Standard Model

Yuval Grossman is professor of physics at Cornell University. He is a recipient of the Humboldt Research Award. Yossi Nir is professor of physics at the Weizmann Institute of Science. He is the author (with Helen R. Quinn) of The Mystery of the Missing Antimatter (Princeton).

• Preface1 Lagrangians1.1 Introduction1.2 Examples of Simple Lagrangians1.2.1 Scalars1.2.2 Fermions1.2.3 Fermions and Scalars1.3 Symmetries1.4 Model BuildingAppendix1.A Discrete Spacetime Symmetries: C, P, and T1.A.1 C and P1.A.2 CP Violation and Complex CouplingsProblems2 Abelian Symmetries2.1 Global Symmetries2.1.1 Global Discrete Symmetries2.1.2 Global Continuous Symmetries2.1.3 Charge2.1.4 Product Groups and Accidental Symmetries2.1.5 Symmetries and Fermion Masses2.2 Local Symmetries2.2.1 Introducing Local Symmetries2.2.2 Charge2.3 SummaryProblems3 QED3.1 QED with One Fermion3.1.1 Defining QED3.1.2 The Lagrangian3.1.3 The Spectrum3.1.4 The Interactions3.1.5 Parameter Counting3.2 QED with More Fermions3.2.1 Two Dirac Fermions3.2.2 Accidental Symmetries3.2.3 Even More Fields3.3 Experimental Tests of QEDProblems4 Non-Abelian Symmetries4.1 Introduction4.2 Global Symmetries4.2.1 Scalars and SO(N)4.2.2 Vectorial Fermions and U(N)4.2.3 Chiral Fermions and U(N) × U(N)4.3 Local Symmetries4.4 Running Coupling Constants4.5 SummaryProblems5 QCD5.1 Defining QCD5.2 The Lagrangian5.3 The Spectrum5.4 The Interactions5.5 The Parameters5.6 Confinement5.7 Accidental Symmetries5.8 Combining QCD with QEDProblems6 Spontaneous Symmetry Breaking6.1 Introduction6.2 Global Discrete Symmetries: Z26.3 Global Abelian Continuous Symmetries: U(1)6.4 Global Non-Abelian Continuous Symmetries: SO(3)6.5 Fermion Masses6.6 Local Symmetries: The Higgs Mechanism6.7 SummaryProblems7 The Leptonic Standard Model7.1 Defining the LSM7.2 The Lagrangian7.2.1 ℒkin and the Gauge Symmetry7.2.2 ℒψ7.2.3 ℒY uk7.2.4 ℒϕ and SSB7.2.5 Summary7.3 The Spectrum7.3.1 Scalars: Back to ℒϕ7.3.2 Vector Bosons: Back to ℒkin(ϕ)7.3.3 Fermions: Back to ℒY uk7.3.4 Summary7.4 The Interactions7.4.1 The Higgs Boson7.4.2 QED: Electromagnetic Interactions7.4.3 Neutral Current Weak Interactions7.4.4 Charged Current Weak Interactions7.4.5 The Fermi Constant7.4.6 Gauge Boson Self-interactions7.4.7 Summary7.5 Global Symmetries and Parameters7.5.1 Accidental Symmetries7.5.2 The Interaction Basis and the Mass Basis7.5.3 Parameter Counting7.5.4 The LSM Parameters7.6 Low-Energy Tests7.6.1 Charged Current Neutrino–Electron Scattering7.6.2 Neutral Current Neutrino–Electron ScatteringProblems8 The Standard Model8.1 Defining the Standard Model8.2 The Lagrangian8.2.1 ℒkin and the Gauge Symmetry8.2.2 ℒψ8.2.3 ℒϕ and SSB8.2.4 ℒY uk8.2.5 Summary8.3 The Spectrum8.3.1 Bosons8.3.2 Fermions8.3.3 The CKM Matrix8.3.4 Summary8.4 The Interactions8.4.1 Electromagnetic (QED) and Strong (QCD) Interactions8.4.2 The Higgs Boson Interactions8.4.3 Neutral Current Weak Interactions8.4.4 Charged Current Weak Interactions8.4.5 Gauge Boson Self-interactions8.4.6 Summary8.5 Global Symmetries and Parameters8.5.1 Accidental Symmetries8.5.2 The Standard Model Parameters8.5.3 “A Standard Model” versus “the Standard Model”8.5.4 Discrete Symmetries: P, C, and CPAppendix8.A Anomalies and Nonperturbative Effects8.A.1 The Strong CP Parameter8.A.2 AnomaliesProblems9 Flavor Physics9.1 Introduction9.2 The CKM Matrix9.2.1 The Standard Parameterization9.2.2 The Wolfenstein Parameterization9.2.3 CP Violation9.2.4 Unitarity Triangles9.3 Tree-Level Determination of the