Broken Supersymmetry and Application to Particle Physics

Abstract

We pointed out in the previous chapter that in the exact supersymmetric limit fermions and bosons are degenerate in mass, a situation for which there appears to be no evidence in nature. Therefore, in order to apply super-symmetry to particle physics, we must consider models where supersymmetry is broken. There are two ways to break symmetries of Lagrangian field theories (see Chapter 2): first, where extra terms are added to the Lagrangian that are not invariant under the symmetry; and second, the Lagrangian is kept invariant whereas the vacuum is allowed to be noninvariant under the symmetry. The first method introduces an arbitrariness into the theory thereby reducing its predictive power. The condition that the divergence structure should not be altered very much reduces this arbitrariness somewhat; yet it is not a very satisfactory approach. On the other hand, the second method, the Nambu—Goldstone realization of the symmetry provides a unique, appealing, and more predictive way to study the consequences of symmetry noninvariances. We will, therefore, study this approach in this chapter.