In this chapter, we devise a set of Feynman rules to describe matrix elements of processes involving spin-1/2 fermions. The rules are developed for two-component fermions and are then applied to tree-level decay and scattering processes and the fermion self-energy functions in the one-loop approximation.

Despite the successes of the Standard Model, it seems very likely that new physics is present at the TeV scale.

In this chapter, we present example Feynman diagrammatic calculations of supersymmetric decay and scattering processes, employing the two-component fermion techniques developed in . We present the first calculations in some detail to get the reader acquainted with the technical details.

In this chapter, we present example one-loop Feynman diagrammatic calculations in the Standard Model and MSSM, employing the two-component fermion techniques developed in Chapter 2.

Despite the inherent beauty of supersymmetric field theories, we know that supersymmetry cannot be an exact symmetry of Nature. The observed spectrum of fundamental particles does not consist of mass-degenerate supermultiplets. Hence, supersymmetry must be broken. In this chapter, we shall discuss how supersymmetry (SUSY) breaking can arise.

So far, the experimental study of supersymmetry has unfortunately been confined to setting limits. As noted in Section 13.6, there can be indirect signals for supersymmetry from processes that are rare or forbidden in the Standard Model but have contributions from sparticle loops.

Quantum fields possess definite transformation properties under the Lorentz and Poincaré groups. In the 1960s, with the discovery of new global internal symmetry groups such as the flavor SU(3) group of the quark model (based on the three quarks $u$, $d$, and $s$ that were known at that time), the following question was considered.

There are a number of reasons to consider realistic models of supersymmetry that go beyond the MSSM. The first reason is connected to the $\mu$ problem, which was introduced in Section 14.6. Naively, one would expect the dimensionful parameter $\mu$ to be of the same order of magnitude as the largest possible mass scale.

In the Standard Model of particle physics presented in Section 4.7, the three neutrinos are exactly massless. However, the experimental observation of neutrino mixing strongly suggests that at least two of the three neutrinos are massive.

To motivate the introduction of four component spinors for spin-1/2 particles, it is instructive to compare real and complex scalar fields that describe spin-0 particles. Consider a free scalar field theory with two real, mass-degenerate scalar fields ${\varphi }_1\left(x\right)$ and ${\varphi }_2\left(x\right)$.

Supersymmetry can be given a geometric interpretation using superspace, a manifold obtained by adding four fermionic coordinates to the usual bosonic spacetime coordinates $t,x,y,z$. Points in superspace are labeled by coordinates