Absence of $μ$-Problem in Grand Unification
Gia Dvali, Anna Jankowsky
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.