  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 ell (ell= 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 ell.
Semileptonic transitions like tau -> ell pi pi are sensitive to flavor-changing
scalar couplings while decays such as tau -> ell eta(') 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 -> ell pi pi transitions, improving over
previous treatments in the literature.
