Sterile neutrinos and $R_K$

Abstract

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 $W\ell \nu$ vertices, arising from a non-unitarity 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 $P=K,\pi$. These enhancements are illustrated in the case of the inverse seesaw, 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.

7 pages, 2 figures. Contribution to the proceedings of Discrete 2012

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