Absence of the μ -problem in grand unification

Abstract

Using properties of Goldstino, we show that in generic grand unified theories with gravity-mediated supersymmetry breaking the $\ensuremath{\mu}$-problem is nonexistent. What happens is that supersymmetry breaking universally induces the shifts of the heavy fields that generate $\ensuremath{\mu}$ and ${B}_{\ensuremath{\mu}}$ terms. In the leading order, these are given by the mass of gravitino and are insensitive to the scale of grand unification. The mechanism works regardless whether doublet-triplet splitting is achieved via fine-tuning or not. Moreover, we illustrate this general phenomenon on explicit examples of theories that achieve doublet-triplet splitting dynamically. These include the theories with Higgs doublet as a pseudo-Goldstone boson, as well as the approach based on spontaneous decoupling of the light color triplet from quarks and leptons.