The Standard Model of particle physics

Particle physics is at the heart of our understanding of the laws of nature. It is concerned with the fundamental constituents of the Universe, the elementary particles, and the interactions between them, the forces. Our current understanding is embodied in the Standard Model of particle physics, which provides a unified picture where the forces between particles are themselves described by the exchange of particles. Remarkably, the Standard Model provides a successful description of all current experimental data and represents one of the triumphs of modern physics.

The fundamental particles

In general, physics aims to provide an effective mathematical description of a physical system, appropriate to the energy scale being considered. The world around us appears to be formed from just a few different particles. Atoms are the bound states of negatively charged electrons (e−) which orbit around a central nucleus composed of positively charged protons (p) and electrically neutral neutrons (n). The electrons are bound to the nucleus by the electrostatic attraction between opposite charges, which is the low-energy manifestation of the fundamental theory of electromagnetism, namely Quantum Electrodynamics (QED).

The Standard Model

The ultimate theory of particle physics might consist of a (simple) equation with relatively few free parameters, from which everything else followed. Whilst the Standard Model (SM) is undoubtedly one of the great triumphs of modern physics, it is not this ultimate theory. It is a model constructed from a number of beautiful and profound theoretical ideas put together in a somewhat ad hoc fashion in order to reproduce the experimental data. The essential ingredients of the Standard Model, indicated in Figure 18.1, are: the Dirac equation of relativistic quantum mechanics that describes the dynamics of the fermions; Quantum Field Theory that provides a fundamental description of the particles and their interactions; the local gauge principle that determines the exact nature of these interactions; the Higgs mechanism of electroweak symmetry breaking that generates particle masses; and the wide-reaching body of experimental results that guide the way in which the Standard Model is constructed. The recent precision tests of the Standard Model and the discovery of the Higgs boson have firmly established the validity of the Standard Model at energies up to the electroweak scale. Despite this success, there are many unanswered questions.

Probing the structure of the proton

Electron–proton scattering provides a powerful tool for probing the structure of the proton. At low energies, the dominant process is elastic scattering where the proton remains intact. Elastic scattering is described by the coherent interaction of a virtual photon with the proton as a whole, and thus provides a probe of the global properties of the proton, such as its charge radius. At high energies, the dominant process is deep inelastic scattering, where the proton breaks up. Here the underlying process is the elastic scattering of the electron from one of the quarks within the proton. Consequently, deep inelastic scattering provides a probe of the momentum distribution of the quarks.

The precise nature of the e−p → e−p scattering process depends on the wavelength of the virtual photon in comparison to the radius of the proton.

Neutrino flavours

Unlike the charged leptons, which can be detected from the continuous track defined by the ionisation of atoms as they traverse matter, neutrinos are never directly observed; they are only detected through their weak interactions. Different neutrino flavours can only be distinguished by the flavours of charged lepton produced in charged-current weak interactions. Consequently, the electron neutrino νe, is defined as the neutrino state produced in a charged-current weak interaction along with an electron. Similarly, by definition, the weak charged-current interactions of a νe will produce an electron. For many years it was assumed that the νe, νμ and ντ were massless fundamental particles. This assumption was based, at least in part, on experimental evidence. For example, it was observed that the interactions of the neutrino/antineutrino produced along with a positron/electron in a nuclear β-decay, would produce an electron/positron as indicated in Figure 13.1.

The need for the Higgs boson

The apparent violation of unitarity in the e+e− → W+W− cross section was resolved by the introduction of the Z boson. A similar issue arises in the W+W− → W+W− scattering process, where the cross section calculated from the Feynman diagrams shown in Figure 17.1 violates unitarity at a centre-of-mass energy of about 1 TeV. The unitarity violating amplitudes originate from WL WL → WL WL scattering, where the W bosons are longitudinally polarised. Consequently, unitary violation in WW scattering can be associated with the W bosons being massive, since longitudinal polarisation states do not exist for massless particles. The unitarity violation of the WL WL → WL WL cross section can be cancelled by the diagrams involving the exchange of a scalar particle, shown in Figure 17.2. In the Standard Model this scalar is the Higgs boson.

The weak charged-current interaction

At the fundamental level, QED and QCD share a number of common features. Both interactions are mediated by massless neutral spin-1 bosons and the spinor part of the QED and QCD interaction vertices have the same ū(p′)γμ u(p) form. The charged-current weak interaction differs in almost all respects. It is mediated by massive charged W± bosons and consequently couples together fermions differing by one unit of electric charge. It is also the only place in the Standard Model where parity is not conserved. The parity violating nature of the interaction can be directly related to the form of the interaction vertex, which differs from that of QED and QCD.

Parity

The parity operation is equivalent to spatial inversion through the origin, x → −x.