In the eight years since the first edition, the Standard Model has not been seriously discredited as a description of particle physics in the energy region (<2 TeV) so far explored. The principal discovery in particle physics since the first edition is that neutrinos carry mass. In this new edition we have added chapters that extend the formalism of the Standard Model to include neutrino fields with mass, and we consider also the possibility that neutrinos are Majorana particles rather than Dirac particles.

The Large Hadron Collider (LHC) is now under construction at CERN. It is expected that, at the energies that will become available for experiments at the LHC (∼20 TeV), the physics of the Higgs field will be elucidated, and we shall begin to see ‘physics beyond the Standard Model’. Data from the ‘B factories’ will continue to accumulate and give greater understanding of CP violation. We are confident that interest in the Standard Model will be maintained for some time into the future.

Cambridge University Press have again been most helpful. We thank Miss V. K. Johnson for secretarial assistance. We are grateful to Professor Dr J. G. Körner for his corrections to the first edition, and to Professor C. Davies for her helpful correspondence.

Reductionism complete?

The Standard Model, extended to include neutrinos carrying mass, gives a remarkably successful account of the experimental data of particle physics obtained up to 2006. Any subsequent theory must, in some sense, correspond to the Standard Model in the energy range that has so far been explored.

Many questions remain to be answered. Why is there the internal electroweak and strong group structure U(1) × SU(2) × SU(3), with the three coupling constants g1, g2, g3? Is the origin of mass really to be found in the Higgs field with its two parameters: the Higgs mass and the expectation value of the Higgs field? In the electroweak sector, why are the masses of the charged leptons as they are? There are three parameters here. Another set of parameters comes with allowing neutrinos to have mass: three neutrino masses and four parameters of the mass mixing matrix (or six if it appears that neutrinos correspond to Majorana fields rather than Dirac fields). In the quark sector ten more parameters are introduced: six quark masses, and four parameters in the Kobayashi–Maskawa matrix.

Are these twenty five or twenty six parameters really independent?

Some of these questions may be answered when experimentalists have the LHC (Large Hadron Collider) at CERN, probing to higher energies and thereby to smaller distances to make progress into finding common origins of what are now diverse elements of the Standard Model.

Introduction

It is more than a century since the discovery by J. J. Thomson of the electron. The electron is still thought to be a structureless point particle, and one of the elementary particles of Nature. Other particles that were subsequently discovered and at first thought to be elementary, like the proton and the neutron, have since been found to have a complex structure.

What then are the ultimate constituents of matter? How are they categorised? How do they interact with each other? What, indeed, should we ask of a mathematical theory of elementary particles? Since the discovery of the electron, and more particularly in the last sixty years, there has been an immense amount of experimental and theoretical effort to determine answers to these questions. The present Standard Model of particle physics stems from that effort.

The Standard Model asserts that the material in the Universe is made up of elementary fermions interacting through fields, of which they are the sources. The particles associated with the interaction fields are bosons.

Four types of interaction field, set out in Table 1.1., have been distinguished in Nature. On the scales of particle physics, gravitational forces are insignificant. The Standard Model excludes from consideration the gravitational field. The quanta of the electromagnetic interaction field between electrically charged fermions are the massless photons. The quanta of the weak interaction fields between fermions are the charged W+ and W− bosons and the neutral Z boson, discovered at CERN in 1983.

The ‘Standard Model’ of particle physics is the result of an immense experimental and inspired theoretical effort, spanning more than fifty years. This book is intended as a concise but accessible introduction to the elegant theoretical edifice of the Standard Model. With the planned construction of the Large Hadron Collider at CERN now agreed, the Standard Model will continue to be a vital and active subject.

The beauty and basic simplicity of the theory can be appreciated at a certain ‘classical’ level, treating the boson fields as true classical fields and the fermion fields as completely anticommuting. To make contact with experiment the theory must be quantised. Many of the calculations of the consequences of the theory are made in quantum perturbation theory. Those we present are for the most part to the lowest order of perturbation theory only, and do not have to be renormalised. Our account of renormalisation in Chapter 8 is descriptive, as is also our final Chapter 19 on the anomalies that are generated upon quantisation.

A full appreciation of the success and significance of the Standard Model requires an intimate knowledge of particle physics that goes far beyond what is usually taught in undergraduate courses, and cannot be conveyed in a short introduction. However, we attempt to give an overview of the intellectual achievement represented by the Model, and something of the excitement of its successes. In Chapter 1 we give a brief résumé of the physics of particles as it is qualitatively understood today.