The Standard Model and Beyond

The following sections are included:

• Dedication
• Preface
• Contents

In this chapter we make a very simple exposition of the elements of group theory that one needs to know in order to understand the essentials of the Standard Model (SM) of particle physics. For a more complete treatment the reader is referred to standard group theory texts, see e.g. [Vergados (2016)] and references therein.

The following sections are included:

• Preliminaries; the Klein–Gordon equation
• The Dirac equation
  • The spinors u and υ
  • Projection operators
  • Various representations of the Dirac matrices
• Interpretation of negative energy solutions
• Transformation of spinors under space inversion
• The notion of helicity
• Charge conjugation for 4-spinors
• Types of currents
  • Problems

The following sections are included:

• Brief history
• The essential ingredients of the Standard Model
• The notion of a local symmetry
• Maxwell’s equations; an example of Abelian gauge symmetry
  • Maxwell’s equations in terms of the potentials
  • Maxwell’s equations involving the electromagnetic tensor
• Non Abelian gauge transformations
  • Transformations associated with a non Abelian group
  • Some examples
• Gauge invariant Lagrangians
  • Only gauge fields
  • The Lagrangian in the presence of scalar fields
  • The Lagrangian in the presence of Fermion fields
• The form of the SM Lagrangian
  • The electroweak part
  • The strong part

The following sections are included:

• The Higgs mechanism in global gauge transformations
  • A complex scalar field
  • Two real scalar fields
  • A scalar transforming as a doublet under SU_I(2)
  • Symmetry restoration
• The Higgs mechanism in gauge theories
  • The spontaneous symmetry braking (SSB); the unitary gauge
  • How the gauge bosons acquire a mass
  • The electroweak Lagrangian after the SSB
  • Summary
• What happened to the Goldstone bosons?
• The ρ parameter
• Fundamental theorem of Higgs mechanism
• Problems

The following sections are included:

• Fermion masses
  • Hermitian mass matrices
  • Non Hermitian mass matrices; left-right similarity transformations
• The currents
  • The left handed currents
  • The right handed currents
  • Both left and right handed currents combined
  • The EM current
  • The charged currents; the KM matrix
  • The neutral currents
• The contact interaction
• Determination of the Standard Model parameters
• The vector boson self-couplings
• Summary

The following sections are included:

• Quantum chromodynamics QCD
• The color structure of the one gluon exchange potential involving quarks
• Approximations at low energies; interaction potentials between quarks
  • One gluon exchange potential in a process involving only baryons
  • One gluon exchange potential in processes involving the creation of a $q\overline{q}$ pair
  • One gluon exchange potential in processes involving meson spectra
• Low energy formalism
  • The orbital part at the quark level
  • The kinetic energy part
  • The confining potential
  • Fitting the strength of the confining potential
• Matrix elements involving two quarks
  • The confining potential
  • The one gluon exchange potential

In this chapter, using the tools previously developed, we will evaluate some quantities of phenomenological interest. Those not familiar with introductory particle physics may want to look at the appendix at the end of the book before proceeding further.

The following sections are included:

• Introduction
• The particle content of MSSM
  • Gauge particles
  • Fermions and s-fermions
  • The Higgs content
• The Higgs mechanism
• The Fermion masses
• Supersymmetry breaking
• Some remarks about the particle spectrum

The following sections are included:

• Mathematical Introduction
• The structure of the GUT SU(5)
• The particle content
  • The Fermions
  • The gauge bosons
  • The Higgs content
• The Higgs mechanism
• The gauge boson masses
• Gauge couplings
• Baryon asymmetry

In this chapter we are going to discuss recent developments in cosmology with emphasis on those aspects related to particle physics. As we will see the word, derived from the Greek word κo′σμoς, which means beautiful in the Greek view of the universe, indeed describes our current model of the universe 3000 years later.

The following sections are included:

• The elusive neutrino
• Lepton flavor conservation
• History of neutrino oscillations
• Aspects of neutrino masses and mixing
  • The Majorana neutrino mass
  • Transformation properties under C
  • The see-saw mechanism
• Neutrino oscillations in the case of two generations
• The three generation formalism
• Neutrino oscillation experiments
• The elusive absolute scale of the neutrino mass
• Neutrinos as probes
• Problems

In particle physics of special interest are groups with two elements T and E, with T² = E, where E the identity element. These are like reflection symmetries. Examples: i) space reflection (P), ii) time inversion (T), iii) charge conjugation (C) iv) A combination of any two of them v) The product of all three. We will examine these symmetries and their possible violation. We will also discuss the three historic experiments, namely parity and CP non conservation as well as the determination of the neutrino helicity.

The following sections are included:

• The natural system of units
• The Planck natural system of units
• Invariants in kinematics
• Cross sections and luminosities
  • Luminosity in fixed target experiments
  • Luminosity in colliding beam experiments
• Kinematics of particle decay
• Invariants in the scattering of two particles
• Detection of resonances
  • The signature of a resonance
  • The notion of a resonance
• Transformation properties of non invariant quantities
• Problems

The following sections are included:

• Bibliography
• Index