Enhanced CP asymmetries in B→Kμ${}^{+}$μ${}^{\text{â}}\text{ˆ}\text{’}$

We show that the current values of R${}_K^{exp}$ and R${}_{K^{\text{â}}\text{ˆ}\text{—}}^{exp}$ can be accommodated by allowing a nonzero New Physics coupling δC${}_9^{\mu \mu }$ to be complex, both in the scenario in which only δC${}_9^{\mu \mu }$ is affected, and in the scenario with complex δC${}_{9,10}^{\mu \mu }$ satisfying δC${}_9^{\mu \mu }$=−δC${}_{10}^{\mu \mu }$. A presence of the weak CP-violating phase can then be tested by measuring the CP-asymmetry, A${}_{CP}$. We show that this asymmetry is enhanced around the peak of each $c\overline{c}$-resonance, and in fact more pronounced in the close vicinity of J/ψ and ψ(2S). Therefore, measuring A${}_{CP}$ 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.