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Electroweak Radiative B-Decays As a Test of the Standard Model and Beyond Andrey Tayduganov

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Electroweak Radiative B-Decays As a Test of the Standard Model and Beyond Andrey Tayduganov Electroweak radiative B-decays as a test of the Standard Model and beyond Andrey Tayduganov To cite this version: Andrey Tayduganov. Electroweak radiative B-decays as a test of the Standard Model and beyond. Other [cond-mat.other]. Université Paris Sud - Paris XI, 2011. English. NNT : 2011PA112195. tel-00648217 HAL Id: tel-00648217 https://tel.archives-ouvertes.fr/tel-00648217 Submitted on 5 Dec 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LAL 11-181 LPT 11-69 THESE` DE DOCTORAT Pr´esent´eepour obtenir le grade de Docteur `esSciences de l’Universit´eParis-Sud 11 Sp´ecialit´e:PHYSIQUE THEORIQUE´ par Andrey Tayduganov D´esint´egrationsradiatives faibles de m´esons B comme un test du Mod`eleStandard et au-del`a Electroweak radiative B-decays as a test of the Standard Model and beyond Soutenue le 5 octobre 2011 devant le jury compos´ede: Dr. J. Charles Examinateur Prof. A. Deandrea Rapporteur Prof. U. Ellwanger Pr´esident du jury Prof. S. Fajfer Examinateur Prof. T. Gershon Rapporteur Dr. E. Kou Directeur de th`ese Dr. A. Le Yaouanc Directeur de th`ese Dr. M.-H. Schune Examinateur Contents R´esum´e 7 Abstract 9 Introduction 11 1 Flavour physics in the Standard Model and beyond 13 1.1 The Standard Model .............................. 13 1.2 Motivation for New Physics beyond the Standard Model . 17 1.3 b sγ in the SM ................................ 19 → 1.3.1 Photon polarization of the quark level b sγ process in the SM . 20 → 1.3.2 Possible contamination of “wrong” chirality contribution due to the term ................................. 25 O2 1.4 Photon polarization with new physics ..................... 27 1.4.1 Extra source of flavour violation in MSSM . 28 1.4.2 Mass Insertion Approximation ..................... 29 2 The B K γ (Kππ)γ decay and polarization measurement 31 → 1 → 2.1 How to measure the polarization: basic idea . 31 2.2 Photon polarization determination with B K γ decay . 32 → 1 2.3 Master formula for B K γ (Kππ)γ decays . 35 → 1 → 2.3.1 Master formula ............................. 35 2.3.2 Derivation of the master formula ................... 37 2.3.3 Hadronic parameters .......................... 41 2.4 Determination of λγ in the DDLR method . 43 2.4.1 The previous method of Gronau et al. 43 2.4.2 Application of the DDLR method for the λγ determination . 44 3 Strong interaction decays of the K1-mesons 49 3.1 Overview of the previous K1-decay studies . 49 3.1.1 Experimental overview ......................... 49 3.1.2 Theoretical overview .......................... 50 3.2 Theoretical model ................................ 52 3.2.1 The mixing of the kaon resonances . 53 4 CONTENTS 3 3.2.2 P0 Quark-Pair-Creation Model .................... 54 3.2.3 The issue of the damping factor .................... 58 3.3 How to compare the theoretical model computation with the experimental data? ....................................... 59 3.3.1 The K-matrix formalism ........................ 60 3.3.2 Observed problems in the K-matrix analysis . 63 3.4 Numerical results ................................ 68 3.4.1 Fit of parameters γ and θK1 ...................... 69 3.4.2 Model predictions for partial widths . 71 3.4.3 Prediction of signs of decay amplitudes and the “off-set” phase issue 73 3.4.4 The issue of the κπ channel ...................... 78 4 Sensitivity studies of the polarization measurement with B K1(1270)γ in the DDLR method → 81 4.1 Statistical error on the polarization parameter . 81 4.2 Theoretical uncertainties of the hadronic model and error on the polariza- tion parameter ................................. 85 4.2.1 Theoretical uncertainty due to the K1 mixing angle . 86 4.2.2 Theoretical uncertainty due to the “off-set” phase δρ . 87 4.3 Discussion on the importance of the D-waves and the cut-off . 90 5 Future prospects of the photon polarization measurement 93 5.1 Comparison to the other methods ....................... 93 5.1.1 Up-down asymmetry of GGPR .................... 93 + 5.1.2 The angular analysis of B K∗ℓ ℓ− . 93 → 5.1.3 Methods invoking CP -asymmetries . 97 5.2 New physics constraints combining various methods of the polarization determination .................................. 98 6 Conclusions 103 6.1 The general method of Gronau et al.: a critical view . 103 6.2 Improvement of statistical errors by the DDLR method . 105 6.3 The treatment of the full system of the K1-decays . 105 6.3.1 Critical view of the experimental analyses of the K1-system of strong decays ..................................105 6.3.2 A semi-theoretical treatment of the K1-system of strong decays . 