Impact of indirect CP violation on Br(KS → μ+μ−)ℓ=0

The decay $K_S \to (\mu^+\mu^-)_{\ell=0}$, with the final muon pair in an angular-momentum zero state, is a sensitive probe of short-distance physics. It has recently been shown how to extract this branching ratio from neutral kaon data. We point out that impact indirect CP violation on standard-model prediction mode, while nominally order $|\epsilon_K| \sim 10^{-3}$, enhanced by large amplitude and leads shift Br$(K_S \mu^+\mu^-)_{\ell=0}$ few percent, depending size relative phase can be extracted also update contribution.