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Phenomenology of Left-Right Models in the Quark Sector

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Phenomenology of Left-Right Models in the Quark Sector NNT : 2016SACLS249 These` de doctorat de l’Universite´ Paris-Saclay prepar´ ee´ a` l’Universite´ Paris-Sud Ecole doctorale n◦576 Particules, hadrons, ´energie, noyau, instrumentation, image, cosmos et simulation (PHENIICS) Sp´ecialit´ede doctorat: Physique des particules par M. Luiz Henrique Vale Silva Ph´enom´enologie de Mod`eles `aSym´etrie Droite-Gauche dans le secteur des quarks Th`ese pr´esent´ee et soutenue `aOrsay, le 20 Septembre 2016. Composition du Jury : M. Hagop Sazdjian Professeur ´em´erite (Pr´esident du jury) arXiv:1611.08187v1 [hep-ph] 24 Nov 2016 IPN Orsay M. Ulrich Nierste Prof.Dr. (Rapporteur) TTP Karlsruhe Mme Renata Zukanovich Funchal Prof. (Rapporteur) IF S˜ao Paulo M. Jer´ omeˆ Charles Charg´ede Recherche (Examinateur) CPT Marseille Mme Veronique´ Bernard Directeur de Recherche (Directrice de th`ese) IPN Orsay M. Sebastien´ Descotes-Genon Directeur de Recherche (Directeur de th`ese) LPT Orsay Phenomenology of Left-Right Models in the quark sector Abstract A natural avenue to extend the Standard Model (SM) is to embed it into a more symmetric framework. Here, I focus in Left-Right (LR) Models, which treat left- and right-handed chiralities on equal footing. Important information about the structure of LR Models comes from meson-mixing observables. Due to the impact of the new contributions to these processes, I consider the calculation of the short-distance QCD effects correcting the LR Model contributions to meson-mixing observables at the Next- to-Leading Order. I then revisit the phenomenology of a simple realization of LR Models, containing doublet scalars, and combine in a global fit electroweak precision observables, direct searches of the new gauge bosons and meson oscillation observables, a task performed within the CKMfitter statistical framework. Finally, I also cover a different issue, namely the modeling of theoretical uncertainties, a class of uncertainties specially important for flavour physics. Different frequentist schemes are compared, and their differences are illustrated with flavour-oriented examples. Contents Introduction 5 1 The Standard Model 8 1.1 IntroductiontotheSM ............................. ... 8 1.1.1 Gaugesymmetries ............................... 9 1.1.2 Matterfields .................................. 9 1.1.3 EWsymmetrybreaking . .. .. .. .. .. .. .. .. .. .. .. .. 11 1.1.4 Fullmodel.................................... 13 1.2 EWPOfortestingtheSM............................. .. 13 1.2.1 Inputs...................................... 14 1.2.2 Parameterization .. .. .. .. .. .. .. .. .. .. .. .. .. .. 15 1.2.3 Globalfit .................................... 16 1.3 CKMmatrixphenomenologyandfit . .... 18 1.3.1 TheCKMmatrix................................ 18 1.3.2 Observables................................... 21 1.3.3 Theoreticalinputs . .. .. .. .. .. .. .. .. .. .. .. .. .. 24 1.3.4 CKMfitter ................................... 26 1.3.5 Results ..................................... 28 1.4 Conclusionsandwhatcomesnext. ...... 30 2 Left-Right Models 32 2.1 Mattercontent ................................... .. 33 2.2 Spontaneous symmetry breaking in the LR Model . ........ 34 2.3 Gaugebosonspectrum.............................. ... 36 2.4 Massesinthefermionicsector. ....... 38 2.5 Discrete symmetries and the scalar potential . ........... 39 2.6 Couplingstofermions ............................. .... 41 2.6.1 Couplings of the gauge bosons to the fermions . ....... 41 2.6.2 Couplings of the scalars to the fermions . ....... 43 2.7 Structure of the mixing matrix V R .......................... 44 2.8 Tripletmodel .................................... .. 45 2.9 Conclusions ..................................... .. 47 3 Testing the SSB pattern of LR Models through EWPO and direct searches 49 3.1 Corrections from the Left-Right Model to the EWPO . ......... 49 3.1.1 EffectiveLagrangians . .. 50 3.1.2 Parametersusedinthefit . .. 51 3.1.3 ExpressionsforLRModelcorrections . ...... 52 1 3.2 DirectsearchesforLRModelparticles . ......... 54 3.3 Resultsoftheglobalfits .. .. .. .. .. .. .. .. .. .. .. ..... 55 3.4 Conclusions ..................................... .. 58 4 Overview of meson-mixing observables 60 4.1 Contributionstomeson-mixing . ....... 60 4.1.1 SM........................................ 61 4.1.2 LRModels ................................... 63 4.1.3 Including short-distance QCD corrections in the LR Model ........ 67 4.2 EFTformeson-mixinginLRModels. ..... 68 4.2.1 OperatorProductExpansion . ... 68 4.2.2 Integratingoutheavyparticles . ...... 68 4.2.3 Setofoperators................................ 69 4.3 RenormalizationGroupEquations . ....... 71 4.4 MethodofRegions ................................. .. 