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One-loop determination of $\tau \to \pi (K) \nu_{\tau}[\gamma]$ branching ratios and new physics tests
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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
Forward citations
Cited by 4 Pith papers
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Electroweak precision physics via angular distributions in hadronic $\tau$ decays
Angular moments in two-pseudoscalar tau decays give form-factor-independent SM relations that tensor new physics and scalar mass effects can break.
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Comment on "Radiative corrections to tau -> pi(K) nu_tau[gamma]: A reliable new physics test"
The GR10–DF dictionary has the wrong axial sign, so GR10 matches the chiral axial prediction but opposes the anomaly in the vector sector; the numerical shift in δr_SD is tiny (−0.004% for pions).
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CP violation studies at Super Tau-Charm Facility
A future Super Tau-Charm Facility is projected to test CP violation in hyperon, tau, and charm decays at 1e-4 to 1e-3 sensitivities and improve the kaon CPT mass-difference limit tenfold.
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Radiative corrections to one- and two-meson tau decays for precise new physics tests
Improved radiative corrections bring the pion tau-decay ratio into one-sigma agreement with lepton universality and sharpen CKM-unitarity and non-standard-interaction constraints.
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