The TCP theorem

The TCP theorem, derived in different forms by several workers (Schwinger in 1953, Luders in 1954 and Pauli in 1955), states that for locally interacting fields, a Lagrangian which is invariant under proper Lorentz transformations is invariant with respect to the combined operation TCP. By the operation TCP is meant the set of operations time reversal, charge conjugation (i.e. particle-antiparticle exchange) and the parity transformation, taken in any order. The proof applies only to the combined set of operations even though the theory may not be invariant under the individual operations T, C and P.

It is an obvious consequence of the TCP theorem that if an interaction is not invariant under one of the operations it must also fail to be invariant under the product of the other two.

We have already seen that for weak decays parity is not conserved, so that if these processes are to be invariant under time reversal they cannot be invariant under charge conjugation. A number of tests have demonstrated that this is in fact the case. For instance, in the decay of muons we have already mentioned that the decay electrons are fully polarised. If charge conjugation holds, we should expect that the helicity of the positron from µ+-decay should be the same as that of the electron from µ--decay, since these two processes are the charge conjugates of each other and since the only effect of the charge conjugation operator is to interchange particle and antiparticle.

Introduction

We shall see later (chapter 10) that it is now clear that particles such as protons, neutrons and π-mesons (pions), once thought to be ‘elementary’ are, in fact, made from more basic constituents, the quarks. Thus the force between, say, two neutrons is basically the resultant of the forces between two groups, each of three quarks. In this respect it is approximately analogous to the Van der Waals force between two molecules, each of which consists of several atoms. As in the case of atomic or molecular problems, so for particles it is in many instances, however, very useful to treat the forces between particles such as nucleons rather than the forces between their constituent quarks. Although many of the ideas concerning particle interactions were developed before quarks were identified as the constituents of nucleons and mesons, these ideas are, in general, not invalidated by the discovery of the quark structure and, indeed, the subject is perhaps best understood by means of this semi-historical approach.

Prediction of the π-mesons by Yukawa

The prediction of the existence of mesons, by Yukawa in 1935, and their subsequent discovery in the cosmic radiation, present one of the most striking examples of the interaction of theory and experiment in modern physics.

We can understand Yukawa's argument in a qualitative way as follows. It had become well established that electromagnetic forces could be well understood in terms of a field of which the quanta were photons.

Particle physicists sometimes complain that there has been ‘no exciting new development since last year's conference’. The complaint is justified only because the overall pace of discovery in this field has been so great. In the past decade the pace has been maintained with the discovery of the Z and W bosons and the establishment of three as the number of light neutrinos thus most probably fixing the number of the lepton and quark generations in the Universe.

Technical achievements have included the bringing into successful operation of LEP at CERN and the Tevatron at Fermilab and the collision of microscopically tightly focussed beams at SLAC. The detectors at these accelerators are among the most sophisticated pieces of hardware ever built. The great proton decay detectors have detected no decaying protons but have opened a new window on the Universe in neutrino astronomy.

In the 1960s and much of the 1970s particle physics was primarily concerned with getting the data on which QCD and Electroweak Unification have been built. Our understanding of the fundamental structure of matter has been transformed by these achievements. Current and future work is focussed on very fundamental questions which were not even crystallised in the earlier era. There remain many challenging problems:

This book is intended for undergraduates or others coming to the subject of particle physics for the first time. For this reason the only prior knowledge assumed is of the elements of quantum theory and statistical mechanics.

The story of the development of particle physics in the years since the Second World War has been one of almost continuous excitement. Much of this has been due to an unceasing interplay of experiment and theory in the best classical tradition. Few years have passed without a remarkable advance in theory or experiment, such as the discovery of the antiproton; of the strange particles; the Gell-Mann–Nishijima scheme; parity non-conservation; the difference between electron and muon neutrinos; the strongly-decaying resonances; the SU(3) symmetry scheme and the omega particle; evidence for quarks and for gluons; neutral currents; charm and beauty; electromagnetic-weak unification; the discovery of the W and Z bosons and a good many others.

This rapid progress has been a consequence of, and a justification for, parallel progress in technology and instrumentation. In the first chapter of the book I have outlined the principal techniques used in this work. I hope that this will enable the student to understand how the many experiments referred to in later parts of the book have actually been carried out, since I believe that such an understanding is essential to a proper appreciation of the subject.

