Probing lepton-flavour universality with K→πνν¯ decays

We analyse the rare processes K→πνν¯ 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→πνν¯ decays turn out to be particularly interesting: these are the only kaon decays with third-generation leptons (the τ 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×U(2)ℓ flavour symmetry. In this framework we show that O(1) deviations from the Standard Model predictions in K→πνν¯ branching ratios, closely correlated to similar effects in B→K(∗)νν¯, are naturally expected. The correlation of B(K→πνν¯), B(B→K(∗)νν¯), and the LFU violations in B decays would provide a very valuable tool to shed more light on this interesting phenomenon.