This book is about the Standard Model of elementary particle physics. If we set the beginning of the modern era of particle physics in 1947, the year the pion was discovered, then the ensuing years of research have revealed the existence of a consistent, self-contained layer of reality. The energy range which defines this layer of reality extends up to several hundred GeV, or in terms of length, down to distances of order 10−16 cm. The Standard Model is a field-theoretic description of strong and electroweak interactions at these energies. It requires as input nineteen independent parameters. These parameters are not explained by the Standard Model; their presence implies the need for an understanding of Nature at an even deeper level. Nonetheless, processes described by the Standard Model possess a remarkable insulation from signals of such new physics. Although the strong interactions remain a calculational challenge, the Standard Model would appear to have sufficient content to describe all existing data. Thus far, it is a theoretical structure which has worked splendidly.

Quarks and leptons

In the Standard Model, the fundamental fermionic constitutents of matter are the quarks and the leptons. Quarks, but not leptons, engage in the strong interactions as a consequence of their color-charge. Each quark and lepton has spin one-half. Collectively, they display conventional Fermi-Dirac statistics. No attempt is made in the Standard Model either to explain the variety and number of quarks and leptons or to compute any of their properties.

A central feature of the Standard Model is the spontaneous symmetry breaking in the electroweak sector which gives mass to fermions and to the W± and Z0 gauge bosons. The sole physical remnant of this process is the Higgs boson. Although its couplings to the other particles in the theory are fully specified, the Higgs mass is undetermined. As a consequence, efforts to detect this particle cover the widest possible range of mass values [GuHKD 90, Ei 91].

Mass and couplings of the Higgs boson

Although a complex doublet of Higgs fields is initially introduced in the Weinberg–Salam model, there remains following spontaneous symmetry breaking precisely one physical Higgs state, a neutral scalar particle H0. That is, if we define the number of degrees of freedom for Higgs and gauge boson states respectively as NH and NG, then before the symmetry breaking we have NH = 4, NG = 8 whereas afterwards we find NH = 1, NG = 11. To obtain these values, recall that massive vector particles have three spin components whereas massless vector particles have just two. Although the total of Higgs and gauge-boson degrees of freedom remains fixed (NH + NG = 12), there is a transfer of three states from the Higgs sector to the gauge-boson sector. These Higgs states become the longitudinal spin modes of the W±, Z0 particles.

A gauge theory involves two kinds of particles, those which carry ‘charge’ and those which ‘mediate’ interactions between currents by coupling directly to charge. In the former class are the fundamental fermions and nonabelian gauge bosons, whereas the latter consists solely of gauge bosons, both abelian and nonabelian. The physical nature of charge depends on the specific theory. Three such kinds of charge, called color, weak isospin, and weak hypercharge, appear in the Standard Model. The values of these charges are not predicted from the gauge symmetry, but must rather be determined experimentally for each particle. The strength of coupling between a gauge boson and a particle is determined by the particle's charge, e.g. the electron-photon coupling constant is –e, whereas the u-quark and photon couple with strength 2e/3. Because nonabelian gauge bosons are both charge carriers and mediators, they undergo self-interactions. These produce substantial nonlinearities and make the solution of nonabelian gauge theories a formidable mathematical problem. Gauge symmetry does not generally determine particle masses. A fermion mass term, although violating chiral symmetry, is consistent with gauge invariance. Although gauge-boson mass would seem to be at odds with the principle of gauge symmetry, the Weinberg-Salam model contains a dynamical procedure, the Higgs mechanism, for generating mass for both gauge bosons and fermions alike.

Quantum Electrodynamics

Historically, the first of the gauge field theories was electrodynamics. Its modern version, Quantum Electrodynamics (QED), is the most thoroughly verified physical theory yet constructed.

Application of the concept of symmetry leads to some of the most powerful techniques in particle physics. The most familiar example is the use of gauge symmetry to generate the lagrangian of the Standard Model. Symmetry methods are also valuable in extracting and organizing the physical predictions of the Standard Model. Very often when dealing with hadronic physics, perturbation theory is not applicable to the calculation of quantities of physical interest. One turns in these cases to symmetries and approximate symmetries. It is impressive how successful these methods have been. Moreover, even if one could solve the theory exactly, symmetry considerations would still be needed to organize the results and to make them comprehensible. The identification of symmetries and near symmetries has been considered in Chap. I. This chapter is devoted to their further study, both in general and as applied to the Standard Model, with the intent of providing the foundation for later applications.

Symmetries of the Standard Model

The treatment of symmetry in Sects. I–4, I–6 was carried out primarily in a general context. In practice, however, we are most interested in the symmetries relevant to the Standard Model. Let us briefly list these, reserving for some a much more detailed study in later sections.

Gauge symmetries: As discussed in Chap. II, these are the SU(3)c × SU(2)L × U(1)y gauge invariances. It is interesting to compare their differing realizations.

This Chapter is devoted to the exploration of double beta decay, a remarkable rare transition between two nuclei with the same mass number, which involves a change of the nuclear charge number by two units. It has long been recognized that a particular mode of double beta decay, in which two electrons and no neutrinos are emitted, is a powerful tool for the study of lepton conservation in general, and neutrino properties in particular. The description of the neutrinoless double beta decay involves an intricate mixture of elementary particle physics and physics of the nucleus. Among the particle physics issues which we wish to address with the help of double beta decay are the questions: is the neutrino a Majorana particle and if so, what is its mass? and, is there evidence that the weak interactions contain leptonic currents with a small right-handed component? The principal nuclear physics issues have to do with the identification and evaluation of the nuclear matrix elements responsible for the decay rate. As it is our goal to arrive at a quantitative answer for the mentioned particle properties, we have no choice but to learn first how to understand the nuclear mechanisms.

