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.

This chapter presents the last interaction described by the Standard Model of particle physics, i.e. the weak interaction. A historical approach is followed, trying to explain the evolution of its theoretical description from the experimental discoveries: we start from Fermi theory before introducing the charged and neutral currents. The mixing matrices both in the quark sector and in the leptonic sector are described. The phenomenon of neutrino oscillation is also detailed. The chapter concludes with a detailed discussion of CP violation.

This chapter explains how we can reconcile massive particles within a gauge symmetry. The notion of spontaneous symmetry breaking is introduced, first in a simple model and then with the gauge group of the Standard Model. The Brout–Englert–Higgs mechanism is then presented in detail. The rest of the chapter is devoted to the experimental discovery of the Higgs boson and its properties with the most up-to-date experimental measurements.

This chapter shows how gauge theories underlie all elementary interactions described in the Standard Model. Surprisingly, this necessitates encompassing electromagnetism and the weak interaction into a unified theory called the electroweak interaction theory. A modern description of the weak neutral current is then formulated with the introduction of the Weinberg angle. The various Feynman rules are derived step by step in detail.

This chapter introduces how we can use the quantum fields introduced in the previous chapter to access amplitudes and, thus, measurable quantities, such as the cross sections and the particle lifetime. More specifically, an educational tour of quantum electrodynamics (QED), which describes the interaction of electrons (or any charged particles) with photons, is proposed. Although this chapter uses concepts from quantum field theory, it is not a course on that topic. Rather, the aim here is to expose the concepts and prepare the reader to be able to do simple calculations of processes at the lowest order. The notions of gauge invariance and the S-matrix are, however, explained. Many examples of Feynman diagrams and the calculation of the corresponding amplitudes are detailed. Summation and spin averaging techniques are also presented. Finally, the delicate concept of renormalisation is explained, leading to the notion of the running coupling constant.