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

Abstract

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