Abstract
The ratios $R_{\tau/P}\equiv \Gamma(\tau \to P \nu_\tau [\gamma]) / \Gamma(P \to\mu \nu_\mu[\gamma])$ ($P=\pi, K$) provide sensitive tests of lepton universality $\left|g_\tau/g_\mu\right|=1$ and are a useful tool for new physics searches. The radiative corrections to $R_{\tau/P}$ are computed following a large-$N_C$ expansion to deal with hadronic effects: Chiral Perturbation Theory is enlarged by including the lightest multiplets of spin-one heavy states such that the relevant Green functions are well-behaved at high energies. We find $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\delta R_{\tau/K}=(0.97\pm 0.58 )\%$, which imply $\left|g_\tau/g_\mu\right|_\pi=0.9964\pm 0.0038$ and $\left|g_\tau/g_\mu\right|_K=0.9857\pm 0.0078$, compatible with and at $1.8\sigma$ of lepton universality, respectively. We test unitarity and bind non-standard effective interactions with the $\tau \to P \nu_\tau [\gamma]$ decays.
Highlights
Lepton universality (LU) is a basic tenet of the Standard Model of particles interactions
The radiative corrections to Rτ=P are computed following a large-NC expansion to deal with hadronic effects: Chiral Perturbation Theory is enlarged by including the lightest multiplets of spin-one heavy states such that the relevant Green functions are well behaved at high energies
Where gμ 1⁄4 gτ according to LU,1 the radiative corrections are encoded in δRτ=P and Rðτ0=ÞP is the leading-order result, Rðτ0=ÞP
Summary
Lepton universality (LU) is a basic tenet of the Standard Model of particles interactions. A large diversity of weak interaction processes is compatible with the fact that lepton doublets have identical couplings gl to the W-boson. A few anomalies observed in semileptonic B meson decays [1] seem to challenge this principle or require new nonuniversal weak interactions. Lower energy observables where very precise comparison of theory and experiments can be done, currently provide the most precise test of LU [2]. We aim to test muon-tau lepton universality through the ratio (P 1⁄4 π, K) [3,4]
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