Ultraviolet completion with suppressed higgsino mass

Construct a consistent ultraviolet completion in which a single dominant modulus with Kähler potential coefficient c = 12 and matter bilinear scaling power p = 2 suppresses the higgsino mass parameter μ while leaving the scalar soft masses and bμ term nonzero.

Background

The paper studies modulus-mediated supersymmetry breaking in which the physical higgsino mass can vanish through a cancellation between the gravitino-mass contribution and a modulus F-term contribution. For a single dominant modulus, the desired pattern requires p = 2 and c = 12: μ cancels, whereas bμ and the scalar soft masses do not.

The authors note that this is precisely the structure needed for the phenomenological scenario, but state that they know of no ultraviolet completion realizing a Kähler potential with c = 12. Known string- and M-theory examples cited in the paper have c ≤ 7, making the construction of such a completion an unresolved model-building problem.

References

The next interesting case is p = 2, c = 12, for which μ cancels but bμ and mi2 do not. This is precisely what we are looking for, but unfortunately, we know of no UV completion with c = 12.

— Higgsino Above the Sea of Fog  (2609.01504 - Fan et al., 1 Sep 2026) in Section 4, subsection “Suppressing μ in modulus mediation,” subsubsection “Single-modulus dominance”