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.

A quick introduction to the standard model of particle physics is given. The general concepts of elementary particles, interactions and fields are outlined. The experimental side of particle physics is also briefly discussed: how elementary particles are produced with accelerators or from cosmic rays and how to observe them with detectors via the interactions of particles with matter. The various detector technologies leading to particle identification are briefly presented. The way in which the data collected by the sensors is analysed is also presented: the most frequent probability density functions encountered in particle physics are outlined. How measurements can be used to estimate a quantity from some data and the question of the best estimate of that quantity and its uncertainty are explained. As measurements can also be used to test a hypothesis based on a particular model, the hypothesis testing procedure is explained.

The notion of symmetry is essential in the determination of particle properties. It reveals quantities that are conserved in collisions or decays. It also constrains the mathematical formulation of theories. This chapter introduces these concepts and explains how the notion of symmetry is implemented in quantum mechanics. It reviews the quantities conserved in particle collisions or decays: energy-momentum and total angular momentum, and also the internal symmetries, such as parity, charge conjugation, baryon and lepton numbers.

This concluding chapter recaps what has been learnt in the previous chapters about the Standard Model. This model is highly successful in describing particle physics phenomena. Some of its successes are briefly underlined, such as the number of light neutrino families. However, as with any model, it also has its weaknesses, which are also provided. The most important open questions of particle physics are addressed in the second part of the chapter, in particular, the matter–antimatter asymmetry, the hypothetical presence of the dark matter. Possible extensions of the Standard Model are presented to incorporate massive neutrinos.