Higher order QCD corrections in exclusive charmless B-decays [Elektronische Ressource] / vorgelegt von Guido Bell

Guido Bell

Sujets

• Physik

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2006
• Nombre de lectures: 7
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Fakult˜at fur˜ Physik
der
Ludwig-Maximilians-Universit˜at Munchen˜
HIGHER ORDER QCD CORRECTIONS
IN EXCLUSIVE CHARMLESS B DECAYS
GUIDO BELL
Oktober 2006Dissertation der Fakult˜at fur˜ Physik
der
Ludwig-Maximilians-Universit˜at Munchen˜
HIGHER ORDER QCD CORRECTIONS
IN EXCLUSIVE CHARMLESS B DECAYS
vorgelegt von
GUIDO BELL
aus
Neuwied am Rhein
Munchen,˜ den 31. Oktober 2006Dissertation der Fakult˜at fur˜ Physik
der Ludwig-Maximilians-Universit˜at Munc˜ hen
vorgelegt von Dipl.-Phys. Guido Bell
aus Neuwied am Rhein
1. Gutachter: Univ.-Prof. Dr. Gerhard Buchalla
2. Gutachter: Priv.-Doz. Dr. Stefan Dittmaier
Tag der mundlic˜ hen Prufung:˜ 13. Dezember 2006Abstract
We discuss exclusive charmless B decays within the Standard Model of particle
physics. These decays play a central role in the on-going process to constrain the
parametersoftheCKMmatrixandtoclarifythenatureofCPviolation. Inorderto
exploit the rich source of data that is currently being collected at the experiments,
asystematictheoreticaltreatmentofthecomplicatedhadronicdynamicsisstrongly
desired. QCD Factorization represents a model-independent framework to compute
hadronic matrix elements from flrst principles. It is based on a power expansion in
⁄ =m and allows for the systematic implementation of perturbative corrections.QCD b
In particular, we consider hadronic two-body decays as B!…… and perform a con-
ceptual analysis of heavy-to-light form factors which encode the strong interaction
efiects in semi-leptonic decays as B!…‘”.
Concerning the hadronic decays we compute NNLO QCD corrections which are
particularly important with respect to strong interaction phases and hence direct
CP asymmetries. On the technical level, we perform a 2-loop calculation which is
based on an automatized reduction algorithm and apply sophisticated techniques
for the calculation of loop-integrals. We indeed flnd that the considered quantities
are well-deflned as predicted by QCD Factorization, which is the result of a highly
complicated subtraction procedure. We present results for the imaginary part of
the topological tree amplitudes and observe that the considered corrections are sub-
stantial. The calculation of the real part of the amplitudes is far more complicated
and we present a preliminary result which is based on certain simpliflcations. Our
calculation is one part of the full NNLO analysis of nonleptonic B decays within
QCD Factorization which is currently pursued by various groups.
In our conceptual analysis of the QCD dynamics in heavy-to-light transitions we
consider form factors between non-relativistic bound states which can be addressed
inperturbationtheory. WeperformaNLOanalysisoftheseformfactorsanddiscuss
some open questions of the general factorization formula which is obtained from the
heavy-quark expansion in QCD. These include the origin and resummation of large
logarithms and the non-factorization of soft and collinear efiects in the so-called
soft-overlap contribution. We show that the latter can be calculated in our set-up
and address the issue of endpoint singularities. As a byproduct of our analysis, we
calculate leading-twist light-cone distribution amplitudes for non-relativistic bound
states which can be applied for the description of B and · mesons.c cContents
I Introduction 1
II Formalism 9
1 Exclusive charmless B decays 11
1.1 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.1 QCD Factorization . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.2 Soft-Collinear Efiective Theory . . . . . . . . . . . . . . . . . 17
1.1.3 Alternative approaches . . . . . . . . . . . . . . . . . . . . . . 20
1.2 Hadronic two-body decays . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2.2 Factorization Formula . . . . . . . . . . . . . . . . . . . . . . 25
1.2.3 Perturbative corrections . . . . . . . . . . . . . . . . . . . . . 26
1.2.4 Power corrections . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.3 Heavy-to-light form factors . . . . . . . . . . . . . . . . . . . . . . . . 34
1.3.1 Factorization Formula . . . . . . . . . . . . . . . . . . . . . . 34
21.3.2 Closer look at »(q ) . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Perturbative corrections 39
2.1 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Decomposition of Tensor Integrals . . . . . . . . . . . . . . . . . . . . 42
2.3 Reduction to Master Integrals . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Calculation of Master Integrals . . . . . . . . . . . . . . . . . . . . . 49
2.4.1 Feynman Parameters . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.2 Method of Difierential Equations . . . . . . . . . . . . . . . . 51
2.4.3 Expansion by Momentum Regions . . . . . . . . . . . . . . . . 56
2.4.4 Mellin-Barnes Techniques . . . . . . . . . . . . . . . . . . . . 58
2.4.5 Sector Decomposition . . . . . . . . . . . . . . . . . . . . . . . 61III Applications 63
3 Hadronic two-body decays I: Imaginary part 65
3.1 Change of operator basis . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 2-loop calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3 Renormalization and IR subtractions . . . . . . . . . . . . . . . . . . 72
3.3.1. . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.2 Factorization in NNLO . . . . . . . . . . . . . . . . . . . . . . 73
3.3.3 IR subtractions . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4 Tree amplitudes in NNLO . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4.1 fi in CMM basis . . . . . . . . . . . . . . . . . . . . . . . . . 781
3.4.2 fi and fi in QCDF basis . . . . . . . . . . . . . . . . . . . . 801 2
3.4.3 Convolution with distribution amplitude . . . . . . . . . . . . 81
3.5 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5.1 Vertex corrections . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5.2 Full NNLO result . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Hadronic two-body decays II: Real part 87
4.1 2-loop calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Renormalization and IR subtractions . . . . . . . . . . . . . . . . . . 89
4.2.1. . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.2 IR subtractions . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3 Tree amplitudes in NNLO . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.1 fi in CMM basis . . . . . . . . . . . . . . . . . . . . . . . . . 931
4.3.2 Convolution with distribution amplitude . . . . . . . . . . . . 94
4.3.3 Preliminary numerical result . . . . . . . . . . . . . . . . . . . 95
5 Heavy-to-light form factors for NR bound states 97
5.1 Non-relativistic approximation . . . . . . . . . . . . . . . . . . . . . . 97
5.2 Perturbative calculation . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2.1 Tree level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2.2 1-loop calculation . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.3 Form factors in NLO . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Factorization Formula . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3.1 Endpoint singularities . . . . . . . . . . . . . . . . . . . . . . 107
5.3.2 Factorization of tree level result . . . . . . . . . . . . . . . . . 111
5.3.3 F in NLO . . . . . . . . . . . . . . . . . . . . . . . 112IV Conclusion 117
V Appendix 123
A Master Integrals 125
A.1 Hadronic two-body decays I . . . . . . . . . . . . . . . . . . . . . . . 125
A.2 two-body decays II . . . . . . . . . . . . . . . . . . . . . . . 133
A.3 Heavy-to-light form factors . . . . . . . . . . . . . . . . . . . . . . . . 144
B Form factors in NLO 149
Bibliography 151
Acknowledgements 160