CP Violation in $B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ Decays: New Opportunities in the High-Precision Era

Experimental data on rare $B$-meson decays indicate deviations from Standard Model predictions. In studies of these decays, possible new sources of CP violation are often neglected. We discuss CP violation in the rare $B$-meson decays $B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}(\mathrm{\ell }=\mu ,e)$ and point to two phenomena that arise when new sources of CP violation are included. First, the Wilson coefficients $C_{9\mathrm{\ell }}$ and $C_{10\mathrm{\ell }}$ become complex, and we show how we can extract their values from measurements of direct and mixing-induced CP asymmetries. Second, new sources of CP violation can generate nontrivial lepton flavour universality violation. Such a violation is usually measured through ratios like $R_K$ and $R_{K^{\ast }}$, but we show that measuring only these ratios leaves a large parameter space unexplored. These results bring exciting opportunities to reveal New Physics effects in the high-precision era.