Probing Lepton Flavour Universality with $K\to \pi \nu \bar{\nu }$ decays

Abstract

We analyse the rare processes $K\to \pi \nu \bar{\nu }$ in view of the recent hints of violations of Lepton Flavour Universality (LFU) observed in B meson decays. If, as suggested by present data, the new interactions responsible for LFU violations couple mainly to the third generation of left-handed fermions, $K\to \pi \nu \bar{\nu }$ decays turn out to be particularly interesting: these are the only kaon decays with third-generation leptons (the $\tau$ neutrinos) in the final state. In order to relate B-physics anomalies and K decays we adopt an Effective Field Theory approach, assuming that the new interactions satisfy an approximate $U(2{)}_q\times U(2{)}_{\ell }$ flavour symmetry. In this framework we show that O(1) deviations from the Standard Model predictions in $K\to \pi \nu \bar{\nu }$ branching ratios, closely correlated to similar effects in $B\to K^{(\ast )}\nu \bar{\nu }$, are naturally expected. The correlation of $\mathcal{B}(K\to \pi \nu \bar{\nu })$, $\mathcal{B}(B\to K^{(\ast )}\nu \bar{\nu })$, and the LFU violations in B decays would provide a very valuable tool to shed more light on this interesting phenomenon.

arXiv comment11 pages, 2 figures

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