Types of interactions

In chapter 2 we have seen that the nuclear interaction is very much stronger than the electromagnetic interaction; their relative strengths are characterised by the difference in the ‘coupling constants’ which are discussed in more detail below. We may recognise at this stage two other forms of interaction, gravitational forces and the so-called ‘weak’ interaction. One of the most notable milestones of recent years has been the unification of the weak and electromagnetic interactions as different aspects of the same underlying force, in the theory of Glashow, Weinberg and Salam, and the discovery of the W and Z particles, the additional quanta of the unified interaction, with the properties predicted. This topic is treated in more detail in chapter 11.

We may summarise as follows:

Strong interactions are responsible for the interactions between nucleons, nucleons and mesons and a number of other particles. The mesons act as the quanta of the strong interaction on the nuclear scale. These interactions reflect the interaction between quarks due to the exchange of gluons on the sub-nucleon level.

Electromagnetic interactions are responsible for the force between electrically-charged particles and are mediated by the exchange of photons.

Weak interactions are responsible for many particle decays such as radioactive decay (the basic process n → p + e- + vg), pion and muon decay and a number of other decay processes.

Gravitational interactions exist between all particles having mass and are believed to be mediated by the so far undetected gravitons.

Introduction

There have always been close links between physics and astronomy and physics and cosmology. This is to be expected since astronomy and cosmology are fields of science which apply physics in an attempt to understand observations of the cosmos and to comprehend the structure, origin and evolution of the universe. Equally our understanding of physical laws and in particular their apparent universality in space and time, has in a number of instances depended crucially on astronomical data.

In the first half of the twentieth century a number of common areas of interest – relativity theory, nuclear reactions and stellar evolution, and cosmic rays, among others – provided fruitful points of contact between particle and nuclear physics on the one hand and cosmology on the other. After a period of less interaction common interests have increased dramatically over the last 10–15 years in a way which has been highly stimulating for both subjects.

Most fundamentally the development and general acceptance of the Big Bang model implies energy densities during the first instants after the Big Bang which can now be even distantly approached only in high energy particle collisions. On the other hand it is clear that no experiments we can ever do will attain the energies at which we might expect unification of all four forces including gravity (energies ∼ Planck mass ∼ 1019 GeV/c2) or even Grand Unification energies ∼ 1015 GeV, so that the only laboratory for direct study of these phenomena existed in the first instants after the Big Bang.

Introduction

The discovery of such a wealth of apparently ‘elementary’ particles stimulated new activity in the search for a pattern amongst them, as a first step towards the understanding of their nature. The discovery of such a pattern is analogous to, for instance, the discovery of the Rydberg formula in atomic spectroscopy. The Bohr atom finally provided an explanation of the formula, and we shall see that the quark model provides an explanation of the symmetry pattern of the elementary particles.

We have already become familiar with the limited symmetry of isotopic spin multiplets. In that case we grouped together particles which were the same except for properties associated with the electric charge. The degeneracy of the multiplet is removed by the symmetry-breaking Coulomb interaction. Alternatively, we can regard the members of the multiplet as states linked by rotations in isotopic spin space and we can define a group of rotation operators which enable us to step from one state to another.

The Coulomb interaction is not strong compared with the so called ‘strong’ interactions, and the symmetry breaking to which it gives rise is small. For instance, the masses of particles in the same isotopic spin multiplet differ only by at most a few per cent. In order to extend the symmetry, to group larger numbers of particles together, we must recognise the existence of much stronger symmetry breaking forces since the mass differences between, say, I-spin multiplets, are substantial, even compared with the particle masses themselves.

Introduction

An important part of the study of particle physics is an understanding of experimental tools – the accelerators, beams and detectors by means of which particles are accelerated, their trajectories controlled and their properties measured. There exist a limited number of types of accelerators and detectors in common use or which have in the past proved crucial to the progress of the subject. No more technical detail is included here than is essential to an understanding of the uses of these techniques in the study of particle physics. In the chapters which follow we shall assume that these techniques are familiar to the student, so that it will generally not be necessary to describe in detail the technique used in particular experiments.

Particle accelerators and beams

Introduction

Particle accelerators and their associated external beam lines are key elements in most particle physics experiments.

Charged particles are accelerated by passing across a region of potential difference which in practice is normally a cavity fed with radiofrequency power and phased such that the particle is accelerated as it passes through. Since practicable fields and dimensions are such that a single passage through the cavity can produce only a rather small acceleration, the particle must either pass through many such cavities or pass many times through the same group of cavities by guidance around a cyclic path.