First measurement of time-dependent $CP$ violation in the flavor-changing neutral-current decay $B^0\to K_S^0{\mu }^{+}{\mu }^{-}$

A flavor-tagged time-dependent analysis of $B^0\to K_S^0{\mu }^{+}{\mu }^{-}$ decays is performed across the full dimuon mass range excluding the $J\mathrm{/}\psi$ and $\psi (2S)$ resonance regions. The analysis uses proton-proton collision data collected by the LHCb experiment in 2011–2018 at center-of-mass energies of 7, 8 and 13TeV, corresponding to an integrated luminosity of 9$f{b}^{-1}$. The CP violation parameters are determined to be $C=-0.13\pm 0.32\pm 0.04$ and $S=+0.82\pm 0.29\pm 0.05$, where the first uncertainties are statistical and the second are systematic. The results are consistent with the Standard Model prediction. This is the first experimental study of time-dependent CP violation in $b\to s{l}^{+}{l}^{-}$ processes.