The Fourth Generation: a Comprehensive Analysis
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TECHNISCHE UNIVERSITAT¨ MUNCHEN¨ Lehrstuhl T31 f¨ur Theoretische Elementarteilchenphysik The Fourth Generation: A Comprehensive Analysis Christoph Promberger Vollst¨andiger Abdruck der von der Fakult¨at f¨ur Physik der Technischen Universit¨at M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. StefanSch¨onert Pr¨ufer der Dissertation: 1. Univ.-Prof. Dr. Andrzej J. Buras 2. Univ.-Prof. Dr. Alejandro Ibarra Die Dissertation wurde am 24.5.2011 bei der Technischen Universit¨at M¨unchen eingereicht und durch die Fakult¨at f¨ur Physik am 6.6.2011 angenommen. Zusammenfassung Gegenstand dieser Arbeit ist eine systematische ph¨anomenologische Analyse der als SM4 bezeichneten Standardmodell-Erweiterung durch eine vierte Generation von Quarks und Leptonen. In diesem Rahmen behandeln wir neben direkten Messungen der beteiligten Parameter vor allem elektroschwache Pr¨azisionstests sowie Flavor- und CP-verletzende Ob- servablen im Quark- wie im Lepton-Sektor. Unsere Analyse elektroschwacher Pr¨azisionstests widerlegt die weit verbreitete Annahme, eine vierte Generation w¨urde durch solche Messungen bereits ausgeschlossen. Allerdings wird der verf¨ugbare Parameterraum dadurch stark eingeschr¨ankt, insbesondere die Misch- ung zwischen Quarks der dritten und vierten Familie sowie die m¨oglichen Massendifferenzen innerhalb der neuen Quark- und Lepton-Duplets. Im Weiteren berechnen wir mehr als 30 Prozesse im Quark- und Lepton-Sektor, in de- nen flavor-¨andernde neutrale Str¨ome und/oder Verletzungen der CP-Symmetrie auftreten. Es wird gezeigt, wie im SM4 die bestehenden Anomalien im Unitarit¨atsdreieck sowie in den CP Asymmetrien Sψφ und SφKS gleichzeitig behoben werden k¨onnen. Eine globale nu- merische Untersuchung aller behandelter Observablen schr¨ankt den Parameterraum weiter ein und offenbart charakteristische Korrelationsmuster zwischen bestimmten Messgr¨oßen. Die hierdurch erhaltenen ph¨anomenologischen Signaturen erlauben es, das SM4 eindeutig von anderen Modellen neuer Physik zu unterscheiden. Abstract The subject of this thesis is a systematic phenomenological analysis of the SM4, the stan- dard model of particle physics extended by a fourth generation of quarks and leptons. In this framework we study the impact of direct measurements of the involved parameters, electroweak precision tests, as well as flavor and CP violation observables in the quark and lepton sector. The analysis of electroweak precision tests disproves the commonly held assumption that a fourth generation would be excluded by these constraints. Yet, they impose severe bounds on the involved parameter space, particularly the quark mixing between the third and fourth family and the possible mass differences within the new quark and lepton doublets. Subsequently, we calculate more than 30 flavor changing neutral current and CP-violating processes in the quark and lepton sector. It is shown how the existing anomalies in the unitarity triangle fits as well as in the CP asymmetries Sψφ and SφKS can be explained simultaneously in the SM4. A global numerical analysis of all calculated observables further constrains the parameter space and reveals characteristic patterns of correlation between certain measurable quantities. The phenomenological signatures obtained in this way allow to clearly distinguish the SM4 from other new physics scenarios. Contents 1. Introduction 3 2. The SM4 9 2.1. ParticlesandProperties ............................. 9 2.1.1. ExtendingtheSM ............................ 9 2.1.2. DirectSearchesandMassLimits . 10 2.1.2.1. Mass Limits for Fourth Generation Quarks . 10 2.1.2.2. Mass Limits for Fourth Generation Leptons . 11 2.1.2.3. UpperMassBoundsfromPerturbativity . 12 2.2. FermionMixing.................................. 12 2.2.1. The 4 4 Quark Mixing Matrix V .................. 13 × SM4 2.2.1.1. Parametrization and Unitarity . 13 2.2.1.2. TreeLevelCKMConstraints . 15 2.2.1.3. Simplifications, Wolfenstein Expansion and Scaling Scenarios 17 2.2.1.4. CP-Violating Invariants . 19 2.2.2. The 4 4 Lepton Mixing Matrix U ................. 20 × SM4 3. Electroweak Precision Tests 23 3.1. Electroweak Precision Observables . ... 23 3.1.1. ObliqueParameters............................ 24 3.1.1.1. GeneralIntroduction. 24 3.1.1.2. Oblique Parameters in the SM4 . 25 3.1.2. Non-Oblique Effects: Zb¯b Vertex .................... 26 3.2. Numerical Analysis of Electroweak Precision Tests in the SM4 . ..... 28 3.2.1. Outline .................................. 28 3.2.2. Bound on s34 ............................... 29 3.2.3. MassSplitting............................... 30 4. Flavor and CP Violation Observables 33 4.1. Preliminaries: Effective Hamiltonians and Loop Functions . ... 