Absence of $\mu$-Problem in Grand Unification

TL;DR

This paper demonstrates that in gravity-mediated grand unified theories, the $mbda$-problem does not arise due to supersymmetry breaking effects universally inducing shifts in heavy fields, independent of the unification scale.

Contribution

It shows that the $mbda$-problem is absent in generic GUTs with gravity mediation, regardless of doublet-triplet splitting mechanisms, supported by explicit models.

Findings

The $mbda$-problem is non-existent in these theories.

Supersymmetry breaking induces shifts proportional to gravitino mass.

The mechanism is effective across different doublet-triplet splitting methods.

Abstract

Using properties of Goldstino, we show that in generic grand unified theories with gravity-mediated supersymmetry breaking the $\mu$-problem is non-existent. What happens is that supersymmetry breaking universally induces the shifts of the heavy fields that generate $\mu$ and $B_{\mu}$ 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.