Effective-field theory analysis of the ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays

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.

v3: Lattice QCD determination of the tensor charge used, theoretical error of the vector form factor accounted for, a couple of improved observables for Dalitz plots and forward-backward asymmetries have been introduced. Rewording and updated references included. 23 pages, 12 figures, 1 tables, JHEP style

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