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We study constraints and implications of the recent LHCb measurement of${\cal B}(B_s \to \mu^+\mu^-)$ for tree-level Higgs-mediated flavor-changingneutral current (FCNC) interactions. Combined with experimental data on $B_s$mass difference $\Delta m_s$, the $h \to \mu \tau$, and the $h \to\tau^+\tau^-$ decay branching ratios from the LHC, we find that the Higgs FCNCcouplings are severely constrained. The allowed regions for $B_s \to \mu \tau$,$\tau\tau$ and $h \to sb$ decays are obtained. Current data allow large CPviolation in the $h \to \tau^+ \tau^-$ decay. Consequences of the Cheng-Sheransatz for the Higgs Yukawa couplings are discussed in some detail.

Constraints and Implications on Higgs FCNC Couplings from Precision Measurement of $B_s \to \mu^+\mu^-$ Decay