Effective-field theory analysis of the $\tau^-\to \pi^-\pi^0\nu_\tau$ decays

TL;DR

This paper uses effective field theory to analyze tau decays into pions and neutrinos, setting bounds on new physics interactions and highlighting the potential of future measurements to detect or constrain such effects.

Contribution

It provides the first comprehensive EFT analysis of tau to two-pion decays, constraining non-standard tensor interactions with current data and proposing future experimental strategies.

Findings

Bounds on non-standard tensor interactions are competitive with other measurements.

Future Belle-II data can significantly improve constraints or confirm new physics signals.

Di-pion mass spectrum and angular distributions are sensitive probes for non-standard interactions.

Abstract

We perform an effective field theory analysis of the $\tau^- \to \pi^- \pi^0 \nu_\tau$ 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 $\tau^-$ and $\pi^-$ momenta can also be helpful if measured with less than $10\%$ accuracy, both for non-standard scalar and tensor interactions.