33 4.1.1. Introduction to Effective Field Theories . 33 4.1.2. Gauge Independent Loop and Master Functions in the SM4 . .. 34 4.1.2.1. GaugeIndependentLoopFunctions. 35 4.1.2.2. MasterFunctions........................ 35 4.2. Quark Flavor and CP Violation . 37 4.2.1. Particle-Antiparticle Mixing (∆F = 2) and Indirect CP Violation . 37 4.2.1.1. K0 K¯ 0 Mixing (∆S =2)................... 37 − Contents 4.2.1.2. B0 B¯0 Mixing (∆B =2)................... 39 q − q 4.2.1.3. D0 D¯ 0 Mixing (∆C =2)................... 41 − 4.2.2. LeptonicDecays.............................. 42 + 4.2.2.1. KL µ µ− ........................... 42 → + 4.2.2.2. B µ µ− .......................... 43 s,d → 4.2.3. Semi-LeptonicDecays .......................... 45 4.2.3.1. K+ π+νν¯ and K π0νν¯ ................. 45 → L → 4.2.3.2. B X νν¯ ........................... 46 → d,s 4.2.4. RadiativeDecays ............................. 47 4.2.4.1. B Xsγ ............................ 47 → + 4.2.4.2. B Xsℓ ℓ− .......................... 49 → 0 + 4.2.4.3. K π ℓ ℓ− .......................... 49 L → 4.2.5. CP Violation in K and B Decays .................... 51 4.2.5.1. Preliminaries . 51 4.2.5.2. Direct CP Violation in the K system: ε′/ε .......... 51 4.2.5.3. CP-Violating B Decays into CP Eigenstates . 52 4.2.5.4. A (b sγ)intheSM4.................... 56 CP → 4.3. Lepton Flavor Violation . 57 4.3.1. Preliminaries . 57 4.3.2. Dipole Transitions (ℓ ℓ γ) ...................... 57 a → b 4.3.3. Four-LeptonTransitions . 58 + 4.3.3.1. The Decays τ − ℓb−ℓc ℓb− ................... 58 → + 4.3.3.2. The Decays τ − ℓb−ℓc ℓc− ................... 59 → + 4.3.3.3. The Decays ℓ− ℓ−ℓ ℓ− ................... 60 a → b b b 4.3.4. Semi-Leptonic τ Decays ......................... 61 4.3.5. Lepton-Flavor Violating B and K Decays ............... 63 4.3.5.1. K µe and K π0µe ................. 63 L,S → L,S → 4.3.5.2. B ℓ ℓ ........................... 64 q → c d 4.3.6. µ e ConversioninNuclei........................ 65 − 4.3.7. AnomalousMagneticMomentoftheMuon. 66 5. Numerical Analysis 69 5.1. NumericalAnalysisoftheQuarkSector. ... 69 5.1.1. Preliminaries . 69 5.1.2. Violation of Universality . 71 5.1.3. Correlations within the K System.................... 72 5.1.4. Correlations Involving the B System .................. 77 bsγ 5.1.5. The CP Asymmetries Sψφ, SφKS and ACP ............... 79 5.1.6. The Ratio ε′/ε .............................. 81 5.1.7. Violation of CKM Unitarity . 84 5.1.8. Patterns of Correlation and Comparison with other Models . ... 85 5.2. AnatomyoftheQuarkSector . 87 5.2.1. Step1:ParameterScenarios . 87 5.2.2. Step 2: Anticipating LHCb Results . 88 Contents 1 5.3. Determining the Matrix VSM4 .......................... 89 5.3.1. Preliminaries . 89 5.3.2. BasicObservables............................. 91 5.3.3. Anatomyof4GMixingAnglesandCPPhases . 95 5.4. NumericalAnalysisoftheLeptonSector . 102 5.4.1. Preliminaries . 102 + 5.4.2. µ− e−γ, µ− e−e e− and µ e Conversion . 102 5.4.3. The→ Decays τ →µγ and τ eγ−..................... 105 → → 5.4.4. The Semi-Leptonic τ Decays and τ µγ ................ 105 0 → 5.4.5. KL µe and KL π µe ........................ 106 5.4.6. UpperBounds...............................→ → 107 5.4.7. Patterns of Correlation and Comparison with other Models . 108 6. Summary and Conclusions 111 A. Effective FCNC Vertices 115 A.1.GenericEffectiveVertices . 115 A.1.1. GenericBoxVertex.. .. .. 115 A.1.2. Generic Z0 PenguinVertex........................ 117 A.1.3. GenericPhotonPenguinVertex . 118 A.1.3.1. Off-Shell γ Penguin....................... 118 A.1.3.2. On-Shell γ Penguin....................... 119 A.1.4. Generic Gluon Penguin Vertex . 120 A.2. Wilson Coefficients and Gauge-Independent Loop Functions . ...... 120 A.2.1. Wilson Coefficients for ∆F =2FourFermionOperators . 120 A.2.2. Wilson Coefficients for ∆F =1FourFermionOperators . 121 B. Reference: Loop Functions 123 Bibliography 127 Danksagung 146 1. Introduction The world around us is composed of only three types of basic elementary particles: Up- and down-quarks are the principal components of all atomic nuclei, and electrons constitute the atomic shells. In addition, there is the electron neutrino first postulated by Pauli in 1931 [1] and discovered in 1956 [2], which is too volatile to act as a constituent of matter. These four fermions – two quarks and two leptons – comprise what we call today the first generation. The first indication that this is not the end of the story came from the discovery of the muon in 1937 [3,4], which is approximately 200 times heavier than the electron but identical in all other properties. The surprise which this particle caused in the physical community is probably best captured by I.I. Rabi’s famous question: “Who ordered that?” [5]. Throughout the following decades, the