As a result of recent theoretical and experimental progress, we are entering a new
era of precision hadronic physics. The purpose of this program is twofold: to
understand better the theory that describes the strong interaction (QCD: Quantum
Chromodynamics) and the hadron dynamics at low energy, and to search for extensions
of the Standard Model that would manifest at low energy as small deviations from its
predictions, complementing the high-energy direct searches for new particles at the
Large Hadron Collider (LHC). Theoretical advances in this context have been spurred
by developments in different methods such as Chiral Perturbation Theory, dispersive
techniques, lattice QCD and their combination to achieve a more model independent
and reliable prediction of the observables at play.

In this talk, I will present one of my recent studies within this research program,
and show how we can probe new (lepton flavour violating) couplings of the recently
discovered Higgs-like boson by studying the hadronic decays of the tau lepton. In
particular, I will discuss the special role played by tau -> l pi pi decays, whose
hadronic part can be precisely described using dispersion relations. 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.