Search for $H/A \to \mu\mu$ and $\tau\mu$ at the LHC

The Expected experimental sensitivity to the heavy neutral Higgs boson decays H/A -> mu mu and H/A -> tau mu at the LHC is discussed in the framework of the MSSM and of two Type-III Two-Higgs-Doublet models allowing for lepton flavour violation (LFV), respectively. Despite a small branching fraction, the H/A -> mu mu decay allows for a precise measurement of the Higgs boson mass and for an evaluation of the ratio of the vacuum expectation values of the two Higgs doublets, tan beta. The search for the LFV decay H/A -> tau mu allows stringent constraints to be set on the LFV coupling parameter lambda_tau mu.