Flavor issues in the Higgs sector

We discuss the conditions under which the flavor structure of SUSY model induces, either radiatively or through mixing, new flavor-violating interactions in the Higgs sector. The radiative flavor mediation mechanism is illustrated using the minimal SUSY extension of the SM (MSSM) with generic trilinear A-terms, and applied to evaluate the corrections to Lepton Flavor-Violating (LFV) and Flavor-Conserving (LFC) Higgs vertices. Flavor mediation through mixing is discussed within the context of an $E_6$-inspired multi-Higgs model, suplemented with an abelian flavor symmetry. Tevatron and LHC can probe the flavor structure of these models through the detection of the LFV Higgs mode h->tau mu, while NLC can perform high-precision tests of the LFC mode h ->tau+ tau-.