Preface

CP violation is an intriguing, elusive subject and our current knowledge of it is rather limited, both at the experimental and theoretical levels. On the one hand, CP violation has only been observed in the neutral-kaon system; on the other hand, in that system CP violation is very solidly established. From the theoretical standpoint, CP violation can be incorporated in the three-generation standard model (SM), which easily leads to the right order of magnitude for that effect, after one takes into account the experimental values for the quark mixing angles. However, we lack a fundamental understanding of the origin of CP violation. This is all the more important, because CP violation is one of the crucial ingredients necessary to generate the observed matter-antimatter asymmetry of the Universe. It is now believed that it is not possible to generate a baryon asymmetry of the observed size exclusively with the CP violation present in the SM. New sources of CP violation in models beyond the SM can play an important role in the explanation of the observed size of this asymmetry.

In spite of the importance of the phenomenon of CP violation, at present there is no self-contained textbook on the subject, covering both its phenomenological and theoretical aspects. It is this lack that we have aimed at eliminating. We have tried to write a text which, starting from basic and well known concepts, can lead graduate students and professional physicists alike into a reasonable understanding of the intricacies of CP violation. We have been particularly keen about adopting a consistent notation, and about self-containedness: we only assume knowledge of ordinary quantum mechanics, in the first part of the book, and of the standard model of electroweak interactions, from the second part onwards. We have also not hesitated in providing a detailed derivation of many results which remain poorly or only superficially explained in the literature.

The book is divided in four parts, aiming at an increasingly specialized group of readers. Most of the topics in the first two parts of the book might be included in a standard particle-physics course discussing electroweak interactions. The intended readership for the first part is very broad, including any student or physicist wishing to learn the basics of CP violation; this part is accessible to anyone familiar with ordinary quantum mechanics, and only little knowledge of particle physics and field theory is assumed. We explain what CP violation is and what are its basic observed features. Special emphasis is given to the phenomenology of CP violation in neutral-meson systems, considering the specific cases of the neutral kaons and neutral-B mesons and the approximations relevant for each of them. We discuss various ways to measure CP violation, especially in the neutral-B systems. Throughout, we use quantities which are invariant under arbritary rephasings of the state vectors, using that property to identify the physical, measurable quantities.

Part II deals with the Kobayashi–Maskawa mechanism of CP violation in the SM. The readers are assumed to have some familiarity with gauge theories in general and the SM in particular. We study the unitarity triangles and their relevance for CP violation, describe various parametrizations of the Cabibbo–Kobayashi–Maskawa matrix, and discuss the experimental constraints on that matrix; we then review the computation of the CP-violating parameters $ϵ$ and $ϵ′/ϵ$⁠, being careful to present the analysis in such a way that it can easily incorporate new experimental data.

The third and fourth parts are narrower in scope. Part III is devoted to the model-building subtleties related to CP violation, and to various possible CP-violation mechanisms. Specific models are considered, the intention being to illustrate particular mechanisms of CP violation within minimal extensions of the SM. Thus, each model should be taken as representative of a whole set of possibilities. We work out models with, in turn, an extended scalar sector, fermion sector, and gauge sector. We also discuss the strong CP problem and describe some of its possible solutions.

We repeatedly emphasize the fact that CP violation arises as a clash between the CP-transformation properties of different terms in the Lagrangian. Although CP violation is due to the presence of complex phases in field theory, physical CP-violating quantities should not depend on the particular basis that one chooses to work in. This philosophy naturally leads to the construction of weak-basis-invariant CP-violating quantities; those quantities automatically eliminate the spurious phases which may always be brought in and out of the Lagrangian by means of rephasings of the fundamental fields.

It is generally believed that a deeper understanding of CP violation will require its experimental observation outside the neutral-kaon complex. This lacuna will be partially filled by the upcoming experimental studies at B factories; various tests of the SM, and the corresponding searches for new physics, will be conducted at those machines. These exciting prospects have provided further motivation for writing this book, which we hope will prove to be a timely publication. Thus, Part IV is specifically dedicated to the possibilities for the study of CP violation, in particular through the observation of CP asymmetries, at B factories. Our analysis is mostly model-independent, and we try to distinguish between theoretical expectations and the actual measuring capabilities.

It is not possible to cover all aspects of CP violation in a book of this size and, of course, our experience and interests have influenced the choice of topics. Three important subjects which are not dealt with in this book are electric dipole moments, baryogenesis, and supersymmetric models. These are very specialized areas of research which would require considerable space for a thorough and pedagogical introduction. However, the new sources of CP violation which arise in models beyond the SM, presented in detail in Chapters 22–26, will have an impact on baryogenesis. Furthermore, the techniques introduced in those chapters can be readily extended to the case of supersymmetric models. We may refer the interested reader to the existing monographs on baryogenesis (Cohen et al. 1993; Turok 1993; Rubakov and Shaposhnikov 1996; Trodden 1998) and on electric dipole moments (Khriplovich and Lamoreaux 1997).

There are many chapters and sections in the book which, having been included for the sake of completeness, may be skipped without undue loss of continuity or understanding. We have marked those chapters and sections with an asterisk in the Contents, and we have usually also called attention to this fact in the beginning of the chapter or section.

Whenever using experimental data, we have used the values given in the 1996 edition of the Review of Particle Properties (Particle Data Group 1996). The 1998 edition (Particle Data Group 1998) was not used because it appeared only shortly before completion of the manuscript; moreover, the physics in this book does not rely heavily on any precise experimental values.

In our bibliography we have made an effort to cite the original relevant literature on each topic which appeared up to the summer of 1998. But, in a field which evolves as rapidly as CP violation, it is impossible to keep track of all the relevant articles in the literature. The fact that many topics have been studied for a long time only makes things worse. We apologize for any omissions, which should not be interpreted as reflecting any negative opinion on our part.

Lisbon, Portugal

November 1998

G. C. Branco

L. Lavoura

J. P. Silva