Explaining the $B_{d,s}\rightarrow {K^{(*)}\bar K^{(*)}}$ non-leptonic puzzle and charged-current $B$-anomalies via scalar leptoquarks

Abstract

We present a model based on $S_1$ scalar leptoquarks to solve the tension observed in the recently proposed non-leptonic optimized observables $L_{K^{*} \bar{K}^{*}}$ and $L_{K \bar{K}}$. These observables are constructed as ratios of U-spin related decays based on $B_{d,s}^0\rightarrow {K^{(*)0}\bar K^{(*)0}}$. The model gives a one-loop contribution to the Wilson coefficient of the chromomagnetic dipole operator needed to explain the tension in both non-leptonic observables, while naturally avoiding large contributions to the corresponding electromagnetic dipoles. The necessary chiral enhancement comes from an $O(1)$ Yukawa coupling with a TeV-scale right-handed neutrino running in the loop. We endow the model with a $U(2)$ flavor symmetry, necessary to protect light-family flavor observables that otherwise would be in tension. Furthermore, we show that the same $S_1$ scalar leptoquark is capable of simultaneously explaining the hints of lepton flavor universality violation observed in charged-current $B$-decays. The model therefore provides a potential link between two puzzles in $B$-physics and TeV-scale neutrino mass generation. Finally, the combined explanation of the $B$-physics puzzles unavoidably results in an enhancement of $\mathcal{B}(B\rightarrow K \nu \bar \nu)$, yielding a value close to present bounds.