From B-meson anomalies to Kaon physics with scalar leptoquarks

In this work we study possible connections between B-meson anomalies and Kaon physics observables in the context of combined solutions with the singlet and triplet scalar leptoquarks S-1 and S-3. By assuming a flavor structure for the leptoquark couplings dictated by a minimally broken U(2)(5) flavor symmetry we can make a sharp connection between these two classes of observables. We find that the bound on B(K+ -> pi(+)nu nu) from NA62 puts already some tension in the model, while the present limits on B(K-L -> mu(+)mu(-)) and mu -> e conversion in nuclei can be saturated. Relaxing instead the flavor assumption we study what values for B(K+ -> pi(+)nu nu), as well as for B(K-L -> pi(0)nu nu) and B(K-L,K-S -> mu(+)mu(-)), are viable compatibly with all other phenomenological constraints.