Sterile neutrinos and $R_K$

We study the violation of lepton flavour universality in light meson decays due to the presence of non-zero mixings between the active neutrinos with new sterile states. The modified $W \ell ν$ vertices, arising from a non-unitarity 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 $P=K, π$. These enhancements are illustrated in the case of the inverse seesaw, 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.

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