One-loop determination of $\tau \to \pi (K) \nu_{\tau}[\gamma]$ branching ratios and new physics tests

TL;DR

This paper calculates tau decay ratios at one loop using an advanced chiral perturbation theory approach, testing lepton universality, CKM unitarity, and exploring new physics in tau decays.

Contribution

It provides the first precise one-loop calculations of tau to pion and kaon decay ratios incorporating resonances and QCD constraints, with implications for lepton universality and CKM unitarity tests.

Findings

Calculated decay ratios with uncertainties below 1%.

Confirmed lepton universality within experimental precision.

Identified slight deviations from CKM unitarity at 1.5-2.1 sigma.

Abstract

We calculate the ratios $R_{\tau / P}\equiv \Gamma \left( \tau \to P \nu_{\tau}[\gamma] \right) / \Gamma \left(P\to \mu \nu_{\mu}[\gamma]\right)$ ($P=\pi,K$) at one loop following a large-$N_C$ expansion where Chiral Perturbation Theory is enlarged by including the lightest resonances and respecting the short-distance behavior dictated by QCD. We find $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\delta R_{\tau/K}=(0.97\pm 0.58 )\%$, where the uncertainties are induced fundamentally by the counterterms. We test the lepton universality, obtaining $\left|g_\tau/g_\mu\right|_\pi=0.9964\pm 0.0038$ and $\left|g_\tau/g_\mu\right|_K=0.9857\pm 0.0078$, and analyze the CKM unitarity, getting results at $2.1\sigma$ and $1.5\sigma$ from unitarity via $|V_{us}/V_{ud}|$ and $|V_{us}|$, respectively. We also update the search for non-standard interactions in $\tau$ decays. As a by-product, we report the theoretical radiative corrections to the $\tau \to P \nu_{\tau}[\gamma]$ decay rates: $\delta_{\tau \pi} = -(0.24 \pm 0.56) \%$ and $\delta_{\tau K} = -(0.15 \pm 0.57) \%$.} \maketitle