CP violation in K → μ⁺μ⁻ with and without time dependence through a tagged analysis

We point out that using current knowledge of BKL0→μ+μ− and BKL0→γγ, one can extract short-distance information from the combined measurement of the time-integrated CP asymmetry, A_CP(K⁰→ μ⁺μ⁻), and of BKS0→μ+μ−. We discuss the interplay between this set of observables, and demonstrate that determining sign[A_CP(K⁰ → μ⁺μ⁻)] would eliminate the discrete ambiguity in the Standard Model prediction for BKL0→μ+μ−. We then move on to feasibility studies within an LHCb-like setup, using both time-integrated and time-dependent information, employing K⁰ and K¯0 tagging methods. We find that, within an optimistic scenario, the short-distance amplitude, proportional to the CKM parameter combination ∣A2λ5η¯∣, could be constrained by LHCb at the level of about 35% of its Standard Model value, and the discrete ambiguity in BKL0→μ+μ−SM could be resolved at more than 3σ by the end of the high luminosity LHC.