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 singlet triplet scalar leptoquarks $S_1$ $S_3$. By assuming a flavor structure for leptoquark couplings dictated by minimally broken $U(2)^5$ symmetry can make sharp connection these two classes observables. We find that bound on $\mathcal{B}(K^+ \rightarrow \pi^+ \nu\nu)$ from NA62 puts already some tension model, while present limits $\mathcal{B}(K_L \mu^+ \mu^-)$ $\mu \to e$ conversion nuclei be saturated. Relaxing instead assumption what values \rightarrow\pi^+ \nu\nu)$, as well \rightarrow\pi^0 $\mathcal{B}(K_{L,S} \rightarrow\mu^+ \mu^-)$, are viable compatibly all other phenomenological constraints.