Our principal concern, as everywhere in this book, is the problem of extracting information on neutrino mass from these nuclear experiments. Accordingly, we begin with Section 6.1 on the phenomenology of double beta decay and how it relates to neutrino mass. This is followed in Section 6.2 with a discussion on the nuclear physics aspects. We then proceed with a description of the experimental results in Section 6.3, both from laboratory work and from studies of geological samples.

In this Chapter we shall discuss how neutrino mass can be determined from purely kinematic considerations of weak interaction processes. For simplicity, we assume here that only one neutrino is involved in a reaction or decay, leaving the more general situation of neutrino mixing until Chapter 4. We shall explore how finite neutrino mass will affect the momenta and energies of the charged particles emitted in a weak decay, as well as the overall decay rate. A complete review of all aspects of lepton spectroscopy can be found in Bullock & Devenish (83) and in the review article by Robertson & Knapp (88).

In treating the kinematics of weak decays, we shall first focus our attention on nuclear beta decay. We shall show that beta decay is a very sensitive tool for studying the electron antineutrino mass. Near the endpoint of the beta spectrum, a massive neutrino has so little kinetic energy that it becomes nonrelativistic, with the result that the decay probability depends linearly on mass. Of particular interest here is the low energy beta decay of tritium which, as we shall see, has the potential of determining neutrino mass down to a few eV. (It is customary to give the mass in units eV as well as eV/c2.) As this is by far the most sensitive kinematic test for neutrino mass, we present in Section 2.1 a comprehensive discussion of several tritium experiments. We then turn to the muon neutrino and discuss the two-body decays of the pion into charged particles and neutrinos (Section 2.2), followed by the brief Section 2.3 on the tau neutrino mass.

In preparing this book, we have set ourselves the goal of presenting a unified picture of the physics of neutrinos as it now emerges from studies of nuclear physics, particle physics, astrophysics, and cosmology. While describing all aspects of neutrino physics, we focus strongly on what we know and hope to learn about the neutrino's mass and particle-antiparticle symmetry, as we consider these to be among the most burning questions.

As our readers we have in mind students in nuclear and particle physics at graduate level as well as researchers in these fields. The book thus may serve as a text in a specialized course, or as a supplement to a standard text in nuclear or particle physics. We have written each chapter sufficiently selfcontained that it can be read independently. To keep the length of the text within limits, we have provided each chapter with references to specialized review articles. Also, for the same reason, we have elected only to touch upon several topics that are not directly related to the problem of neutrino mass and mixing, such as neutral current interactions of neutrinos, electron neutrino scattering, and deep inelastic neutrino nucleon scattering.

Throughout, we have attempted to stress physical concepts, treating theoretical developments and experimental techniques on an equal footing, while including material up to Fall 1986. The prospect of finding massive neutrinos and its repercussions on our fundamental understanding of particles is exciting, as is the ingenuity of the experimental approaches in exploring neutrino mass.

We are grateful to Peter Rosen and Garry Steigman for reading the manuscript and for offering useful suggestions.

In this second edition we have followed the framework of the original edition, changing or expanding the text only when warranted by new developments. The field of neutrino physics itself has been expanding at a rapid pace (as witnessed by our bibliography which has increased by 50% in just four years). Among the notable advances in the intervening years let us mention the opening of neutrino astronomy with the observation of the neutrino signal of SN1987A. The next supernova in, or near, our galaxy, is eagerly awaited by a number of “supernova watch” detectors. The detection of solar neutrinos has become an important subject of neutrino physics. Four detectors are running now, and several more are being built. The suppression of the solar neutrino flux (at least at higher energies) has been confirmed, and many physicists believe that solar neutrinos will represent the first observational manifestation of the neutrino mass and mixing. Double beta decay is another topic that has expanded considerably. The twoneutrino decay has been seen in the laboratory in three nuclei, thus it has become well established. The lifetime limits and the corresponding neutrino mass limits from the neutrinoless decay are continually improving. Better understanding of the nuclear matrix elements also puts double beta decay on a firmer footing.

In the broader context of particle physics as a whole the standard electroweak model appears to describe all observable phenomena. Yet, despite its success, it must eventually be replaced by a broader theory, with fewer parameters and deeper insight. The prospect of finding massive neutrinos remains one of the main possible openings to the world “beyond the standard model”.

Neutrino physics is playing a unique role in elucidating the properties of weak interactions. But even more important, neutrino studies are capable of providing new ingredients for future theoretical descriptions of the physics of elementary particles. Although impressive progress has been made in our understanding of neutrino interactions, many important issues remain to be settled, foremost among these are the questions: have neutrinos a nonvanishing rest mass, and are neutrinos, participating in weak interaction, pure states in a quantum mechanical sense? The role of neutrino mass and its various consequences, therefore, will form the central issue throughout this text.

The study of neutrino properties, unlike the study of other elementary particles, has always crossed the traditional disciplinary boundaries. While we think of particle properties as being the domain of high energy physics, much information on neutrino properties has come from low energy nuclear physics, as well as from astrophysics and cosmology. For that reason it will be necessary to explore a number of different disciplines and techniques.

Among the many excellent reviews on weak interaction, we mention the books by Bailin (82), Commins & Bucksbaum (83), Georgi (84), Okun (82), Pietschmann (83), and Taylor (78). Since the first edition of this book several related books have appeared, Grotz & Klapdor (90), Holstein (89), and Kayser, Gibrat-Debu & Perrier (89). More specialized reviews on various aspects of neutrino physics are mentioned at the beginning of each Chapter.

This Chapter provides an introduction to the formal description of neutrinos and their properties.