Lepton flavor changing Higgs Boson decays in a Two Higgs Doublet Model with a fourth generation of fermions

We analyze the flavor changing decay $h\rightarrow \mu \tau $ in the framework of a Two Higgs Doublet Model with a fourth generation of fermions (4G2HDM) which couples only to the heavy scalar doublet. We obtain that the respective branching ratio at one-loop level can reach values as high as $ 10^{-4}-10^{-6} $ for masses of $ 300 $ GeV to $ 1 $ TeV for the heavy leptons in the fourth family and the new heavy Higgs bosons. These radiative corrections are of the same order of magnitude as the tree level prediction of the 4G2HDM.