Using properties of Goldstino, we show that in generic grand unified theories with gravity-mediated supersymmetry breaking the $\mu$-problem is nonexistent. 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.

• Received 23 September 2021
• Accepted 23 December 2021

DOI:https://doi.org/10.1103/PhysRevD.105.016009

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Published by the American Physical Society