Polarization in heavy quark decays [Elektronische Ressource] / Kadeer Alimujiang

Description

Polarization in heavy quark decaysDissertationzur Erlangung des GradesDoktor der Naturwissenschaften“”am Fachbereich Physikder Johannes Gutenberg-Universit¨atin MainzKadeer Alimujianggeboren im Uigurischen Autonomen Gebiet Xinjiang, V. R. ChinaMainz, 2006Date of the oral examination: 30.11.200666AbstractIn this thesis I concentrate on the angular correlations in top quark decays and theirnext–to–leading order (NLO) QCD corrections. I also discuss the leading–order (LO)angular correlations in unpolarized and polarized hyperon decays.In the first part of the thesis I calculate the angular correlation between the top quarkspin and the momentum of decay products in the rest frame decay of a polarized topquark into a charged Higgs boson and a bottom quark in Two-Higgs-Doublet-Models:+t(↑)→ b+H . The decay rate in this process is split into an angular independent part(unpolarized) and an angular dependent part (polar correlation). I provide closed formformulae for theO(α ) radiative corrections to the unpolarized and the polar correlationsfunctions for m = 0 and m = 0. The results for the unpolarized rate agree with theb bexisting results in the literature. The results for the polarized correlations are new. Ifound that, for certain values of tanβ, theO(α ) radiative corrections to the unpolarized,spolarized rates, and the asymmetry parameter can become quite large.

