From B-meson anomalies to Kaon physics with scalar leptoquarks

Abstract

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 $\mathcal{B}(K^{+}\to \ddot{I}{€}^{+}\hat{I}½\hat{I}½)$ from NA62 puts already some tension in the model, while the present limits on $\mathcal{B}(K_L\to \hat{I}{¼}^{+}\hat{I}{¼}^{-})$ and $\hat{I}¼\to e$ conversion in nuclei can be saturated. Relaxing instead the flavor assumption we study what values for $\mathcal{B}(K^{+}\to \ddot{I}{€}^{+}\hat{I}½\hat{I}½)$, as well as for $\mathcal{B}(K_L\to \ddot{I}{€}^0\hat{I}½\hat{I}½)$ and $\mathcal{B}(K_{L,S}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-})$, are viable compatibly with all other phenomenological constraints.

40 pages, 11 figures; v2: references updated