Top-quark pair production at hadron colliders [Elektronische Ressource] / Valentin Ahrens

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Top-Quark Pair Production atHadron CollidersDissertationzur Erlangung des Grades “Doktor der Naturwissenschaften”am Fachbereich Physik, Mathematik und Informatikder Johannes Gutenberg-Universit¨at in MainzValentin AhrensGeboren in MainzMainz, September 2011Tag der Promotion8 Dezember 2011GutachtertestAbstractIn this thesis we investigate several phenomenologically important properties of top-quarkpair production at hadron colliders. We calculate double differential cross sections in twodifferent kinematical setups, pair invariant-mass (PIM) and single-particle inclusive (1PI)kinematics. In pair invariant-mass kinematics we are able to present results for the doubledifferential cross section with respect to the invariant mass of the top-quark pair and thetop-quarkscattering angle. Workingin the threshold region, where the pairinvariant mass√M is close to the partonic center-of-mass energy sˆ, we are able to factorize the partoniccross section into different energyregions. We use renormalization-group(RG) methodstoresum large threshold logarithms to next-to-next-to-leading-logarithmic (NNLL) accuracy.On a technical level this is done using effective field theories, such as heavy-quark effectivetheory(HQET)andsoft-collineareffectivetheory(SCET).Thesametechniquesareappliedwhen working in 1PI kinematics, leading to a calculation of the double differential crosssection with respect to transverse-momentum p and the rapidity of the top quark.

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Publié le 01 janvier 2011
Nombre de lectures 7
Langue English
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Top-Quark Pair Production at
Hadron Colliders
Dissertation
zur Erlangung des Grades “Doktor der Naturwissenschaften”
am Fachbereich Physik, Mathematik und Informatik
der Johannes Gutenberg-Universit¨at in Mainz
Valentin Ahrens
Geboren in Mainz
Mainz, September 2011Tag der Promotion
8 Dezember 2011
Gutachter
testAbstract
In this thesis we investigate several phenomenologically important properties of top-quark
pair production at hadron colliders. We calculate double differential cross sections in two
different kinematical setups, pair invariant-mass (PIM) and single-particle inclusive (1PI)
kinematics. In pair invariant-mass kinematics we are able to present results for the double
differential cross section with respect to the invariant mass of the top-quark pair and the
top-quarkscattering angle. Workingin the threshold region, where the pairinvariant mass√
M is close to the partonic center-of-mass energy sˆ, we are able to factorize the partonic
cross section into different energyregions. We use renormalization-group(RG) methodsto
resum large threshold logarithms to next-to-next-to-leading-logarithmic (NNLL) accuracy.
On a technical level this is done using effective field theories, such as heavy-quark effective
theory(HQET)andsoft-collineareffectivetheory(SCET).Thesametechniquesareapplied
when working in 1PI kinematics, leading to a calculation of the double differential cross
section with respect to transverse-momentum p and the rapidity of the top quark. WeT
restrict the phase-space such that only soft emission of gluons is possible, and perform a
NNLL resummation of threshold logarithms.
The obtained analytical expressions enable us to precisely predict several observables,
and a substantial part ofthis thesis is devoted to their detailed phenomenological analysis.
Matching our results in the threshold regions to the exact ones at next-to-leading order
(NLO) in fixed-order perturbation theory, allows us to make predictions at NLO+NNLL
order in RG-improved, and at approximate next-to-next-to-leading order (NNLO) in fixed
order perturbation theory. We give numerical results for the invariant mass distribution
of the top-quark pair, and for the top-quark transverse-momentum and rapidity spectrum.
We predict the total cross section, separately for both kinematics. Using these results, we
analyzesubleadingcontributionstothetotalcrosssectionin1PIandPIMoriginatingfrom
power corrections to the leading terms in the threshold expansions, and compare them to
previous approaches. We latercombine ourPIM and 1PIresults forthe totalcross section,
this way eliminating uncertainties due to these corrections. The combined predictions for
the total cross section are presented as a function of the top-quark mass in the pole, the
minimal-subtraction(MS), andthe1S massscheme. Inaddition, wecalculatetheforward-
¯backward (FB) asymmetry at the Tevatron in the laboratory, and in the tt rest frames as
a function of the rapidity and the invariant mass of the top-quark pair at NLO+NNLL.
We also give binned results for the asymmetry as a function of the invariant mass and the
¯rapidity difference of the tt pair, and compare those to recent measurements. As a last
applicationwe calculatethechargeasymmetryattheLHCasafunctionofalowerrapidity
cut-off for the top and anti-top quarks.
3Time flies like an arrow. Fruit flies like a banana.
