Abstract
We analyse the rare processes Krightarrow 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, Krightarrow 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)_qtimes U(2)_ell flavour symmetry. In this framework we show that O(1) deviations from the Standard Model predictions in Krightarrow pi nu bar{nu } branching ratios, closely correlated to similar effects in Brightarrow K^{(*)}nu bar{nu }, are naturally expected. The correlation of mathcal {B}(K rightarrow pi nu bar{nu }), mathcal {B}(Brightarrow K^{(*)}nu bar{nu }), and the LFU violations in B decays would provide a very valuable tool to shed more light on this interesting phenomenon.
Highlights
The hints of lepton-flavour universality (LFU) violations in semileptonic B decays are among the most interesting deviations from the standard model (SM) reported by experiments in the last few years
A motivated class of models are those based on a U (2)q ×U (2) flavour symmetry acting on the light generations of SM fermions [29,30], that turns out to be quite successful in addressing these anomalies while satisfying all existing bounds [26]
Recent B-physics data hints toward violations of Lepton Flavour Universality in charged- and neutral-current semileptonic processes
Summary
The hints of lepton-flavour universality (LFU) violations in semileptonic B decays are among the most interesting deviations from the standard model (SM) reported by experiments in the last few years. Left-handed four-fermion operators are the most natural candidates to build a connection between anomalies in charged and neutral-current semileptonic processes These observations have led to identify the EFT approach based on the U (2)q ×U (2) flavour symmetry as a convenient framework (both successful and sufficiently general) to analyse B-physics anomalies and discuss possible correlations with other low-energy observables [14,25,26]. NP is directly coupled only to left-handed quark and lepton singlets in flavour space (i.e. only operators containing only q3L or 3L fields are affected by tree-level matching conditions at the NP scale ) Given these assumptions, we can identify only two independent operators of dimension six affected by NP and contributing to semileptonic decays at the tree level, namely the electroweak singlet and triplet current-current interactions,. The overall scale of this operator defines the NP scale , while c13 denotes the ratio between the singlet and triplet Wilson coefficients
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