### Massive matters

I found the book by Mohapatra and Pal completely by chance, roaming the FSU bookstore once a few months ago. It looked like another cool hit in World Scientific physics series and I bought it. "Massive neutrinos in physics and astrophysics" fully keeps its promise. Like few other books, it keeps a very good balance between theoretical modeling and discussion of experimental and observational results.

The book begins with a slow pace introduction to early results about neutrinos, such as the presence of different flavors deduced from the observation of muon decays. One gets quickly into the four-Fermi interaction for charged and neutral currents and sees how this leads to the presence of non-renormalizable terms. The Higgs

mechanism is introduced and the authors explain very clearly why giving masses to particles through the symmetry breaking and Higgs field is a winning approach over trying to introduce by hand mass terms in the Lagrangian (the latter would be non-renormalizable while by a famous result of `t Hooft the Higgs mechanism leads to

a renormalizable theory). The compatibility between renormalization and gauge symmetries leads naturally to the problem of anomalies and to a discussion of the "trouble with gamma5" that destroys current conservation (axial anomaly). The second chapter of he book introduces the role of neutrinos in the standard model (SM) of elementary particle physics. The symmetries SU(2)xU(1) of weak interaction are

broken down to the U(1) of electromagnetism (different from the previous U(1) of hypercharge) by the Higgs mechanism which gives masses to the gauge bosons of the weak interaction while leaving the photon massless. In the standard model the neutrinos are massless particles, not by virtue of an unbroken gauge symmetry, but by an ad hoc recipe that allows for only one helicity state (the left handed version) to exist in the model. However, the observed phenomenon of neutrino oscillations (about which a great deal is said in the book) is incompatible with the original standard model with massless neutrinos. Grand unification models, as well as versions of supersymmetric models, also predict massive neutrinos The problem of the observed

smallness of neutrino masses is unexplained in the standard model.

This is the starting point for a throughout investigation of possible ways to incorporate neutrino masses, compatibly with the observations about oscillations, in (enlarged versions of) the standard model. The first issue is whether neutrinos should be modeled by Dirac or Majorana fermions. In the original standard model, being massless particles, they are just Weyl fermions and the issue does not arise.

In the massive case the distinction is roughly the following: a massive particle canot travel at light speed. Thus, it is possible to have an observed overtaking the particle. If the particle has a certain helicity (say left handed) then naturally it should appear as right handed to the boosted observer. The antiparticle is also

of the opposite helicity. In the case of a charged particle there is no way to identify the boosted version of the left handed particle with the antiparticle, as these have opposite charges. Neutrinos, however, are neutral, hence the right handed boosted version of a left handed neutrino may or may not be the same as

the antineutrino. Unlike Dirac neutrinos, Majorana neutrinos are their own antiparticles. (Weyl neutrinos move at the speed of light so they have no boosted version.) Once neutrinos are allowed to have masses, the same phenomenon that is present in quarks, known as mixing, becomes possible also for leptons and in particular for neutrinos. The mixing corresponds to the fact that the mass eigenstates are not flavor eigenstates. The two are related by a unitary matrix (the Cabibbo-Kobayashi-Maskawa matrix for quarks and the Pontecorvo-Maki-Nakagawa-Sakata matrix for neutrinos). This means that the particles can be in a superposition of the different flavors, hence that it should be possible to observe transmutations from one flavor to another. This is precisely what happens in neutrino oscillations. The first observation was the "solar neutrino puzzle" by which the number of observed electron type neutrinos emitted by the sun would fall short of the expected theoretical value deduced from models of stellar physics. Effectively, a percentage of the neutrinos emitted by the sun change their flavor before reaching the

earth. Chapter 6 discusses in detail models and experiments about solar neutrino detection and counting. Starting with Chapter 7, several possible extensions of the standard model that include neutrino masses are discussed in detail. Models with enlarged fermion sector, typically with Dirac neutrinos, have the problem of introducing too many new free parameters in the model, which limit its predictive value. Models with Majorana neutrinos and SU(2)xU(1) gauge symmetries are preferable in as they have a see-saw mechanism that accounts for the smallness of the masses of the observed neutrinos. Models with expanded Higgs sector are also considered and in particular the left-right symmetric case with SU(2)xSU(2)xU(1) symmetries (with SU(2) left and right). The book also discusses models with neutrino masses that come from extensions of the standard model either to grand unified theories SU(5), SO(10) and

E6 as well as from supersymmetric extensions. Regardless of the model adopted, an ineresting phenomenon is the fact that, unlike the mixing matrix for the quarks, where the mixing angles are small, the mixing for neutrinos presents large angles (for instance from the observation of solar neutrinos). This leads to interesting models based on maximal mixing and to the possibility of relations between the CKM and the PMNS matrices (quark-lepton complementarity). A lot of interesting phenomenology of neutrino physics is discussed in Chapters 12-16. After a discussion of concrete possible direct or indirect experimental tests of neutrino masses such as beta and pion decay, and tests aimed at checking the Dirac/Majorana property, the authors discuss the phenomenon of electromagnetic properties of neutrinos. Although neutrinos are not charged particles, hence they do not undergo electromagnetic interactions, they can still acquire an anomalous magnetic momentum from the quantum corrections at one or two loops in the quantum field theory. Chapter 17 is dedicated to results from the observation of neutrinos emitted from supernovae, and in particular the results of the observation of the famous supernova SN1987A.

Chapter 18 is dedicated to cosmological aspects of neutrino physics. The bound on the number of species based on He abundance, the main hypotheses on role of neutrinos in the dark matter problem and galaxy formation, as well as the problem of matter/antimatter asymmetry (eg Sakharov's approach) are discussed in detail. The final chapter considers the hypothesis of the simultaneous presence of sterile neutrinos, a different form of neutrinos that truly do not interact with ordinary

matter. All along the authors manage to maintain an excellent balance between theory and discussion of experimental results. The exposition is excellent, coincise and of great clarity. A very highly recommended reading if you want to get a feeling for what is hot in particle physics and for the intricate interplay between astrophysics, cosmology, quantum field theory and gauge theory. Read it! You won't be disappointed.