A new theoretical determination of $R_{\tau/P}$ $(P=\pi,K)$

TL;DR

This paper provides a new theoretical calculation of the ratio of tau decay widths to pion and kaon, testing lepton universality and CKM unitarity with improved assumptions and uncertainty estimates.

Contribution

It introduces an effective approach including resonances and QCD constraints to determine $R_{\tau/P}$ ratios with more reliable uncertainties.

Findings

Results are consistent with previous theories.

Uncertainty in ratios is significantly reduced.

Supports tests of lepton universality and CKM unitarity.

Abstract

We have determined $R_{\tau/P}\equiv \Gamma(\tau \to P \nu_\tau [\gamma]) / \Gamma(P \to\mu \nu_\mu[\gamma])$ ($P=\pi, K$). Whereas $P$ decays are calculated by using Chiral Perturbation Theory (ChPT), $\tau$ decays have been studied with an effective approach where ChPT is enlarged by including the lightest resonances and following the high-energy behavior dictated by QCD. These ratios have allowed us to test the lepton universality and the CKM unitarity and also to search for bounds on non-standard interactions. Our results, $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\delta R_{\tau/K}=(0.97\pm 0.58 )\%$, are consistent with the previous theoretical determinations, but with much more robust assumptions, yielding a reliable uncertainty.