Tree-level lepton universality violation in the presence of sterile neutrinos: impact for $R_K$ and $R_\pi$

TL;DR

This paper explores how sterile neutrinos can cause tree-level violations of lepton universality in light meson decays, potentially explaining deviations in $R_K$ and $R_pi$ within experimental bounds.

Contribution

It introduces a minimal extension of the Standard Model with sterile neutrinos showing a tree-level enhancement of lepton universality violation in meson decays.

Findings

Sterile neutrinos can saturate current bounds on $Delta r_K$ and $Delta r_pi$.

Enhanced deviations are consistent with experimental and observational constraints.

The inverse seesaw model exemplifies these effects.

Abstract

We consider a tree-level enhancement to the violation of lepton flavour universality in light meson decays arising from modified $W \ell \nu$ 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 $R_{P} = \Gamma (P \to e \nu) / \Gamma (P \to \mu \nu)$, with $P=K, \pi$. We illustrate these enhancements in the case of the inverse seesaw model, showing that one can saturate the current experimental bounds on $\Delta r_{K}$ (and $\Delta r_{\pi}$), while in agreement with the different experimental and observational constraints.