Radiative corrections to $\tau \to \pi (K){\nu }_{\tau }[\gamma ]$: A reliable new physics test

The ratios $R_{\tau /P}\equiv \mathrm{\Gamma }(\tau \to P{\nu }_{\tau }[\gamma ])/\mathrm{\Gamma }(P\to \mu {\nu }_{\mu }[\gamma ])$ ($P=\pi$, $K$) provide sensitive tests of lepton universality $|g_{\tau }/g_{\mu }|=1$ 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 ${|g_{\tau }/g_{\mu }|}_{\pi }=0.9964\pm 0.0038$ and ${|g_{\tau }/g_{\mu }|}_K=0.9857\pm 0.0078$, compatible with and at $1.8\sigma$ of lepton universality, respectively. We test unitarity and bind nonstandard effective interactions with the $\tau \to P{\nu }_{\tau }[\gamma ]$ decays.

Figure 1

Feynman diagram corresponding to the structure dependent contributions to $\tau \to P{\nu }_{\tau }$ decays. The gray shaded box stands for the form factors.