Lepton flavor violation in the Higgs sector and the role of hadronic τ-lepton decays

It has been pointed out recently that current low-energy constraints still allow for sizable flavor-changing decay rates of the 125 GeV boson into leptons, h -> tau l (l = e, mu). In this work we discuss the role of hadronic tau-lepton decays in probing lepton flavor violating couplings in the Higgs sector. At low energy, the effective Higgs coupling to gluons induced by heavy quarks contributes to hadronic tau decays, establishing a direct connection with the relevant process at the LHC, pp(gg) -> h -> tau l. Semileptonic transitions like tau -> l pi pi are sensitive to flavor-changing scalar couplings, while decays such as tau -> l eta((l)) probe pseudoscalar couplings, thus providing a useful low-energy handle to disentangle possible Higgs flavor violating signals at the LHC. As part of our analysis, we provide an appropriate description of all the relevant hadronic matrix elements needed to describe Higgs mediated tau -> pi pi transitions, improving over previous treatments in the literature.