| Summary: | Abstract Motivated by the recent LHC data on the lepton-flavor violating (LFV) decays h → ℓ 1 ℓ 2 and B s,d → ℓ 1 ℓ 2, 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 − B ¯ s $$ {B}_s-{\overline{B}}_s $$ mixing, and the μ → eγ decay. In the general case and the MFV framework, allowed ranges of various observables are obtained, such as ℬ $$ \mathrm{\mathcal{B}} $$ (B s → ℓ 1 ℓ 2), ℬ $$ \mathrm{\mathcal{B}} $$ (h → ℓ 1 ℓ 2), ℬ $$ \mathrm{\mathcal{B}} $$ (h → q 1 q 2), 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.
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