Probing Lepton Flavour Violation in the Higgs sector with hadronic tau decays

With the discovery of a new boson with a mass around 125 GeV so far compatible with the standard model Higgs, we have entered a new era in the understanding of the electroweak symmetry breaking mechanism. Searches for lepton flavour violating (LFV) effects at the LHC associated to the Higgs sector offer an interesting possibility to test for new physics scenarios. Low-energy constraints still allow for sizable flavour-changing decay rates of the 125 GeV boson into leptons, h -> tau l (l = e, mu). In this talk, we discuss the special role played by hadronic tau-lepton decays in this quest and in particular by tau -> l pi pi decays. A remarkable feature is that 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 -> l nu. Finally, we will explore the discriminating power of hadronic tau decays on probing LFV in models with an extended Higgs sector.