Abstract
We perform an effective field theory analysis of the τ− → π−π0ντ 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 show that it is possible to 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.
Highlights
The W mass value and its left-handed couplings
Our aim in this paper is to extend our previous analysis to the τ − → π−π0ντ decays, which should not be sensitive to NP charged current scalar interactions but could instead be very competitive restricting charged-current tensor interactions
If the SM input to the considered decays is well under control one can set bounds on NP effective couplings. This is the case for the vector and -to a lesser extent- the scalar interactions but only a theory-driven approach is possible for the tensor form factor
Summary
We will study the semileptonic τ − → π−(Pπ−) π0(Pπ0) ντ (P ) decays, where pions parity determines that only scalar, vector and tensor currents contribute. We will use the best fit results corresponding to case III in this reference, which includes first-order isospin breaking corrections Both statistical and systematic uncertainties on F+(s) are taking into account throughout our numerical analysis. Their result, fT (0) = 0.195±0.010 yields Λ2 = (12.0 ± 0.6) MeV, that we will use in the following This value of Λ2 is roughly a factor three smaller than the prediction for Λ1 obtained using short-distance QCD properties [24], Λ1 = (33 ± 2) MeV. Since both operators displayed in eq (4.3) have the same chiral counting order, one would have guessed Λ2 ∼ Λ1, resulting in an overestimation of Λ2, as we did in ref.
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