Flavor Violating Higgs Couplings in Minimal Flavor Violation

Motivated by the rencent LHC data on the lepton-flavor violating (LFV) decays $h\to \ell_1 \ell_2$ and $B_{s,d}\to \ell_1 \ell_2$, 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 $B_s - \bar B_s$ mixing, and the $\mu \to e \gamma$ decay. In the general case and the MFV framework, allowed ranges of various observables are obtained, such as $\mathcal B (B_s\to \ell_1 \ell_2)$, $\mathcal B (h\to \ell_1 \ell_2)$, $\mathcal B (h\to q_1 q_2)$, and the branching ratio of $\mu \to e$ conversion in Al. Future prospects of searching for the Higgs FCNC interactions at the low-energy experiments and the LHC are discussed.