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 bound on $Br(K^+ to pi^+ u u)$ from NA62 puts already some tension in the model, while the present limits on $Br(K_L to mu^+ mu^-)$ and $mu to e$ conversion in nuclei can be saturated. Relaxing instead the flavor assumption we study what values for $Br(K^+ to pi^+ u u)$, as well as for $Br(K_L to pi^0 u u)$ and $Br(K_{L,S} to mu^+ mu^-)$, are viable compatibly with all other phenomenological constraints.
Download