*Fundamentals of Particle Physics: Understanding the Standard Model*, by Pascal Paganini, Cambridge University Press

This textbook for advanced undergraduate and graduate students, written by experimental particle-physicist Pascal Paganini of Ecole Polytechnique, aims to teach Standard Model calculations of quantities that are relevant for modern experimental research. Each chapter ends with a collection of unsolved problems to help the student practice the discussed calculations. The level is similar to the well-known textbook *Quarks and Leptons *by F Halzen and A D Martin (Wiley, 1984), but with a broader introduction and including more up-to-date material. The notation is also similar, and shared with several other popular textbooks at the same level, making it easy for students to use it along with other resources.

**Comprehensive**

*Fundamentals of Particle Physics* starts with a general introduction that is around 50 pages long and includes information on detectors and statistics. It continues with a recap of relativistic kinematics, quantum mechanics of angular momentum and spin, phase–space calculations for cross sections and decays as well as symmetries. The main part of the book begins with a discussion of relativistic quantum mechanics, covering the equations of motion of spin 0, 1 and ½ particles along with a detailed description of Dirac spinors and their properties. Then, it addresses quantum electrodynamics (QED), including the QED Lagrangian, standard QED cross-section calculations and a section dedicated to magnetic moments (g-2). About 100 pages are devoted to hadronic physics: deep inelastic scattering, parton model, parton-distribution functions and quantum chromodynamics (QCD). Calculations in perturbative QCD are discussed in some detail and there is also an accessible section in non-perturbative QCD that can serve as a very nice introduction to beginner graduate students.

The book continues with weak interactions, covering the Fermi theory, W-boson exchange, CKM matrix, neutrinos, neutrino mixing and CP-violation. The following chapter presents the electroweak theory and introduces gauge-boson interactions. A dedicated chapter is reserved for the Higgs boson. This includes a nice section about the discovery of the particle and the measurements that are performed at the LHC, as well as some comments about the pre-history (LEP and Tevatron) and the future (HL-LHC and FCC). A clear discussion about naturalness and several other conceptual issues offers a light and useful read for students of any level. The final chapter goes through the Standard Model as a whole, including a very useful evaluation of its successes and weaknesses. In terms of beyond-Standard Model physics, only dark matter and neutrino masses are covered.

Although this is not a quantum field-theory textbook, some of its elements are introduced; in particular second quantisation, S-matrix, Dyson’s expansion and a few words about renormalisation are included. These are very useful in bridging the gap between practical calculations and their theoretical background, also serving as a quick reference.

There are several useful appendices, most notably a 30-page introduction to group theory that can serve as a guide for a short standalone course in the subject or as a quick reference. The book also includes elements of the Lagrangian formalism, which could have been a bit more expanded to include a more detailed presentation of Noether’s theorem, probably in an additional appendix.

Overall the book achieves a good balance between calculations and more conceptual discussions. All students in the field can benefit from the sections on the Higgs-boson discovery and the Standard Model. Being concise and not too long, *Fundamentals of Particle Physics* can easily be used as a primary or secondary textbook for a particle-physics course that introduces calculations using Feynman diagrams in the Standard Model to students.