Absence of $μ$-Problem in Grand Unification

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

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