Effective-field theory analysis of the $τ^-\to π^-π^0ν_τ$ decays

Abstract

We perform an effective field theory analysis of the $τ^- \to π^- π^0 ν_τ$ decays, that includes the most general interactions between Standard Model fields up to dimension six, assuming left-handed neutrinos. We constrain as much as possible the necessary Standard Model hadronic input using chiral symmetry, dispersion relations, data and asymptotic QCD properties. As a result, we set precise (competitive with low-energy and LHC measurements) bounds on (non-standard) charged current tensor interactions, finding a very small preference for their presence, according to Belle data. Belle-II near future measurements can thus be very useful in either confirming or further restricting new physics tensor current contributions to these decays. For this, the spectrum in the di-pion invariant mass turns out to be particularly promising. Distributions in the angle defined by the $τ^-$ and $π^-$ momenta can also be helpful if measured with less than $10\%$ accuracy, both for non-standard scalar and tensor interactions.