Recent evidence from observation of the flavor-changing neutral current decay B_s to mu+ mu- by the LHCb collaboration B(B_s to mu^+ mu^-) = (3.2 * 10^-9), is consistent with the latest standard model prediction B(B_s to mu^+ mu^-) = (3.23 +- 0.27) * 10^-9. While New Physics can still affect this decay amplitude, its contribution is certainly not the dominant one. We analyze branching ratios of the decays B_s to mu+ mu- X, with X = a photon or neutrino anti-neutrino pair, which can mimic B_s to

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... mu+ mu- on portions of the parameter space where X is soft. We perform a model-independent standard model calculation of those processes incorporating heavy quark and chiral symmetries of QCD. We show that the considered contributions contribute to B_s to mu+ mu- at a sub-percent level.