One-loop determination of $\ddot{I}„\to \ddot{I}€(K)\hat{I}{½}_{\ddot{I}}„[{\hat{I}}^3]$ branching ratios and new physics tests

Abstract

We calculate the ratios $R_{\ddot{I}„/P}\equiv \hat{I}“\left(\ddot{I}„\to P\hat{I}{½}_{\ddot{I}}„[{\hat{I}}^3]\right)/\hat{I}“\left(P\to \hat{I}¼\hat{I}{½}_{\hat{I}}¼[{\hat{I}}^3]\right)$ ($P=\ddot{I}€,K$) 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 $\hat{I}´R_{\ddot{I}„/\ddot{I}€}=(0.18\pm 0.57)\%$ and $\hat{I}´R_{\ddot{I}„/K}=(0.97\pm 0.58)\%$, where the uncertainties are induced fundamentally by the counterterms. We test the lepton universality, obtaining ${\left|g_{\ddot{I}}„/g_{\hat{I}}¼\right|}_{\ddot{I}}€=0.9964\pm 0.0038$ and ${\left|g_{\ddot{I}}„/g_{\hat{I}}¼\right|}_K=0.9857\pm 0.0078$, and analyze the CKM unitarity, getting results at $2.1\ddot{I}ƒ$ and $1.5\ddot{I}ƒ$ from unitarity via $|V_{us}/V_{ud}|$ and $|V_{us}|$, respectively. We also update the search for non-standard interactions in $\ddot{I}„$ decays. As a by-product, we report the theoretical radiative corrections to the $\ddot{I}„\to P\hat{I}{½}_{\ddot{I}}„[{\hat{I}}^3]$ decay rates: $\hat{I}{´}_{\ddot{I}„\ddot{I}€}=-(0.24\pm 0.56)\%$ and $\hat{I}{´}_{\ddot{I}„K}=-(0.15\pm 0.57)\%$.} \maketitle

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