The Standard Model: From Fundamental Symmetries to Experimental Tests

Yuval Grossman and Yossi Nir

An authoritative, hands-on introduction to the foundational theory and experimental tests of particle physics

Hardcover

Sale Price:: $49.00/£40.60
Price:: ~~$70.00~~/~~£58.00~~
ISBN:
Published:: Sep 26, 2023
Copyright:: 2023
Illus:: 16 b/w illus.

ebook

Sale Price:: $49.00/£40.60
Price:: ~~$70.00~~/~~£58.00~~
ISBN:
Published:: Sep 26, 2023
Copyright:: 2023
Illus:: 16 b/w illus.

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The Standard Model is an elegant and extremely successful theory that formulates the laws of fundamental interactions among elementary particles. This incisive textbook introduces students to the physics of the Standard Model while providing an essential overview of modern particle physics, with a unique emphasis on symmetry principles as the starting point for constructing models. The Standard Model equips students with an in-depth understanding of this impressively predictive theory and an appreciation of its beauty, and prepares them to interpret future experimental results.

Describes symmetry principles of growing complexity, including Abelian symmetries and their application in QED, the theory of electromagnetic interactions, non-Abelian symmetries and their application in QCD, the theory of strong interactions, and spontaneously broken symmetries and their application in the theory of weak interactions
Derives the Lagrangian that implements these symmetry principles and extracts the phenomenology that follows from it, such as elementary particles and accidental symmetries
Explains how the Standard Model has been experimentally tested, emphasizing electroweak precision measurements, flavor-changing neutral current processes, neutrino oscillations, and cosmology
Demonstrates how to extend the model to address experimental and observational puzzles, such as neutrino masses, dark matter, and the baryon asymmetry of the universe
Features a wealth of problems drawing from the latest research
Ideal for a one-semester graduate course and an invaluable resource for practitioners
Online solutions manual (available only to instructors)

