Neutrinos are the most difficult particle to study, because they interact only via weak interactions. However, they have given revolutionary surprises, and it is with neutrinos that physics beyond the SM has been discovered. In the SM, neutrino masses are rigorously zero, but experiments show that they do have a mass. In the SM, neutrino flavour eigenstates are mass eigenstates; experiments show that they are mixtures of them. Two discoveries proved this. One is neutrino oscillations, discovered in atmospheric neutrinos, the other is the adiabatic flavour conversion in matter, discovered in solar neutrinos.

These were with natural neutrinos. Several experiments have been, and are being, performed with artificial neutrinos from reactors or accelerators to measure with increasing accuracy the neutrino mixing matrix and the mass spectrum. We found that the neutrino mixing is much larger than that of the quarks. Nobody knows why.

The SM assumes neutrinos to be different from antineutrinos, but no experimental proof of it exists. Neutrinos and antineutrinos may well be the same particle, a Majorana spinor. We see how this is searched for by looking for the extremely rare double beta decay.

The weak interaction was proposed by Fermi in 1933, to interpret the beta decay. The interaction Lagrangian is the product of two charged currents (CC) – one of the nucleons, one of the leptons. It was later discovered that parity and charge conjugation are not conserved and that the structure of the charged currents is a combination of vector and axial currents, V–A. The beautiful Goldhaber experiment on the helicity of the neutrino.

The coupling of all leptons is universal, but not that of the quarks. To obtain universality, Cabibbo introduced the concept of mixing of the hadronic currents, namely of quarks. Then the Glashow–Iliopoulos–Maiani mechanism solved a problem introducing the hypothesis that a fourth quark would exist, the charm, completing a doublet with the strange one. With the discovery of two more quarks, the quark mixing matrix contains a phase factor that is the origin of CP violation in the Standard Model.

The weak neutral currents were discovered with the Gargamelle bubble chamber at CERN in 1973. This showed a close similarity between weak and electromagnetic interactions and opened the way to their unification.

If the mass of a hadron is large enough, decays into final states that can be reached by strong interaction, that is, without violating any selection rule, are possible. The lifetime is then extremely short, of the order of a yoctosecond (10−24 s). These hadrons decay practically where they were born. We show how they are observed as ‘resonances’.

Hadrons, both baryons and mesons, were discovered in rapidly increasing numbers in the 1950s and early 1960s. How their quantum numbers, spin, parity and isospin were measured. Gradually it became clear that hadrons with the same spin and parity could be grouped in multiplets of the SU(3) symmetry. Proposal of the quark model and experimental verifications of its predictions. With increasing accelerator energies, more surprises were to come. The quarks are not only the three originally known, u, d and s, but three more exist, c, b and t. And more leptons were found, in total three ‘families’ of fundamental fermions, each with two quarks, a charged lepton and its neutrino.

In modern physics, symmetries are a powerful tool to constrain the form of equations, namely the Lagrangian that describes the system. Equations are assumed to be invariant under the transformation of a given group, which may be discrete or a continuous Lie group. Classification of the various types of symmetry. The concept of spontaneous symmetry breaking. It will evolve into the Higgs mechanism, which gives origin to the masses of the vector bosons that mediate the weak interactions, of the quarks and of the charged leptons.

The discrete symmetries, in particular the parity and the particle–antiparticle conjugation operations and the corresponding quantum numbers.

An important dynamical symmetry of the hadrons, the invariance of the Lagrangian under rigid rotations in an ‘internal’ space, the isospin space. The unitary group is SU(2).

The electroweak unification appears mainly in the neutral current processes. The transition probabilities of all of them are predicted in terms of the weak mixing angle. Measuring the weak mixing angle.

Theory predicts the existence of three vector bosons, W+, W− and Z0. It does not predict their masses, but precisely states how they are related with two measured quantities: the Fermi constant and the weak mixing angle. The UA1 experiment and the discovery of the vector bosons.

The precision tests of the electroweak theory performed at the LEP electron–positron collider and at the Tevatron proton–antiproton collider.

The last missing element of the SM, the Higgs boson. The spontaneous symmetry breaking and the boson. The searches at LEP and at the Tevatron. The Large Hadron Collider and the ATLAS and CMS experiments. The discovery of 2012. Checking Higgs physics, measuring its mass and width, its spin and parity, its couplings to the bosons and to the fermions. All agree with the predictions of the Standard Model, so completing the experimental verification of its basic building blocks.

A good knowledge of special relativity and quantum mechanics is essential for studying particle physics. Even if the reader is assumed to be already familiar with these two theories, a brief review of special relativity is given in this chapter with emphasis on the covariant and contravariant notations, which may be less well mastered but are very useful in particle physics. Important aspects of quantum mechanics for particle physics, such as the angular momentum, are also addressed.

The determination of particle properties relies mostly on experimental measurements based on their collisions and decays. This chapter introduces the concepts of reaction cross section and particle decay rate. For unstable particles, the origin of its lifetime as well as the notion of branching ratios is presented. Many formulas involving the reactions between two particles are derived in detail, and phase spaces involving three-body decays are presented with Dalitz diagrams. The notion of cross reactions is also presented.

In this chapter, the notion of partons is introduced. Evidence of the substructure of the nucleon is given, and the formalism of the deep inelastic scattering is presented. The form factors and the Bjorken scaling properties are explained in detail. Finally, the parton density functions are presented, and the chapter concludes with the open question of the origin of the proton spin.

The purpose of this chapter is to clearly define the mathematical objects that describe particles of various kinds: bosons (spin-0 and spin-1) or spin-1/2 fermions. Starting from the Schrödinger equation, the Klein–Gordon equation, the Dirac equation and the Maxwell equations are detailed, leading to the description of the associated quantised field – a well-adapted framework to treat states composed of many particles that can be created or annihilated when they interact. The notion of 4-current is introduced, and the quantisation of the various fields is presented. With the Dirac equation, the spinor’s properties are described extensively. The interpretation of the solutions of the Dirac equation in terms of antiparticles and spin or helicity degrees of freedom is then detailed. Helicity and chirality are also treated carefully. Finally, the Maxwell field and the Proca field are described, highlighting their specificities in terms of polarisation degrees of freedom.

This chapter is divided into two parts. The first part introduces the quark model, following more or less the historical developments. It led to an approximate symmetry, based on the SU(3) flavour group, where u, d and s quarks are the three degrees of freedom. The second part introduces the quantum chromodynamics theory (QCD), i.e. the true formal gauge theory of the strong interaction. Here again, the symmetry group is SU(3), but the degrees of freedom are the three quark colours. This symmetry is assumed to be exact, which has consequences on the existence of gluons and their properties, the carriers of the strong interaction at the elementary particle level, briefly mentioned in the previous chapter. The QCD interaction is the first non-Abelian interaction encountered in the book. The non-perturbative regime of QCD is also presented with a short introduction to lattice QCD. A discussion about the colour confinement and the hadronisation of quarks is also given.