Flavor violating Higgs couplings in minimal flavor violation

Motivated by the recent LHC data on the lepton-flavor violating (LFV) decays h → ℓ₁ℓ₂ and B_s,d → ℓ₁ℓ₂, we study the Higgs-mediated flavor-changing neutral current (FCNC) interactions in the effective field theory (EFT) approach without and with the minimal flavor violation (MFV) hypothesis, and concentrate on the later. After considering the B and K physics data, the various LFV processes, and the LHC Higgs data, severe constraints on the Higgs FCNC couplings are derived, which are dominated by the LHC Higgs data, the $B_s-{\overline{B}}_s$ mixing, and the μ → eγ decay. In the general case and the MFV framework, allowed ranges of various observables are obtained, such as $B$(B_s → ℓ₁ℓ₂), $B$(h → ℓ₁ℓ₂), $B$(h → q₁q₂), and the branching ratio of μ → e conversion in Al. Future prospects of searching for the Higgs FCNC interactions at the low-energy experiments and the LHC are discussed.