Preface
1 Lagrangians
- 1.1 Introduction
- 1.2 Examples of Simple Lagrangians
  - 1.2.1 Scalars
  - 1.2.2 Fermions
  - 1.2.3 Fermions and Scalars
- 1.3 Symmetries
- 1.4 Model Building
- Appendix
- 1.A Discrete Spacetime Symmetries: C, P, and T
  - 1.A.1 C and P
  - 1.A.2 CP Violation and Complex Couplings
- Problems
2 Abelian Symmetries
- 2.1 Global Symmetries
  - 2.1.1 Global Discrete Symmetries
  - 2.1.2 Global Continuous Symmetries
  - 2.1.3 Charge
  - 2.1.4 Product Groups and Accidental Symmetries
  - 2.1.5 Symmetries and Fermion Masses
- 2.2 Local Symmetries
  - 2.2.1 Introducing Local Symmetries
  - 2.2.2 Charge
- 2.3 Summary
- Problems
3 QED
- 3.1 QED with One Fermion
  - 3.1.1 Deﬁning QED
  - 3.1.2 The Lagrangian
  - 3.1.3 The Spectrum
  - 3.1.4 The Interactions
  - 3.1.5 Parameter Counting
- 3.2 QED with More Fermions
  - 3.2.1 Two Dirac Fermions
  - 3.2.2 Accidental Symmetries
  - 3.2.3 Even More Fields
- 3.3 Experimental Tests of QED
- Problems
4 Non-Abelian Symmetries
- 4.1 Introduction
- 4.2 Global Symmetries
  - 4.2.1 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 Symmetries
- 4.4 Running Coupling Constants
- 4.5 Summary
- Problems
5 QCD
- 5.1 Deﬁning QCD
- 5.2 The Lagrangian
- 5.3 The Spectrum
- 5.4 The Interactions
- 5.5 The Parameters
- 5.6 Conﬁnement
- 5.7 Accidental Symmetries
- 5.8 Combining QCD with QED
- Problems
6 Spontaneous Symmetry Breaking
- 6.1 Introduction
- 6.2 Global Discrete Symmetries: Z2
- 6.3 Global Abelian Continuous Symmetries: U(1)
- 6.4 Global Non-Abelian Continuous Symmetries: SO(3)
- 6.5 Fermion Masses
- 6.6 Local Symmetries: The Higgs Mechanism
- 6.7 Summary
- Problems
7 The Leptonic Standard Model
- 7.1 Deﬁning the LSM
- 7.2 The Lagrangian
  - 7.2.1 ℒkin and the Gauge Symmetry
  - 7.2.2 ℒψ
  - 7.2.3 ℒY uk
  - 7.2.4 ℒϕ and SSB
  - 7.2.5 Summary
- 7.3 The Spectrum
  - 7.3.1 Scalars: Back to ℒϕ
  - 7.3.2 Vector Bosons: Back to ℒkin(ϕ)
  - 7.3.3 Fermions: Back to ℒY uk
  - 7.3.4 Summary
- 7.4 The Interactions
  - 7.4.1 The Higgs Boson
  - 7.4.2 QED: Electromagnetic Interactions
  - 7.4.3 Neutral Current Weak Interactions
  - 7.4.4 Charged Current Weak Interactions
  - 7.4.5 The Fermi Constant
  - 7.4.6 Gauge Boson Self-interactions
  - 7.4.7 Summary
- 7.5 Global Symmetries and Parameters
  - 7.5.1 Accidental Symmetries
  - 7.5.2 The Interaction Basis and the Mass Basis
  - 7.5.3 Parameter Counting
  - 7.5.4 The LSM Parameters
- 7.6 Low-Energy Tests
  - 7.6.1 Charged Current Neutrino–Electron Scattering
  - 7.6.2 Neutral Current Neutrino–Electron Scattering
- Problems
8 The Standard Model
- 8.1 Deﬁning the Standard Model
- 8.2 The Lagrangian
  - 8.2.1 ℒkin and the Gauge Symmetry
  - 8.2.2 ℒψ
  - 8.2.3 ℒϕ and SSB
  - 8.2.4 ℒY uk
  - 8.2.5 Summary
- 8.3 The Spectrum
  - 8.3.1 Bosons
  - 8.3.2 Fermions
  - 8.3.3 The CKM Matrix
  - 8.3.4 Summary
- 8.4 The Interactions
  - 8.4.1 Electromagnetic (QED) and Strong (QCD) Interactions
  - 8.4.2 The Higgs Boson Interactions
  - 8.4.3 Neutral Current Weak Interactions
  - 8.4.4 Charged Current Weak Interactions
  - 8.4.5 Gauge Boson Self-interactions
  - 8.4.6 Summary
- 8.5 Global Symmetries and Parameters
  - 8.5.1 Accidental Symmetries
  - 8.5.2 The Standard Model Parameters
  - 8.5.3 “A Standard Model” versus “the Standard Model”
  - 8.5.4 Discrete Symmetries: P, C, and CP
- Appendix
- 8.A Anomalies and Nonperturbative Eﬀects
  - 8.A.1 The Strong CP Parameter
  - 8.A.2 Anomalies
- Problems
9 Flavor Physics
- 9.1 Introduction
- 9.2 The CKM Matrix
  - 9.2.1 The Standard Parameterization
  - 9.2.2 The Wolfenstein Parameterization
  - 9.2.3 CP Violation
  - 9.2.4 Unitarity Triangles
- 9.3 Tree-Level Determination of the CKM Parameters
- 9.4 No FCNC at Tree Level
  - 9.4.1 Photon- and Gluon-Mediated FCNC
  - 9.4.2 Z-Mediated FCNC
  - 9.4.3 Higgs-Mediated FCNC
- Problems
10 QCD at Low Energies
- 10.1 Introduction
- 10.2 Hadronic Properties
  - 10.2.1 General Properties
  - 10.2.2 The Quark Model
  - 10.2.3 Hadron Masses
  - 10.2.4 Hadron Lifetimes
- 10.3 Combining QCD with Weak Interactions
  - 10.3.1 Factorization
  - 10.3.2 The Decay Constant
  - 10.3.3 Form Factors
- 10.4 The Approximate Symmetries of QCD
  - 10.4.1 Isospin Symmetry
  - 10.4.2 Heavy Quark Symmetry
- 10.5 Hadrons in High-Energy QCD
  - 10.5.1 Quark-Hadron Duality
  - 10.5.2 Jets
  - 10.5.3 PDF
- Appendix
- 10.A Names and Quantum Numbers for Hadrons
