by Paul Langacker, CRC Press. Hardback ISBN 9781420079067, £49.99 ($79.95).
The Standard Model of elementary particles and their interactions via the electromagnetic, weak and strong interactions is a fabulously successful theory. Tests of quantum electrodynamics have been made to a precision at the level of better than one part in one billion; electroweak tests approach the one part in one hundred thousand level; and even tests of quantum chromodynamics, which are intrinsically more challenging, are being made at the per cent level.
Yet, despite this, we are still sure that the Standard Model cannot be the “ultimate” theory. We have yet to account theoretically for the exciting observations of the recent decades, namely, massive neutrinos, dark matter and dark energy, which provide direct evidence for new physics processes. We cannot account for the observed patterns of the masses of the fermion building blocks of matter, their manifestation in three generations or “families”, the “mixing” between the generations, or why the universe seems to contain almost no antimatter. And we don’t yet understand how to incorporate gravity in terms of a quantum-field theory.
Theoreticians have not been idle in developing models of the new physics that could underlie the Standard Model and that ought to manifest itself at the tera-electron-volt energy scale, such as alternative spontaneous electroweak symmetry-breaking mechanisms, supersymmetry and string theories, for example. However, within the framework of the Standard Model itself, we have yet to observe the Higgs boson, the presence of which is required to account for the generation of the masses of the W and Z particles.
This substantial book – at more than 600 pages – gives a detailed and lucid summary of the theoretical foundations of the Standard Model, and possible extensions beyond it.
Chapter 1 sets up the required notations and conventions needed for the ensuing theoretical survey. Chapter 2 reviews the basics of perturbative field theory and leads, via an introduction to discrete symmetry principles, to quantum electrodynamics. Group theory, global symmetries and symmetry breaking are reviewed in Chapter 3, which forms the foundation for the presentation of local symmetries and gauge theories in Chapter 4, where the Higgs mechanism is first introduced.
The heart of the book lies in Chapters 5 (strong interactions), 6 (weak interactions) and 7 (the electroweak theory), which at more than 170 pages is the most substantial. These chapters present a clear theoretical discussion of key physical processes, along with the phenomenology required for a comparison with data, and a brief summary of the relevant experimental results. Precision tests of the Standard Model are summarized, and the framework is introduced for parametrizing the head-room for new physics effects that go beyond it.
The final chapter summarises the known deficiencies of the Standard Model and introduces the well developed extensions: supersymmetry, extended gauge groups and grand unified theories. Fortunately, now that the LHC is up and running, we should expect to start to address experimentally at least some of these theoretical speculations. LHC results will provide the sieve for filtering the profound and accurate, versus the merely beautiful and mathematically seductive, models of nature.
The book ranges over huge swathes of theoretical territory and is self-consciously broad, rather than deep, in terms of coverage. I heartily recommend it to particle physicists as a great single-volume reference, especially useful to experimentalists. It also provides a firm, graduate-level foundation for theoretical physicists who plan to pursue concepts beyond the Standard Model to a greater depth.
