Naturalness bounds on gauge mediated soft terms

TL;DR

The paper analyzes naturalness upper bounds on gauge-mediated soft terms in the MSSM context, showing how $M_Z^2$ depends on Higgs-sector soft masses and that gauge mediation can tighten bounds on sparticle masses. It introduces a probabilistic naturalness criterion using the sensitivity measure $\Delta[\wp]$ and demonstrates its application to MSSM with universal boundary conditions. The results indicate that in minimal gauge-mediated scenarios the right-handed slepton mass $M_{\tilde e_R}$ is tightly bounded and typically light, with the bounds sensitive to the messenger scale $M_U$ and the parameter $\eta$, while large messenger content can be disfavored by current bounds. In the NMSSM with gauge mediation, solving the $\mu$-problem via a light singlet generally yields an unphysical vacuum that cosmology can ameliorate but at the cost of substantial fine-tuning, leading to heavy superpartners and large $\tan\beta$; overall, GM remains predictive only when Higgs-sector contributions are kept under control.

Abstract

After a general discussion about the quantitative meaning of the naturalness upper bounds on the masses of supersymmetric particles, we compute these bounds in models with gauge-mediated soft terms. We find interesting upper limits on the right-handed slepton masses that, unless the messenger fields are very light, disfavor minimal models with large messenger content. Deep unphysical minima, that however turn out to be not dangerous, are usually present in such models. The mu-problem can be solved by adding a light singlet only at the price of a large amount of fine tuning that gives also rise to heavy sparticles and large tanβ.

Figures (3)

• Figure 1: Naturalness upper bounds in the plane $(M_1,m_{\tilde{e}_R})$ with $\tan\beta=2$ in the cases of universal supergravity-mediated and of gauge-mediated soft terms in models with different values of $\eta$, defined in eq. (\ref{['eq:GM']}). Above (below) the straight line a slepton (a neutralino) is the lightest super-partner.
• Figure 2: The naturalness upper bound $\Delta<100$ (thick lines) and $\Delta<10$ (thin lines) on the right-handed selectron mass compared with its present experimental bound (horizontal dot-dashed line) and plotted as function of $\tan\beta$ for $M_U=10^6\,{\rm GeV}$ in figure \ref{['fig:2']}a, and as function of $\eta$ for $\tan\beta=2$ in figure \ref{['fig:2']}b.
• Figure 3: Contour-plot of the naturalness upper bound $\Delta<10$ (fig \ref{['fig:CP']}a) and $\Delta<100$ (fig \ref{['fig:CP']}b) on the right-handed slepton masses as function of $(M_U,\tan\beta)$ in the minimal model with $\eta=1$.