- 10.B Extracting |V ud|
- 10.C Extracting |V cb|
- Problems
11 Beyond the Standard Model
- 11.1 Introduction
- 11.2 Experimental and Observational Problems
- 11.3 Theoretical Considerations
- 11.4 The BSM Scale
- 11.5 The SMEFT
- 11.6 Examples of SMEFT Operators
  - 11.6.1 Baryon Number Violation
  - 11.6.2 Higgs Decays
- Problems
12 Electroweak Precision Measurements
- 12.1 Introduction
- 12.2 The Weak Mixing Angle
  - 12.2.1 The Weak Mixing Angle at One Loop
  - 12.2.2 The Weak Mixing Angle within the Standard Model
- 12.3 Custodial Symmetry
- 12.4 Probing BSM
  - 12.4.1 Nonrenormalizable Operators and the q2 Expansion
  - 12.4.2 The S, T, and U Parameters
  - 12.4.3 The Four-Generation Standard Model
- Problems
13 Flavor-Changing Neutral Currents
- 13.1 Introduction
- 13.2 CKM and GIM Suppression in FCNC Decays
  - 13.2.1 Examples: K → πνν̄ and B → πνν̄
- 13.3 CKM and GIM Suppression in Neutral Meson Mixing
  - 13.3.1 Examples: ΔmK, ΔmB, and ΔmBs
  - 13.3.2 CP Violating Suppression
  - 13.3.3 Summary
- 13.4 Testing the CKM Sector
- 13.5 Probing BSM
  - 13.5.1 New Physics Contributions to B0 −B̄0 Mixing
  - 13.5.2 Probing the SMEFT
- Appendix
- 13.A Neutral Meson Mixing and Oscillation
  - 13.A.1 Introduction
  - 13.A.2 Flavor Mixing
  - 13.A.3 Flavor Oscillation
  - 13.A.4 Standard Model Calculations of the Mixing Amplitude
- 13.B CP Violation
  - 13.B.1 Notations and Formalism
  - 13.B.2 CP Violation in Decay
  - 13.B.3 CP Violation in Mixing
  - 13.B.4 CP Violation in Interference of Decays with and without Mixing
- 13.C Standard Model Calculations of CP Violating
  - 13.C.1 Extracting γ from B → DK
  - 13.C.2 Extracting β from B → D+D−
  - 13.C.3 CP Violation from K Decays
- Problems
14 Neutrinos
- 14.1 Introduction
- 14.2 The νSM
  - 14.2.1 Deﬁning the νSM and the Lagrangian
  - 14.2.2 The Neutrino Spectrum
  - 14.2.3 The Neutrino Interactions
  - 14.2.4 Global Symmetries and Parameters
  - 14.2.5 The PMNS Matrix
  - 14.2.6 Testing the νSM
  - 14.2.7 The Scale Λ
- 14.3 The NSM: The Standard Model with Singlet Fermions
  - 14.3.1 Deﬁning the NSM
  - 14.3.2 The NSM Lagrangian
  - 14.3.3 The NSM Spectrum
  - 14.3.4 The NSM Interactions
  - 14.3.5 The Low-Energy Limit of the NSM
  - 14.3.6 The Case of mN ≪ v: Sterile Neutrinos
- 14.4 Open Questions
- Appendix
- 14.A Neutrino Oscillations
  - 14.A.1 Neutrino Oscillations in a Vacuum
  - 14.A.2 The MSW Eﬀect
- 14.B Direct Probes of Neutrino Masses
  - 14.B.1 Kinematic Tests
  - 14.B.2 Neutrinoless Double-Beta (0ν2β) Decay
- Problems
15 Cosmological Tests
- 15.1 The Interplay of Particle Physics and Cosmology
- 15.2 Dark Matter
  - 15.2.1 The Observational Evidence
  - 15.2.2 Neutrinos Cannot Be the Dark Matter
  - 15.2.3 The χSM
- 15.3 Baryogenesis
  - 15.3.1 The Observational Evidence
  - 15.3.2 Sakharov Conditions
  - 15.3.3 Leptogenesis
- 15.4 Open Questions
- Appendix
- 15.A Introduction to Cosmology
  - 15.A.1 The Dynamical Metric
  - 15.A.2 Thermodynamics in the Universe
  - 15.A.3 Observables
- Problems
What’s Next?
Appendix: Lie Groups
- A.1 Groups
- A.2 Representations
- A.3 Lie Groups and Lie Algebras
- A.4 Roots and Weights
- A.5 SU(2)
- A.6 SU(3)
- A.7 Classiﬁcation and Dynkin Diagrams
- A.8 Naming Representations
- A.9 Combining Representations
- Problems
References
Index

“Grossman and Nir present an original approach to the Standard Model, proceeding step-by-step with an emphasis on symmetries. The language is very clear and the scholarship is of a high level, and there are many modern and engaging problems.”—Elisabetta Gallo, University of Hamburg

“Grossman and Nir build the Standard Model from the input of the various symmetry representations of its constituent fields and investigate the testable physical consequences. They are experts in the phenomenology of the Standard Model and their many years of experience come through clearly in their intuitive explanations for many phenomena.”—Yonatan Kahn, University of Illinois, Urbana-Champaign

“This concise and up-to-date textbook will successfully bring students from a simple and formal understanding of quantum field theory and put them in a great position to begin making calculations useful for our field. The Standard Model absolutely fills an important gap.”—Christopher Mauger, University of Pennsylvania

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