Direct CP Violation in K→μ^{+}μ^{-}

A rare decay K_{L}→μ^{+}μ^{-} has been measured precisely, while a rare decay K_{S}→μ^{+}μ^{-} will be observed by an upgrade of the LHCb experiment. Although both processes are almost CP-conserving decays, we point out that an interference contribution between K_{L} and K_{S} in the kaon beam emerges from a genuine direct CP violation. It is found that the interference contribution can change K_{S}→μ^{+}μ^{-} standard-model predictions at O(60%). We also stress that an unknown sign of A(K_{L}→γγ) can be determined by a measurement of the interference, which can much reduce a theoretical uncertainty of B(K_{L}→μ^{+}μ^{-}). We also investigate the interference in a new physics model, where the ε_{K}^{'}/ε_{K} tension is explained by an additional Z-penguin contribution.