",CDFNote5991. [37] H.Stadie,W.Wagner,T.Muller,\VxPriminRunII",CDFNote6047. [38] J.F.Arguin,B.Heinemann,A.Yagil,\Thez-VertexAlgorithminRunII",CDFNote6238. [39] CDFcollaboration,JetEnergyGroup,\JetEnergyCorrectionsatCDF",CDFNote7543. [40] A.A.Bhatti,K.Hatakeyama,\RelativejetenergycorrectionsusingmissingEtprojectionfractionanddijetbalancing",CDFNote6854. [41] B.Cooper,M.D'Onofrio,G.Flanagan,\Multipleinteractioncorrections",CDFNote7365. [42] A.Bhatti,F.Canelli,\Absolutecorrectionsandtheirsystematicuncertainties",CDFNote5456. [43] J.F.Arguin,B.Heinemann,\UnderlyingeventcorrectionsforRunII",CDFNote6293. [44] A.Bhatti,F.Canelli,L.Galtieri,B.Heinemann,\Out-of-ConecorrectionsandtheirSystematicUncertainties",CDFNote7449. [45] R.Wagner,\ElectronIdenticationforRunII:algorithms",CDFNote5456. [46] J.Bellinger,\AguidetomuonreconstructionandsoftwareforRun2",CDFNote5870. [47] D.Glenzinski,\AdetailedstudyoftheSECVTXalgorithm",CDFNote2925. [48] D.Acosta,\IntroductiontoRunIIjetprobabilityheavyavortagging",CDFNote6315. [49] L.Cerrito,A.Taard,\AsoftmuontaggerforRunII",CDFNote6305. [50] P.Azzi,A.Castro,A.Gresele,J.Konigsberg,G.LunguandA.Sukhanov,\NewkinematicalselectionforAll-hadronictteventsintheRunIImultijetdataset",CDFNote7717. [51] P.Azzi,A.Castro,A.Gresele,J.Konigsberg,G.LunguandA.Sukhanov,\B-taggingeciencyandbackgroundestimateintheRunIImultijetdataset",CDFNote7723. [52] RogerBarlow,\ApplicationoftheBootstrapresamplingtechniquetoParticlePhysicsexperiments",MAN/HEP/99/4April142000. [53] J.F.Arguin,P.Sinervo,\b-jetsEnergyScaleUncertaintyFromExistingExperimentalConstraints",CDFNote7252. 179

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GheorgheLunguwasborninGalati,GalatiCounty,Romania,onDecember16th1977.Aftergraduatingfromhighschoolin1996hewasacceptedinthePhysicsDepartmentoftheUniversityofBucharest.HegraduatedwithaB.Sc.inphysicsin2000,enteredthePhysicsGraduateDepartmentatUniversityofFloridain2001andmovedtoFermilabin2003forresearchwithintheCDFcollaborationunderthesupervisionofProf.JacoboKonigsberg. 181