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Aspects of hadronic B decays in and beyond the standard model [Elektronische Ressource] / vorgelegt von Leonardo Vernazza

231 pages
Aspects of Hadronic B Decays in andBeyond the Standard ModelVon der Fakult¨at fu¨r Mathematik, Informatik undNaturwissenschaften der RWTH Aachen University zurErlangung des akademischen Grades eines Doktors derNaturwissenschaften genehmigte Dissertationvorgelegt vonDottore Magistrale in FisicaLeonardo Vernazzaaus Savona, ItalienBerichter: Universita¨tsprofessor Martin BenekeUniversit¨atsprofessor Werner BernreutherTag der mu¨ndlichen Pru¨fung: 16 Oktober 2009Diese Dissertation ist auf den Internetseiten der Hochschulbibliothekonline verfu¨gbar.iiAbstractIn this thesis we address various issues of hadronic B decays, in the Standard Model andbeyond. Concerning the first aspect, we focus on the problem of understanding betterlow energy strong interactions in these decays. We consider in particular B decays intoa charmonium state and a light meson. We develop a complete treatment of low energyQCD interaction in the context of QCD factorization, treating the charmonia as non-relativistic bound states. This allows us to demonstrate that, in the heavy-quark limit,a perturbative treatment of these decays is possible, even in case of decays into P-waves,which were found to be non-factorizing in previous studies. We achieve this, includingin the analysis the bound state scales of charmonium, which in turn requires to considercharmonium production through colour-octet operators.
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Aspects of Hadronic B Decays in and
Beyond the Standard Model
Von der Fakult¨at fu¨r Mathematik, Informatik und
Naturwissenschaften der RWTH Aachen University zur
Erlangung des akademischen Grades eines Doktors der
Naturwissenschaften genehmigte Dissertation
vorgelegt von
Dottore Magistrale in Fisica
Leonardo Vernazza
aus Savona, Italien
Berichter: Universita¨tsprofessor Martin Beneke
Universit¨atsprofessor Werner Bernreuther
Tag der mu¨ndlichen Pru¨fung: 16 Oktober 2009
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek
online verfu¨gbar.iiAbstract
In this thesis we address various issues of hadronic B decays, in the Standard Model and
beyond. Concerning the first aspect, we focus on the problem of understanding better
low energy strong interactions in these decays. We consider in particular B decays into
a charmonium state and a light meson. We develop a complete treatment of low energy
QCD interaction in the context of QCD factorization, treating the charmonia as non-
relativistic bound states. This allows us to demonstrate that, in the heavy-quark limit,
a perturbative treatment of these decays is possible, even in case of decays into P-waves,
which were found to be non-factorizing in previous studies. We achieve this, including
in the analysis the bound state scales of charmonium, which in turn requires to consider
charmonium production through colour-octet operators. Although there are very large
uncertainties, we find reasonable parameter choices, where the main features of the data
– large corrections to (naive) factorization and suppression of the and ℎ final statesc2 c
– are reproduced though the suppression of is not as strong as seen in the data. Ourc2
resultsalsoprovideanexample,whereanendpointdivergenceinhardspectator-scattering
factorizes and is absorbed into colour-octet operator matrix elements.
Thesecondpartofthethesisisdevotedtoaseriesofanalysesofnon-leptonicB decays
in extensions of the Standard Model. The aim of these studies is twofold: on one hand
we are interested in testing the sensitivity of these decays to new physics; on the other
hand,welookforactualdiscrepanciesbetweentheorypredictionsandexperimentalresults,
tryingto explain them in the context of a new physics model. Concerningthe firstaspect,
we consider two well-motivated new physics scenarios, in which large deviations from the
Standard Model are expected, i.e. the MSSM with large tan, and a supersymmetric
GUT in which the large neutrino mixing angles give rise to a large mixing between the
right-handed quarks. We find that, in both cases, effects in non -leptonic B decays are
small, when constraints from other flavour observables, like leptonic B decays, are taken
into account. Concerning the second issue, we focus on the discrepancies between theory
and experiment, which point to new physics in the electroweak penguin sector of the
0theory. Weconsider amodifiedZ penguinscenario, wherethis possibilityis realized, and
we fit the couplings of the model from the B→K decays. We show that, in this class
of models, a sizeable enhancement of the B→ , decays is expected, even if this is
reduced, when constraints from semi-leptonic B decays are considered.
