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We have studied the SUSY scale dependence of supersymmetric radiativecorrections to bottom quark mass on the branching ratio of $B_s^0 \to\mu^+\mu^-$ and its impact on the cMSSM parameter space. The supersymmetricradiative corrections to bottom quark mass is in general evaluated at the SUSYscale, 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 thematching 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 $\sim 0.6 \times10^{-9}$ due variation of bottom quark mass $\sim 35\%$ with the SUSY scale andthese changes are very significant compared to their present uncertainties inthe measurements. Moreover, these variations are very larger at the regions ofparameter space which are favorable for producing higgs mass around 125 GeV.Finally, the confrontation of cMSSM with $B_s^0 \to \mu^+\mu^-$ is drasticallyrelaxed if one lowers the SUSY scale and a significantly large parameter spacebecomes allowed in the phenomenologically interesting regions.

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