Croucho Marx
4Contents
I. Introduction 9
1. Preface 10
¯1.1. tt Production: Theory Overview and Extensions Presented in this Thesis . 11
1.2. Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3. Top-Quark Production: A Short Experimental Overview . . . . . . . . . . 15
2. Effective Field Theories 18
2.1. Soft-Collinear Effective Theory . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1. Gauge Transformation . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.2. Decoupling Transformation . . . . . . . . . . . . . . . . . . . . . . 23
2.1.3. Matching Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2. Heavy-Quark Effective Theory . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3. Factorization and Resummation . . . . . . . . . . . . . . . . . . . . . . . . 27
¯II. tt Production: Theoretical Setup 33
3. Introduction 34
4. Pair Invariant-Mass Kinematics 35
4.1. Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2. Factorization in SCET and HQET . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1. Color-Space Formalism . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.2. Factorization of the Differential Cross Section . . . . . . . . . . . . 46
4.2.3. The Hard Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.4. The Soft Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.5. Threshold Resummation . . . . . . . . . . . . . . . . . . . . . . . . 54
5. Single-Particle Inclusive Kinematics 59
5.1. Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2. Factorization in SCET and HQET . . . . . . . . . . . . . . . . . . . . . . 62
5.2.1. The Soft Functions in 1PI . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.2. Threshold Resummation . . . . . . . . . . . . . . . . . . . . . . . . 65
5Contents
6. Approximate NNLO 69
6.1. Approximate NNLO: PIM . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2. Approximate NNLO: 1PI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2.1. C Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730
6.3. Resummation vs. NNLO Expansion . . . . . . . . . . . . . . . . . . . . . . 74
¯III.tt Production: Phenomenology 77
7. Introduction 78
8. Studies in PIM 82
8.1. Systematic Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.1.1. Threshold Enhancement . . . . . . . . . . . . . . . . . . . . . . . . 82
8.1.2. Scale Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.2. Invariant Mass Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3. Total Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.3.1. Comparison with Previous Calculations . . . . . . . . . . . . . . . . 96
9. Studies in 1PI 101
9.1. Numerical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
9.2. Systematic Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
9.2.1. Threshold Enhancement . . . . . . . . . . . . . . . . . . . . . . . . 102
9.2.2. Scale Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.3. Rapidity and Transverse-Momentum Distributions . . . . . . . . . . . . . . 109
9.4. Total Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.Combined Studies 114
10.1.Total Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.1.1. Theβ Distribution in PIM and 1PI Kinematics . . . . . . . . . . . 114
10.1.2. Combined Cross Sections in the Pole Scheme . . . . . . . . . . . . . 123
10.1.3. Combined Cross Sections in the MS and 1S Schemes . . . . . . . . 125
10.1.4. Comparing to Measurements . . . . . . . . . . . . . . . . . . . . . . 131
10.2.Forward-Backward Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . 132
10.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
10.2.2. FB Asymmetry in the Laboratory Frame . . . . . . . . . . . . . . . 135
¯10.2.3. FB Asymmetry in thett Frame . . . . . . . . . . . . . . . . . . . . 139
10.2.4. Charge Asymmetry at the LHC . . . . . . . . . . . . . . . . . . . . 145
IV.Conclusions 149
11.Summary and Outlook 150
6Contents
A. Appendix 155
.1. RG-Evolution Factors and Anomalous Dimensions . . . . . . . . . . . . . . 155
.2. Integrals for the Soft Functions . . . . . . . . . . . . . . . . . . . . . . . . 158
.3. Comparing NNLL vs. NNLO . . . . . . . . . . . . . . . . . . . . . . . . . 162
test
7testPart I.
Introduction
91. Preface
At themoment the probable mostcomplicated machine ever build bymankind hasbeen in
operationforabout 2years, the large hadroncollider (LHC). Startingconstruction in 1995
itisalsooneofthe biggest, mostexpensive scientific instruments ever made. Thismachine
represents the enormous effort to understand nature, explicitly particle physics, in more
detail. The fact that physicists have to go to such great length, may it be the at LHC or
at the Tevatron, to obtain new data, and observe unknown phenomena can be seen as a
sign ofan already deep understanding of vast areasof nature. Concerning particle physics,
past generations of physicists have been astonishingly successful describing experimental
data better and better. After the big steps at the beginning of the 20th century, when
quantum physics and general relativity changed drastically our view of the world, came an
time were a refinement of the theoretical and experimental tools lead to a discovery of an
abundance of new particles. In the time until the late 70s of the last century the observed
forces, and the apparent zoo of particles were more and more understood. At present we
know about four forces, gravity, electromagnetism, the weak and the strong force. For the
main part of particle physics only the latter three are of importance. In the beginning of
the 1970s it became clear that the electromagnetic and weak force could be unified into
the so called electroweak force. The combination of theses two forces is build upon the
gauge group SU(2) ×U(1) , which is then broken down to U(1) , and the weak forceL Y em
±which is mediate by the massive gauge bosons W and Z. The concept of gauge theory
to describe interactions is one of the most fruitful realizations of theoretical physics in the
20th century. In combination with the Higgs mechanism to spontaneously break a given
gauge-symmetry, it is the base on which the standard model (SM) of particle physics is
founded. This standard model is a SU(3) ×SU(2) ×U(1) gauge group. The SU(3)C L Y C
is the non-abelian gauge group describing the strong interaction, the theory of which is
called quantum chromodynamics (QCD). The form of the QCD Lagrangian isX X1 (a) (a)ν i j i¯ ¯L =− F F +i Ψ γ (D ) Ψ − m Ψ Ψ , (1.1)QCD ij q qiν q q q4
q q
where
(a) a a b cF =∂ A −∂ A −g f A A , (1.2) ν s abcν ν ν
and the covariant derivative is
aXtij a(D ) =δ ∂ +ig A . (1.3) ij ij s 2
a
10