Dynamical determination of the Supersymmetric Higgs mass

TL;DR

The μ-problem and the doublet-triplet splitting challenge in the MSSM motivate a dynamical mechanism where μ is fixed by minimizing the low-energy potential. By promoting μ to a field μ=λS and including soft terms, the authors show a local minimum with μ at the weak scale, roughly μ ≈ (1/2) B sin 2β, and derive constraints on the μ–tanβ plane. The mechanism is most viable in gauge-mediated SUSY breaking, where additional soft terms can arise without destabilizing the hierarchy, and messenger-matter mixing can yield a sizable B to obtain realistic μ. This approach reduces fine-tuning relative to the MSSM and links electroweak symmetry breaking to the structure of the soft-breaking sector, with automatic relief of the doublet-triplet splitting in GUT scenarios under certain conditions.

Abstract

Considering the supersymmetric Higgs mass ($μ$-parameter) as a dynamical variable to be determined by minimizing the energy, we predict its value as a function of the soft masses of the potential. We find that $μ$ has a nonzero value close to the weak scale. This scenario offers a simultaneous solution to the doublet-triplet splitting problem and to the $μ$-problem. We discuss its viability in theories with gauge mediated supersymmetry breaking.

Figures (1)

• Figure 1: Allowed region (in white) of the plane $\mu$--$\tan\beta$ for different values of $B$. The dashed lines correspond to $\mu=B\sin 2\beta/2$.