Enhanced CP asymmetries in $B \rightarrow K \mu ^+ \mu ^-$
Résumé
We show that the current values of $R_K^\mathrm {exp}$ and $R_{K^*}^\mathrm {exp}$ can be accommodated by allowing a nonzero New Physics coupling $\delta C_9^{\mu \mu }$ to be complex, both in the scenario in which only $\delta C_9^{\mu \mu }$ is affected, and in the scenario with complex $\delta C_{9,10}^{\mu \mu }$ satisfying $\delta C_{9}^{\mu \mu }=-\delta C_{10}^{\mu \mu }$. A presence of the weak CP-violating phase can then be tested by measuring the CP-asymmetry, $\mathcal {A}_\mathrm {CP}$. We show that this asymmetry is enhanced around the peak of each $c\bar{c}$-resonance, and in fact more pronounced in the close vicinity of $J/\psi $ and $\psi (2S)$. Therefore, measuring $\mathcal {A}_\mathrm {CP}$ before and after the resonances’ peak could be revelatory of the CP-violation that originates from beyond the Standard Model, or to be a significant constrain when building a realistic scenario of New Physics.