This book is mainly meant to be a presentation of subnuclear physics, at an introductory level, for undergraduate physics students, not necessarily for those specialising in the field. The reader is assumed to have already taken, at an introductory level, nuclear physics, special relativity and quantum mechanics, including the Dirac equation. Knowledge of angular momentum, its composition rules and the underlying group theoretical concepts is also assumed at a working level. No prior knowledge of elementary particles or of quantum field theories is assumed.

The Standard Model is the theory of the fundamental constituents of matter and of the fundamental interactions (excluding gravitation). A deep understanding of the ‘gauge’ quantum field theories that are the theoretical building blocks of this model requires skills that the readers are not assumed to have. However, I believe it to be possible to convey the basic physics elements and their beauty even at an elementary level. ‘ Elementary’ means that only knowledge of elementary concepts (in relativistic quantum mechanics) is assumed. However it does not mean a superficial discussion. In particular, I have tried not to cut corners and I have avoided hiding difficulties, whenever was the case. I have included only well established elements with the exception of the final chapter, in which I survey the main challenges of the present experimental frontier.

The text is designed to contain the material that may be accommodated in a typical undergraduate course. This condition forces the author to hard, and sometimes difficult, choices.

The Standard Model describes the word at elementary level with a few elements, three families of spin 1/2 fermions – the quarks and the leptons – the vector bosons mediators of the strong and electro-weak interactions – one photon, three weak bosons and eight gluons – and one scalar boson – the H at the origin of the vector bosons and elementary fermion masses. In this book we have been faithful to the rule of sticking to the facts, namely to experimentally confirmed theoretical statements. Let us just mention in passing that from time to time experiments report ‘evidence’ of violations of the Standard Model predictions, which, however, are not statistically significant. Indeed, misleading fluctuations of the background can always happen. Consequently, as a rule of thumb, nothing at less than 3 or 4 standard deviations should be considered as evidence.

All of that is not enough and we know that the Standard Model cannot be the final theory, because of the observation of facts that the Model is not able to explain and also for ‘aesthetic’ reasons. We shall briefly mention these problems.

Neutrino mass

As we discussed in Chapter 10, physics beyond the Standard Model has been firmly established with neutrino oscillations and flavour change. A possible way to extend the Standard Model mechanism to give mass to neutrinos is by assuming the existence of right neutrinos, as for the other leptons.

The non-stable particles we have discussed up to now decay by weak or electromagnetic interactions. The distance between their production and decay points is long enough to be observable. If the mass of a hadron is large enough, final states that can be reached by strong interaction, i.e. without violating any selection rule, become accessible to its decay. Therefore, the lifetime is extremely short, of the order of an yoctosecond (10−24 s). These hadrons decay, from the point of view of an observer, exactly where they were born. To fix the orders of magnitude, consider such a particle produced in the laboratory reference frame with a Lorentz factor as large as γ = 300. In a lifetime, it will travel one femtometre (1 fm).

These extremely unstable hadrons can be observed as ‘resonances’ in two basic ways: in the process of ‘formation’, in the energy dependence of a cross-section, or in the ‘production’ process, as a maximum in the invariant mass distribution of a subset of particles in the final states of a reaction. We shall discuss that, after having recalled the features of the resonance phenomenon already present in classical mechanics and electromagnetism.

Such hadrons, baryons and mesons were discovered in a rapidly increasing number, in the 1950s and early 1960s in experiments at proton accelerators by mainly using bubble chambers as detectors. Their quantum numbers, spin, parity and isotopic spin were measured.

In this chapter we begin the study of weak interactions, continuing in Chapter 8 and 9, in which we shall see how electromagnetic and weak interactions are unified. There are two types of fermionic currents in weak interactions: charged currents (CC), mediated by the charged vector bosons W+ and W−, and neutral currents (NC) mediated by the Z0. In the scattering or decay amplitude the vector bosons propagate, as in QED and QCD, between vertices. However, unlike photons and gluons, the weak vector bosons are massive, with masses of the order of 100 GeV. Consequently, at low energies the two vertices appear merged in one and the interaction is point-like.

We shall start by studying the weak decays of the particles. These are CC low-energy phenomena and are described, with a very good approximation, by the Fermi point-like interaction. The interaction amplitudes are universal in the sense that are proportional to the same, very important, quantity, the Fermi constant.

We shall see that parity and particle–antiparticle conjugation are not conserved, rather are maximally violated in CC weak interactions, as shown by the beautiful experiment of C. S. Wu and collaborators. The consequence is that the bi-spinor fields in the CC weak interactions are eigenstates of the Dirac matrix γ5 of negative eigenvalue. We say that they have negative chirality or that they are left. We shall carefully elucidate the delicate issue of the difference between chirality and helicity, two concepts that are often confused.

In this chapter we shall discuss two important aspects, different but correlated, of the weak interactions: the CP-violation phenomena and the oscillations between members of flavoured, electrically neutral meson–antimeson pairs, the K0s, the B0s, the B0ss and the D0s. In each case, the states of definite flavour differ from those of definite mass and lifetime.

We begin with an elementary discussion of the neutral K system that will elucidate which are the states of definite strangeness, those of definite CP and those with definite mass and lifetime. We shall describe the oscillation between the former states, giving the relevant mathematical expressions and discussing the experimental evidence, including the observation of the regeneration of the initial flavour.

We then define the different modes of CP violation: in the wave function (or in the mixing), in the interference between decay with and without mixing, and in the decays. All modes happen for neutral mesons, the last one happens also for charged ones. We will describe how CP violation was discovered in the neutral K system in 1964.

In Section 8.6 we describe oscillations and CP violation in the B0 system, which needs a somewhat more-advanced formalism. In the same section we shall mention the discoveries of B0s oscillation, D0 mixing. These beautiful experimental results have been obtained at high-luminosity electron-positron colliders, KEKB in Japan and PEP2 in California, built on purpose and called beauty factories.