Minimal models of loop-induced lepton flavor violation in Higgs boson decays

The LHC has recently reported a slight excess in the $h\rightarrow \tau \mu$ channel. If this lepton flavor violating (LFV) decay is confirmed, an extension of the Standard Model (SM) will be required to explain it. In this paper we investigate two different possibilities to accommodate such a LFV process: the first scenario is based on flavor off-diagonal $A$-terms in the Minimal Supersymmetric Standard Model (MSSM), and the second is a model where the Higgs couples to new vectorlike fermions that couple to the SM leptons through a LFV four fermion interaction. In the supersymmetric model, we find that the sizes of the $A$-terms needed to accommodate the $h\rightarrow \tau\mu$ excess are in conflict with charge- and color-breaking vacuum constraints. In the second model, the excess can be successfully explained while satisfying all other flavor constrains, with order one couplings, vectorlike fermion masses as low as 15 TeV, and a UV scale higher than 35 TeV.