73 4.5 Calculation of the short-distance QCD corrections in theSM ........... 75 4.5.1 MethodofRegions............................... 76 4.5.2 EFT....................................... 80 4.5.3 Comparison................................... 81 4.6 Conclusion ...................................... 81 5 Short-distance QCD corrections in Left-Right Models 83 5.1 TheMRintheLRModel ............................... 83 5.2 EFT calculation of the cc contributioninLRModels . 86 5.2.1 Basicelements ................................. 89 5.2.2 Evanescentoperators. ... 91 5.2.3 EFT between µW and µc ........................... 92 5.2.4 EFT below µc ................................. 97 5.2.5 Short-distancecorrectionsinEFT . ...... 98 5.3 Discussionoftheresults . ...... 101 5.3.1 Short-range contributions for the cc box................... 101 5.3.2 Short-range contributions for the ct and tt boxes .............. 102 5.3.3 Short-range contribution from neutral and charged Higgsexchange . 103 5.3.4 Set of numerical values for different energy scales . ........... 103 5.4 B mesonsystems.................................... 103 5.5 Conclusions ..................................... 104 6 Global fits 106 6.1 Meson-mixingobservables . ...... 106 6.1.1 Bagparameters................................. 108 6.2 Perturbativity of the potential parameters . ............ 109 6.3 Globalfit ........................................ 110 6.3.1 Inputsandrangesofdefinition . .... 110 6.3.2 Right-handedmixingmatrix . .. 111 6.3.3 Results ..................................... 111 6.4 Conclusion ...................................... 114 2 7 Modeling theoretical uncertainties 117 7.1 Statementoftheproblem . .... 117 7.2 Frequentisttoolbox. .. .. .. .. .. .. .. .. .. .. .. .. ..... 118 7.2.1 Confidence intervals from the p-value . ...... 119 7.2.2 Likelihood: comparisonofhypotheses . ....... 121 7.2.3 Gaussian case without theoretical uncertainties . ............ 122 7.3 Theoreticaluncertainties. ........ 123 7.3.1 Randomapproach: naiveGaussian . .... 124 7.3.2 Externalapproach: Scanmethod . .... 125 7.3.3 Nuisanceapproach .............................. 126 7.3.4 Rfit ....................................... 128 7.3.5 Impact of the modeling of theoretical uncertainties . ............ 129 7.4 Combiningdata................................... 133 7.4.1 Purestatisticalcase . .. 136 7.4.2 Theoreticaluncertainties. ...... 136 7.4.3 Examples .................................... 138 7.5 Globalfitofflavourobservables . ....... 139 7.6 Conclusions ..................................... 142 Conclusion 145 Acknowledgments 148 A EWPO tree level expressions in the SM 149 A.1 Partialwidths................................... .. 149 A.2 Crosssections................................... .. 150 A.3 Asymmetries ..................................... 151 A.4 Atomic Parity Violation (APV) . ...... 152 A.5 Wbosonpartialwidthsandcrosssections . ......... 152 B Parameterization of the EWPO 154 C ρ parameter 157 D Stability conditions 159 E Spectrum of the scalar particles 162 E.1 Tablesofcouplings ............................... .... 164 F Potential and scalar spectrum in the triplet case 168 G RGE formulae 172 H Set of evanescent operators 175 H.1 Operators ∆F =2................................... 175 H.2 Operators |∆F |=1................................... 177 | | I Operators and anomalous dimensions 178 I.1 ∆S =1operators ................................... 178 I.2 |∆S|=2operators ................................... 180 | | 3 J Case at NLO with the method of regions 181 J.1 Contributions with log β ................................ 181 J.2 Contributions without log β .............................. 183 K Inverse of the covariance matrix 185 K.1 Examples ........................................ 187 K.1.1 Twomeasurements............................... 187 K.1.2 n fullycorrelatedmeasurements . 188 K.1.3 Two fully correlated measurements with an uncorrelated measurement . 188 L Correlated theoretical uncertainties 189 4 Introduction The Standard Model (SM) of particle physics is built on top of basic requirements such as Lorentz covariance and renormalizability, and offers a common framework for the description of all known microscopic interactions in terms of local, gauged symmetries. This theory was the fruit of the work of many generations of talented physicists, and is certainly one of the most impressive achievements of sciences. For example, one has tracked a long road to achieve the formulation of the theory of electroweak interactions, unifying Electromagnetism and Weak processes. Indeed, first the weak interactions were introduced as a new fundamental interaction in the 30’s by Fermi [1], formulated at that time as a contact interaction. Later, exactly 60 years ago, parity violation in weak decays was suggested [2], triggering doubts about charge-conjugation and time
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