Tree-level lepton universality violation in the presence of sterile neutrinos: impact for $R_K$ and $R_{\ddot{I}}€$

Abstract

We consider a tree-level enhancement to the violation of lepton flavour universality in light meson decays arising from modified $W\ell \hat{I}½$ couplings in the standard model minimally extended by sterile neutrinos. Due to the presence of additional mixings between the active (left-handed) neutrinos and the new sterile states, the deviation from unitarity of the leptonic mixing matrix intervening in charged currents might lead to a tree-level enhancement of $R_P=\hat{I}“(P\to e\hat{I}½)/\hat{I}“(P\to \hat{I}¼\hat{I}½)$, with $P=K,\ddot{I}€$. We illustrate these enhancements in the case of the inverse seesaw model, showing that one can saturate the current experimental bounds on $\hat{I}”r_K$ (and $\hat{I}”r_{\ddot{I}}€$), while in agreement with the different experimental and observational constraints.

9 pages, 2 eps figures