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 $\mathcal{B}(K^+ \rightarrow π^+ νν)$ from NA62 puts already some tension in the model, while the present limits on $\mathcal{B}(K_L \rightarrow μ^+ μ^-)$ and $μ\to e$ conversion in nuclei can be saturated. Relaxing instead the flavor assumption we study what values for $\mathcal{B}(K^+ \rightarrowπ^+ νν)$, as well as for $\mathcal{B}(K_L \rightarrowπ^0 νν)$ and $\mathcal{B}(K_{L,S} \rightarrowμ^+ μ^-)$, are viable compatibly with all other phenomenological constraints.

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