iiiContents
1 Introduction 1
1.1 Non-leptonic B decays: overview . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 QCD Factorization for Non-leptonic B Decays 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Aspects of QCD Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Non-perturbative parameters . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Non-leptonic decay amplitudes . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Limitations of the factorization formula . . . . . . . . . . . . . . . . 24
2.3 Non-leptonic B decays into two light mesons . . . . . . . . . . . . . . . . . 25
2.3.1 Decay amplitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.2 Short-distance coefficients . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.3 Calculation of the matrix elements in SCET . . . . . . . . . . . . . . 33
2.3.4 NLO results for the topological amplitudes . . . . . . . . . . . . . . 41
2.3.5 Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 QCD factorization for Exclusive b→cc¯D decays 55
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Operator definitions and tree-level results . . . . . . . . . . . . . . . . . . . 58
3.2.1 Effective Hamiltonian and kinematics . . . . . . . . . . . . . . . . . 58
3.2.2 SCET/NRQCD operator definitions . . . . . . . . . . . . . . . . . . 59
3.2.3 Tree-level matching of A-type operators . . . . . . . . . . . . . . . . 61
3.2.4 Estimate of the branching fraction . . . . . . . . . . . . . . . . . . . 62
3.2.5 Overview of next-to-leading order terms: P-waves . . . . . . . . . . 64
3.2.6 Overview of next-to-leading order terms: S-waves. . . . . . . . . . . 65
3.3 Short-distance contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3.1 One-loop short-distance coefficients . . . . . . . . . . . . . . . . . . . 67
3.3.2 Short-distance spectator scattering . . . . . . . . . . . . . . . . . . . 70
3.4 Colour-octet matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4.1 Reduction formula for quarkonium matrix elements . . . . . . . . . . 73
3.4.2 Soft vertex correction . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4.3 Soft spectator-scattering . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.4.4 Further remarks on the endpoint singularity . . . . . . . . . . . . . . 80
iiiiv CONTENTS
3.5 Twist-3 spectator scattering contribution . . . . . . . . . . . . . . . . . . . 81
3.6 Estimates of branching ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 Non-leptonic B decays in the MSSM with large tan 99
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2 Scalar four-quark operators in the MSSM with large tan . . . . . . . . . . 100
+ − + +4.3 Constraints from B → and B → . . . . . . . . . . . . . . . . 104s
4.4 Parameter space analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.5 Hadronic matrix elements for B→M M . . . . . . . . . . . . . . . . . . . 1081 2
4.6 Non-leptonic decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5 Non-leptonic B decays in a supersymmetric grand unified theory 119
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.2 Four-quark operators in the Chang-Masiero-Murayama model . . . . . . . . 121
5.3 Hadronic matrix elements for B→M M . . . . . . . . . . . . . . . . . . . 1371 2
5.4 Non-leptonic decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6 Non-leptonic B decays with new physics in the electroweak penguin
sector 147
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
¯ ¯6.2 Analysis of the B→K modes . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.3 Consequences on other decay modes . . . . . . . . . . . . . . . . . . . . . . 154
¯ ¯6.3.1 The B →, B → decays . . . . . . . . . . . . . . . . . . . . . 154s s
∗ ∗¯ ¯ ¯ ¯ ¯ ¯6.3.2 B→K, B→K and B→K decays . . . . . . . . . . . . . . . 156
06.4 A viable scenario: the flavour-changing Z penguin . . . . . . . . . . . . . . 158
6.4.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
¯6.4.2 Hadronic matrix elements for B→M M . . . . . . . . . . . . . . . 1611 2
6.4.3 Phenomenology of non-leptonic B decays . . . . . . . . . . . . . . . 162
6.4.4 Constraints from semi-leptonic B decays . . . . . . . . . . . . . . . . 164
6.5 Fitting the data: numerical results . . . . . . . . . . . . . . . . . . . . . . . 167
6.5.1 The fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7 Conclusion 179
A Effective Field Theory Review 181
A.1 SCET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182I
A.2 SCET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187IIContents v
A.3 Non-relativistic QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
B Higgs sector in the MSSM with large tan