106 6.4 Theoretical errors on the polarisation measurement . 106 6.5 The need for improvements of our experimental knowledge and some future prospects ....................................106 A Renormalization and running of the Wilson coefficients 109 A.1 Renormalization and operator mixing . 109 A.2 b sγ at Leading Logarithmic Approximation . 110 → CONTENTS 5 B Watson’s theorem 115 C K-matrix formalism 117 C.1 General formalism for the overlapping resonances . 117 C.2 Relation of the couplings in the K-matrix method and the quark model . 120 C.3 Watson’s theorem: another view . 123 C.4 Re-interpreting the ACCMOR result . 124 D QPCM 129 D.1 Spacial integrals in QPCM . 129 D.2 Fixing the relative signs for tree-body decay . 130 D.2.1 Clebsch-Gordan coefficients . 130 D.2.2 Determination of the relative sign of gK∗Kπ and gρππ . 131 D.3 Partial Wave Amplitudes ............................132 D.4 Phase space convention .............................133 E Some notes on statistics 135 E.1 Maximum likelihood method . 135 E.2 General DDLR method .............................136 Bibliography 141 Acknowledgements 147 6 CONTENTS R´esum´e La d´esint´egration radiative du m´eson B en m´eson´etrangeaxiale, B K (1270)γ, a ´et´e → 1 observ´eer´ecemment avec un rapport d’embranchement assez grand que B K∗γ. Ce → processus est particuli`erement int´eressant car la d´esint´egrationdu K1 dans un ´etatfinal `atrois corps nous permet de d´eterminerla polarisation du photon, qui est surtout gauche (droit) pour B(B) dans le Mod`eleStandard tandis que des mod`elesdivers de nouvelle physique pr´edisent une composante droite (gauche) suppl´ementaire. Dans cette th`ese,une nouvelle m´ethode est propos´ee pour d´eterminer la polarisation, en exploitant la distribu- tion totale du Dalitz plot, qui semble r´eduireconsid´erablement les erreurs statistiques de la mesure du param`etrede la polarisation λγ. Cependant, cette mesure de la polarisation n´ecessiteune connaissance d´etaill´eede la d´esint´egration forte K1 Kππ : c’est-`a-direl’ensemble complexe des diff´erentes ampli- tudes d’ondes partielles→ en plusieurs canaux en quasi-deux-corps ainsi que leurs phases relatives. Un certain nombre d’exp´eriencesont ´et´efaites pour extraire ces informations bien qu’il reste divers probl`emes dans ces ´etudes.Dans cette th`ese,nous ´etudionsen d´etail 3 ces probl`emesen nous aidant d’un mod`eleth´eorique.Nous utilisons ainsi le mod`ele P0 de cr´eationd’une paire de quarks pour am´eliorernotre compr´ehensiondes d´esint´egrations fortes du K1. A partir de ce mod`elenous estimons les incertitudes th´eoriques: en particulier, celle venant de l’incertitude de l’angle de m´elangedu K1, et celle due `al’effet d’une phase “off-set” dans les d´esint´egrationsfortes en ondes-S. Selon nos estimations, les erreurs th syst´ematiquesse trouvent ˆetrede l’ordre de σλγ . 20%. D’autre part nous discutons de la sensibilit´edes exp´eriencesfutures, notamment les usines SuperB et LHCb, pour λγ. En estimant na¨ıvement les taux annuels d’´evenements, nous trouvons que l’erreur statistique stat de la nouvelle m´ethode est σλγ . 10%, ce qui est deux fois plus petit qu’en utilisant seulement les distributions angulaires simples. Nous discutons ´egalement de la comparaison avec les autres m´ethodes de mesure de + la polarisation en utilisant les processus tels que B K∗e e−, Bd K∗γ et Bs φγ, → eff →eff → pour la d´eterminationdu rapport des coefficients de Wilson C7′γ /C7γ . Nous montrons eff eff un exemple de contraintes possibles sur C7′γ /C7γ dans plusieurs sc´enariosde mod`eles supersym´etriques. Mots cl´es: Mod`eleStandard, au-del`adu Mod`eleStandard, interaction faible, physique du B, d´esint´egrationradiative de meson-B, polarisation de photon, propri´et´esde meson- K1, mod`eledes quarks, matrice-K, asym´etrie CP , supersym´etrie. 8 R´esum´e Abstract Recently the radiative B-decay to strange axial-vector mesons, B K1(1270)γ, was observed with a rather large branching ratio. This process is particularly→ interesting as the subsequent K1-decay into its three-body final state allows us to determine the polarization of the photon, which is mostly left(right)-handed for B(B) in the Standard Model while various new physics models predict additional right(left)-handed components. In this thesis, a new method is proposed to determine the polarization, exploiting the full Dalitz plot distribution, which seems to reduce significantly the statistical errors on the polarization parameter λγ measurement. This polarization measurement requires, however a detailed knowledge of the K1 Kππ strong interaction decays, namely, the complex pattern of various partial wave am-→ plitudes into the several possible quasi-two-body channels as well as their relative phases.
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