Naturally Nonminimal Supersymmetry

TL;DR

This work extends naturalness bounds on superpartner masses to arbitrary nonminimal SUSY scenarios with variable messenger scales by solving one-loop RG equations for the Higgs sector and applying a sensitivity-based naturalness criterion. It derives bounds on gluino, chargino/neutralino, and scalar masses, highlighting how these limits depend on tan beta and the mediation scale, with distinct tree- and loop-level contributions. Two-loop corrections introduce additional constraints via S1^2, S2^2, S3^2 and T^2, allowing heavier first- and second-generation scalars while keeping naturalness intact. The results quantify how lowering the messenger scale can loosen bounds (by ~15–100%) and underscore the gluino bound as a central MSSM challenge, suggesting low-scale mediation as a potential remedy.

Abstract

We consider the bounds imposed by naturalness on the masses of superpartners for arbitrary points in nonminimal supersymmetric extensions of the standard model and for arbitrary messenger scales. This constitutes a significant generalization of previous work along these lines. We discuss appropriate measures of naturalness and the status of nonminimal supersymmetry in the light of recent experimental results.

Figures (5)

• Figure 1: $\Delta=10$ limit on gluino mass as a function of the messenger scale in the large $\tan \beta$ limit. The scaling of this limit with $\tan \beta$ and $m_A$ is given by equation (\ref{['m3limit']}).
• Figure 2: $\Delta=10$ limits on wino and higgsino mass parameters as a function of the messenger scale in the large $\tan \beta$ limit. The corresponding limit on the bino mass parameter is greater than 1 TeV.
• Figure 3: $\Delta = 10$ limits on left- and right-handed stop masses in the large $\tan \beta$ region as a function of the messenger scale. The solid lines show the limits implied when scalar masses are large compared to gaugino masses; when gaugino masses are comparable, the dashed lines result. The scaling of the solid lines with $\tan \beta$ and $m_A$ is given by equations (\ref{['q3limit']}-\ref{['u3limit']}). The bump in the mass limit on right-handed stops near $10^{13}$ GeV is due to a positive contribution from the bino mass parameter, which is allowed to be large due to a zero in the coefficient with which it contributes to $m_{h_u}$ near this scale.
• Figure 4: $\Delta=10$ limit on generic sparticle masses in $M \ne 0$ models in the large $\tan \beta$ regime as a function of the messenger scale. The scaling of this limit with $\tan \beta$ is determined by equation (\ref{['Meqn']}). The limit for right-handed up-type squarks is more stringent by a factor $\sqrt{2}$.
• Figure 5: $\Delta=10$ limits on sparticle masses from two-loop naturalness in the large $\tan \beta$ limit as a function of the messenger scale.