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

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

arXiv comment28 pages, 3 figures, 3 tables. Version accepted at JHEP with minor changes and new Appendix B

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• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
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• ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay induced by QED one-loop effects
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Electromagnetic corrections in hadronic tau decays