CKM Parameters9.4 No FCNC at Tree Level9.4.1 Photon- and Gluon-Mediated FCNC9.4.2 Z-Mediated FCNC9.4.3 Higgs-Mediated FCNCProblems10 QCD at Low Energies10.1 Introduction10.2 Hadronic Properties10.2.1 General Properties10.2.2 The Quark Model10.2.3 Hadron Masses10.2.4 Hadron Lifetimes10.3 Combining QCD with Weak Interactions10.3.1 Factorization10.3.2 The Decay Constant10.3.3 Form Factors10.4 The Approximate Symmetries of QCD10.4.1 Isospin Symmetry10.4.2 Heavy Quark Symmetry10.5 Hadrons in High-Energy QCD10.5.1 Quark-Hadron Duality10.5.2 Jets10.5.3 PDFAppendix10.A Names and Quantum Numbers for Hadrons10.B Extracting |V ud|10.C Extracting |V cb|Problems11 Beyond the Standard Model11.1 Introduction11.2 Experimental and Observational Problems11.3 Theoretical Considerations11.4 The BSM Scale11.5 The SMEFT11.6 Examples of SMEFT Operators11.6.1 Baryon Number Violation11.6.2 Higgs DecaysProblems12 Electroweak Precision Measurements12.1 Introduction12.2 The Weak Mixing Angle12.2.1 The Weak Mixing Angle at One Loop12.2.2 The Weak Mixing Angle within the Standard Model12.3 Custodial Symmetry12.4 Probing BSM12.4.1 Nonrenormalizable Operators and the q2 Expansion12.4.2 The S, T, and U Parameters12.4.3 The Four-Generation Standard ModelProblems13 Flavor-Changing Neutral Currents13.1 Introduction13.2 CKM and GIM Suppression in FCNC Decays13.2.1 Examples: K → πνν̄ and B → πνν̄13.3 CKM and GIM Suppression in Neutral Meson Mixing13.3.1 Examples: ΔmK, ΔmB, and ΔmBs13.3.2 CP Violating Suppression13.3.3 Summary13.4 Testing the CKM Sector13.5 Probing BSM13.5.1 New Physics Contributions to B0 −B̄0 Mixing13.5.2 Probing the SMEFTAppendix13.A Neutral Meson Mixing and Oscillation13.A.1 Introduction13.A.2 Flavor Mixing13.A.3 Flavor Oscillation13.A.4 Standard Model Calculations of the Mixing Amplitude13.B CP Violation13.B.1 Notations and Formalism13.B.2 CP Violation in Decay13.B.3 CP Violation in Mixing13.B.4 CP Violation in Interference of Decays with and without Mixing13.C Standard Model Calculations of CP Violating13.C.1 Extracting γ from B → DK13.C.2 Extracting β from B → D+D−13.C.3 CP Violation from K DecaysProblems14 Neutrinos14.1 Introduction14.2 The νSM14.2.1 Defining the νSM and the Lagrangian14.2.2 The Neutrino Spectrum14.2.3 The Neutrino Interactions14.2.4 Global Symmetries and Parameters14.2.5 The PMNS Matrix14.2.6 Testing the νSM14.2.7 The Scale Λ14.3 The NSM: The Standard Model with Singlet Fermions14.3.1 Defining the NSM14.3.2 The NSM Lagrangian14.3.3 The NSM Spectrum14.3.4 The NSM Interactions14.3.5 The Low-Energy Limit of the NSM14.3.6 The Case of mN ≪ v: Sterile Neutrinos14.4 Open QuestionsAppendix14.A Neutrino Oscillations14.A.1 Neutrino Oscillations in a Vacuum14.A.2 The MSW Effect14.B Direct Probes of Neutrino Masses14.B.1 Kinematic Tests14.B.2 Neutrinoless Double-Beta (0ν2β) DecayProblems15 Cosmological Tests15.1 The Interplay of Particle Physics and Cosmology15.2 Dark Matter15.2.1 The Observational Evidence15.2.2 Neutrinos Cannot Be the Dark Matter15.2.3 The χSM15.3 Baryogenesis15.3.1 The Observational Evidence15.3.2 Sakharov Conditions15.3.3 Leptogenesis15.4 Open QuestionsAppendix15.A Introduction to Cosmology15.A.1 The Dynamical Metric15.A.2 Thermodynamics in the Universe15.A.3 ObservablesProblemsWhat’s Next?Appendix: Lie GroupsA.1 GroupsA.2 RepresentationsA.3 Lie Groups and Lie AlgebrasA.4 Roots and WeightsA.5 SU(2)A.6 SU(3)A.7 Classification and Dynkin DiagramsA.8 Naming RepresentationsA.9 Combining RepresentationsProblemsReferencesIndex