Radiative corrections to $\ddot{I}„\to \ddot{I}€(K)\hat{I}{½}_{\ddot{I}}„[{\hat{I}}^3]$: a reliable new physics test

Abstract

The ratios $R_{\ddot{I}„/P}\equiv \hat{I}“(\ddot{I}„\to P\hat{I}{½}_{\ddot{I}}„[{\hat{I}}^3])/\hat{I}“(P\to \hat{I}¼\hat{I}{½}_{\hat{I}}¼[{\hat{I}}^3])$ ($P=\ddot{I}€,K$) provide sensitive tests of lepton universality $\left|g_{\ddot{I}}„/g_{\hat{I}}¼\right|=1$ and are a useful tool for new physics searches. The radiative corrections to $R_{\ddot{I}„/P}$ 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 $\hat{I}´R_{\ddot{I}„/\ddot{I}€}=(0.18\pm 0.57)\%$ and $\hat{I}´R_{\ddot{I}„/K}=(0.97\pm 0.58)\%$, which imply ${\left|g_{\ddot{I}}„/g_{\hat{I}}¼\right|}_{\ddot{I}}€=0.9964\pm 0.0038$ and ${\left|g_{\ddot{I}}„/g_{\hat{I}}¼\right|}_K=0.9857\pm 0.0078$, compatible with and at $1.8\ddot{I}ƒ$ of lepton universality, respectively. We test unitarity and bind non-standard effective interactions with the $\ddot{I}„\to P\hat{I}{½}_{\ddot{I}}„[{\hat{I}}^3]$ decays.

5 pages, minor rewording. Accepted for publication as a Letter in Physical Review D