Chapter 4
The Standard Model of Particle Physics

We are now ready to describe the standard model (SM)! It is a renormalizable, quantum Yang-Mills theory, and is illustrated nicely in Figure 4.1. Before electroweak symmetry breaking (EWSB) — a form of spontaneous symmetry breaking (SSB) — it possessed the gauge symmetry $\mathrm{SU}{(3)}_C\times \mathrm{SU}{(2)}_L\times U{(1)}_Y$, with $C$, $L$, and $Y$ standing for color, left, and hypercharge, respectively. These three groups correspond to the strong, weak, and electromagnetic forces, with eight, three, and one generators or gauge bosons, respectively. The relative strengths of each interaction, as well as gravity’s, are shown in Table 4.1, based on the equivalent of the fine structure constant of each force, ${\alpha }_f=\frac{g_f}{4\pi }$, where $g_f$ is the respective coupling constant.

The SM contains six fermions charged and uncharged under the $\mathrm{SU}{(3)}_C$ symmetry each, called the “quarks” and “leptons”, respectively. The left-handed fermions live as pairs in $\mathrm{SU}{(2)}_L$ doublets, while the right-handed fermions in singlets. The six types of fermions are referred to as different “flavors”, grouped into three generations as in Figure 4.1.

The SM also contains a complex scalar $\mathrm{SU}{(2)}_Y$-doublet called the Higgs field, which is associated with EWSB. As shown in Figure 4.1, it initially is at the center of a “sombrero” potential because of which, before EWSB, the gauge bosons, fermions, and the Higgs field are all massless.

EWSB is hypothesized to have occurred during the electroweak epoch (see Figure 1), where the $\mathrm{SU}{(2)}_L\times U{(1)}_Y$ global symmetry broke to the $U{(1)}_{\mathrm{EM}}$ of QED. Through this, the Higgs field obtained a non-zero vacuum expectation value (VEV), imbuing all the fermions, three of the gauge bosons, and the Higgs boson with mass — a process referred to as the Higgs mechanism. The outcome is the state of the universe and physics as we know it.

Of course, as outlined in the introduction, this picture does not explain myriad phenomena in fundamental physics, including dark matter, dark energy, baryon asymmetry, and neutrino masses. This is why it is crucial to test the SM as rigorously and in as broad a phase space as possible, in order to identify any cracks that may point to new physics.

In this chapter, we will briefly walk through different areas of the SM. Having discussed QED in Chapter 3.3, we begin with the remaining two fundamental interactions: quantum chromodynamics (Section 4.1); and weak interactions and electroweak unification (Section 4.2). Finally, in Section 4.3, we will discuss the Higgs sector and pair production of the Higgs boson, which is the focus of this dissertation.