Sujets

• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2007
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Polarization in heavy quark decays
Dissertation
zur Erlangung des Grades
Doktor der Naturwissenschaften“
”
am Fachbereich Physik
der Johannes Gutenberg-Universit¨at
in Mainz
Kadeer Alimujiang
geboren im Uigurischen Autonomen Gebiet Xinjiang, V. R. China
Mainz, 2006Date of the oral examination: 30.11.2006Abstract
In this thesis I concentrate on the angular correlations in top quark decays and their
next–to–leading order (NLO) QCD corrections. I also discuss the leading–order (LO)
angular correlations in unpolarized and polarized hyperon decays.
In the first part of the thesis I calculate the angular correlation between the top quark
spin and the momentum of decay products in the rest frame decay of a polarized top
quark into a charged Higgs boson and a bottom quark in Two-Higgs-Doublet-Models:
+t(↑)→ b+H . The decay rate in this process is split into an angular independent part
(unpolarized) and an angular dependent part (polar correlation). I provide closed form
formulae for theO(α ) radiative corrections to the unpolarized and the polar correlations
functions for m = 0 and m = 0. The results for the unpolarized rate agree with theb b
existing results in the literature. The results for the polarized correlations are new. I
found that, for certain values of tanβ, theO(α ) radiative corrections to the unpolarized,s
polarized rates, and the asymmetry parameter can become quite large.
InthesecondpartIconcentrateonthesemileptonicrestframedecayofapolarizedtop
+quark into a bottom quark and a lepton pair: t(↑)→X +` +ν . I analyze the angularb `
correlations between the top quark spin and the momenta of the decay products in two
different helicity coordinate systems: system 1a with the z–axis along the charged lepton
momentum, and system 3a with the z–axis along the neutrino momentum. The decay
rate then splits into an angular independent part (unpolarized), a polar angle dependent
part (polar correlation)and an azimuthal angle dependent part (azimuthalcorrelation). I
presentclosedformexpressionsfortheO(α )radiativecorrectionstotheunpolarizedparts
and the polar and azimuthalcorrelationsin system 1a and 3a form = 0 andm =0. Forb b
theunpolarizedpartandthepolarcorrelationIagreewithexistingresults. Myresultsfor
the azimuthal correlations are new. In system 1a I found that the azimuthal correlation
vanishes in the leading order as a consequence of the (V −A) nature of the Standard
Model current. The O(α ) radiative corrections to the azimuthal correlation in systems
1a are very small (around 0.24% relative to the unpolarized LO rate). In system 3a the
azimuthal correlation does not vanish at LO. The O(α ) radiative corrections decreasess
the LO azimuthal asymmetry by around 1%.
In the last part I turn to the angular distribution in semileptonic hyperon decays.
Using the helicity method I derive complete formulas for the leading order joint angular
decay distributions occurring in semileptonic hyperon decays including lepton mass and
polarizationeffects. Comparedtothetraditionalcovariantcalculationthehelicitymethod
allowsonetoorganizethecalculationoftheangulardecaydistributionsinaverycompact
and efficient way. This is demonstrated by the specific example of the polarized hyperon
0 + − − − − + 0decayΞ (↑)→ Σ +l +ν¯ (l =e ,μ )followedbythenonleptonicdecayΣ →p+π ,l
which is described by a five–fold angular decay distribution.
66Contents
1 Introduction 1
+2 Polarization Effects in t(↑)→b+H 7
2.1 The Born approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Virtual one–loop corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Vertex corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Quark self–energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Renormalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Renormalized virtual one–loop corrections . . . . . . . . . . . . . . 27
2.3 Real gluon emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 The amplitude squared for the real emissions . . . . . . . . . . . . . 31
2.3.2 The phase space integration . . . . . . . . . . . . . . . . . . . . . . 34
2.3.3 Integration of the soft gluon factor . . . . . . . . . . . . . . . . . . 42
2.3.4 Full real emission contributions . . . . . . . . . . . . . . . . . . . . 49
2.4 TotalO(α ) results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50s
+3 Angular correlations for t(↑)→b+` +ν in system 1a 59`
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 The Born approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Virtual one–loop corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.1 Vertex corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.2 Renormalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.3 Renormalized virtual one–loop correction . . . . . . . . . . . . . . . 80
3.4 Real gluon emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4.1 The amplitude squared for the real emissions . . . . . . . . . . . . . 84
3.4.2 Phase space integration. . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5 TotalO(α ) results for system 1a . . . . . . . . . . . . . . . . . . . . . . . 94s
3.6 Azimuthal correlation atO(α ) . . . . . . . . . . . . . . . . . . . . . . . . 101s
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
+4 Angular correlations for t(↑)→b+` +ν in system 3a 109`
4.1 The Born approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2 Virtual one–loop correction . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 Real gluon emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.4 TotalO(α ) results for system 3a . . . . . . . . . . . . . . . . . . . . . . . 120sii CONTENTS
4.5 Azimuthal correlation atO(α ) . . . . . . . . . . . . . . . . . . . . . . . . 126s
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5 Helicity Analysis of Semileptonic Hyperon Decays 139
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.2 The helicity amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3 Unpolarized decay rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.4 The rate ratio Γ(e)/Γ(μ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.5 Single spin polarization effects . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.5.1 Polarization of the daughter baryon . . . . . . . . . . . . . . . . . . 152
5.5.2 Polarization of the lepton . . . . . . . . . . . . . . . . . . . . . . . 153
5.5.3 Decay of a polarized parent baryon . . . . . . . . . . . . . . . . . . 154
5.6 Joint angular decay distribution . . . . . . . . . . . . . . . . . . . . . . . . 157
5.7 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Appendix 161
A Notations 161
A.1 Dirac matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
A.2 Dirac equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
A.3 Gell–Mann matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
A.4 The CKM matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
A.5 Feynman rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
A.5.1 Outer lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
A.5.2 Propagators in the Feynman gauge . . . . . . . . . . . . . . . . . . 166
A.5.3 Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
B Calculation of the loop integrals 168
B.1 Feynman parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
B.2 Scalar loop integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
C Polylogarithm 178
D Basic integrals for the phase space integrations 181
D.1 Two–body phase space integration R (P;p ,k) . . . . . . . . . . . . . . . . 1812 b
+D.2 Basic z–integrals for t(↑)→H +b . . . . . . . . . . . . . . . . . . . . . . 183
+D.3 Basic z–integrals for t(↑)→b+` +ν . . . . . . . . . . . . . . . . . . . . 186`
D.4 Coefficient functions for system 1a. . . . . . . . . . . . . . . . . . . . . . . 188
D.5 Coefficient functions for system 3a. . . . . . . . . . . . . . . . . . . . . . . 191
D.6 Basic integrals for the azimuthal calculation . . . . . . . . . . . . . . . . . 194
E Some technical notes on the semileptonic hyperon decays 196
E.1 T–odd contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
E.2 Full five-fold angular decay distribution . . . . . . . . . . . . . . . . . . . 197
Bibliography 201List of Figures
1.1 Top quark pair production at the Tevatron . . . . . . . . . . . . . . . . . . 2
1.2 Single top quark production at the Tevatron . . . . . . . . . . . . . . . . . 3
2.1 Definition of the polar angle θ . . . . . . . . . . . . . . . . . . . . . . . . 8P
2.2 LO rates as functions of m /m in model 1 . . . . . . . . . . . . . . . . . 13H t
2.3 Asymmetry parameter as a function of m /m in model 1 . . . . . . . . . 13H t
2.4 LO rates as functions of m /m in model 2 . . . . . . . . . . . . . . . . . 14H t
2.5 Asymmetry parameter a