1st Edition

# An Introduction to Particle Physics and the Standard Model

**Also available as eBook on:**

**An Introduction to the Standard Model of Particle Physics** familiarizes readers with what is considered tested and accepted and in so doing, gives them a grounding in particle physics in general. Whenever possible, Dr. Mann takes an historical approach showing how the model is linked to the physics that most of us have learned in less challenging areas. Dr. Mann reviews special relativity and classical mechanics, symmetries, conservation laws, and particle classification; then working from the tested paradigm of the model itself, he:

- Describes the Standard Model in terms of its electromagnetic, strong, and weak components
- Explores the experimental tools and methods of particle physics
- Introduces Feynman diagrams, wave equations, and gauge invariance, building up to the theory of Quantum Electrodynamics
- Describes the theories of the Strong and Electroweak interactions
- Uncovers frontier areas and explores what might lie beyond our current concepts of the subatomic world

Those who work through the material will develop a solid command of the basics of particle physics. The book does require a knowledge of special relativity, quantum mechanics, and electromagnetism, but most importantly it requires a hunger to understand at the most fundamental level: why things exist and how it is that anything happens. This book will prepare students and others for further study, but most importantly it will prepare them to open their minds to the mysteries that lie ahead. Ultimately, the Large Hadron Collider may prove the model correct, helping so many realize their greatest dreams … or it might poke holes in the model, leaving us to wonder an even more exciting possibility: that the answers lie in possibilities so unique that we have not even dreamt of them.

**Preface **

**Acknowledgements **

**Further Reading **

**Introduction and Overview **

Methods of Study

Overview

The Standard Model

Questions

**A Review of Special Relativity**

Basic Review of Relativity

Spacetime Structure

Momentum and Energy

Collisions

Questions

**Symmetries **

Groups

Lie Groups

Algebras

The Rotation Group SO(3)

Appendix: Lie Algebras from Lie Groups

Questions

**Conservation Laws**

The Action Principle

Noether's Theorem

Spacetime Symmetries and their Noether currents

Symmetries and Quantum Mechanics

Summary

Questions

**Particle Classfication**

General Considerations

Basic Classfication

Spectroscopic Notation

Adding Angular Momenta

Questions

**Discrete Symmetries**

Parity

Time-reversal

Charge Conjugation

Positronium

The CPT Theorem

Questions

**Accelerators**

DC Voltage Machines

Linacs

Synchrotrons

Colliders

The Future of Accelerators

Questions

**Detectors**

Energy Transfer and Deposition

Detector Types

Modern Collider Detectors

Questions

**Scattering **

Lifetimes

Resonances

Cross Sections

Matrix Elements

2-body Formulae

Detailed Balance Revisited

Questions

**A Toy Theory**

Feynman Rules

*A*-Decay

Scattering in the Toy Theory

Higher-order Diagrams

Appendix: n-dimensional integration

Questions

**Wave Equations for Elementary Particles **

Klein-Gordon Equation

Dirac Equation

Physical Interpretation

Antiparticles

Appendix: The Lorentz Group and its Representations

Questions

**Gauge Invariance **

Solutions to the Dirac Equation

Conserved Current

The Gauge Principle

The Maxwell-Dirac Equations

The Wavefunction of the Photon

Questions

**Quantum Electrodynamics **

Feynman Rules for QED

Examples

Obtaining Cross Sections

Appendix: Mathematical Tools for QED

Questions

**Testing QED**

Basic Features of QED Scattering

Major Tests of QED

Questions

**From Nuclei to Quarks **

Range of the Nuclear Force

Isospin

Strangeness

Flavor

Color

Questions

**The Quark Model**

Baryons

Mesons

Mass Relations

Magnetic Moments

Questions

**Testing the Quark Model **

Vector-Meson Decay

Hadron Production

Elastic Scattering of Electrons and Protons

Deep Inelastic Scattering

Quark Model Predictions

Quark Structure Functions

Questions

**Heavy Quarks and QCD**

Charm

Bottom

Top

QCD

Appendix: QCD and Yang-Mills Theory

Questions

**From Beta Decay to Weak Interactions**

Fermi's Theory of Beta-Decay

Neutrino Properties

Kaon Oscillation

Questions

**Charged Leptonic Weak Interactions **

Neutrino-Electron Scattering

Muon Decay

Appendix: Mathematical Tools for Weak Interactions

Appendix: 3-body phase space decay

Questions

**Charged Weak Interactions of Quarks and Leptons**

Neutron Decay

Pion Decay

Quark and Lepton Vertices

The GIM Mechanism

The CKM Matrix

Questions

**Electroweak Unfication**

Neutral Currents

Electroweak Neutral Scattering Processes

The SU(2) _ U(1) Model

Questions

**Electroweak Symmetry Breaking**

The Higgs Mechanism

Breaking the SU(2) Symmetry

Fermion Masses

Appendix: Feynman Rules for Electroweak Theory

Questions

**Testing Electroweak Theory**

Discovery of the W and Z bosons

Lepton Universality and Running Coupling

The Search for the Higgs

Questions

**Beyond the Standard Model**

Neutrino Oscillation

Neutrino Experiments

Neutrino Masses and Mixing Angles

Axions and the Neutron Electric Dipole Moment

Frontiers

Summing Up

Questions

**Notation and Conventions**

Natural Units

Relativistic Notation

Greek Alphabet

**Kronecker Delta and Levi-Civita Symbols **

Kronecker Delta

Levi-Civita Symbol

**Dirac Delta-Functions**

**Pauli and Dirac Matrices**

Pauli Matrices

Dirac Matrices

Identities and Trace Theorems

**Cross-Sections and Decay Rates**

Decays

Cross-Sections

**Clebsch-Gordon Coefficients**

**Fundamental Constants **

**Properties of Elementary Particles**

**Feynman Rules for the Standard Model **

**The Large Hadron Rap **

### Biography

Robert Mann

… thoroughly recommended for a final-year specialist or first-year postgraduate study level especially for those engaged in experimental high energy physics research. The author has performed an excellent service in making accessible the language and results of field theory applied to elementary particle physics.

—John J. Quenby,Contemporary Physics, 52, 2011The first chapter shows how clearly the author can write and even though the subject matter gets more complex through the book, the clarity continues. … giv[es] readers greater insights into how the maths and the reality match (or don’t match!) and hopefully exciting them into further consideration of what may be ‘hidden behind the curtain’. … while most of the book is limited to final year and postgraduate students, the first and last chapters of the book should be accessible to any interested reader wanting to understand the present knowledge and future directions of particle physics. The author has intended the book to be used as a course of study … he has used the material himself in this way with success for two decades. … Every chapter ends with … well thought out, relevant questions …

—Jack McArdle,Reviews, Volume 11, Issue 1, 2010