SUSY scale uncertainties in $m_b(m_b)$: $Br[B_s^0 \to \mu^+\mu^-]$ and cMSSM

TL;DR

This paper investigates how the SUSY scale affects the bottom quark mass corrections and the branching ratio of B_s^0 to mu+mu-, revealing significant variations that impact the cMSSM parameter space.

Contribution

It introduces a detailed analysis of SUSY scale dependence on bottom quark mass corrections and their effect on B_s^0 decay predictions within the cMSSM framework.

Findings

Branching ratio varies by about 0.6×10^{-9} with a 35% change in bottom quark mass.

Variations are larger in regions with a Higgs mass around 125 GeV.

Lowering the SUSY scale relaxes constraints on the cMSSM parameter space.

Abstract

We have studied the SUSY scale dependence of supersymmetric radiative corrections to bottom quark mass on the branching ratio of $B_s^0 \to \mu^+\mu^-$ and its impact on the cMSSM parameter space. The supersymmetric radiative corrections to bottom quark mass is in general evaluated at the SUSY scale, which is normally considered to be the geometric mean of stop masses. Then, the running of bottom quark mass is considered from the SUSY scale to the matching scale $M_W$ of the effective Hamiltonian which describes this decay. It is found that the branching ratio varies drastically with the SUSY scale. Typically the $Br[B_s^0 \to \mu^+\mu^-]_{\rm untagged}$ varies $\sim 0.6 \times 10^{-9}$ due variation of bottom quark mass $\sim 35\%$ with the SUSY scale and these changes are very significant compared to their present uncertainties in the measurements. Moreover, these variations are very larger at the regions of parameter space which are favorable for producing higgs mass around 125 GeV. Finally, the confrontation of cMSSM with $B_s^0 \to \mu^+\mu^-$ is drastically relaxed if one lowers the SUSY scale and a significantly large parameter space becomes allowed in the phenomenologically interesting regions.