Experimental study of the rare decays ${\mathit{K}}_{\mathit{L}}^0$→μe, ${\mathit{K}}_{\mathit{L}}^0$→ee, ${\mathit{K}}_{\mathit{L}}^0$→μμ, and ${\mathit{K}}_{\mathit{L}}^0$→eeee

An experiment to search for the ${\mathit{K}}_{\mathit{L}}^0$→μe and ${\mathit{K}}_{\mathit{L}}^0$→ee decays and to measure the branching ratio of the ${\mathit{K}}_{\mathit{L}}^0$→μμ decay was performed at the KEK 12-GeV Proton Synchrotron. The single-event sensitivity of the present experiment for these channels was around 4×${10}^{\mathrm{-}11}$. No event was observed in the fiducial region for the ${\mathit{K}}_{\mathit{L}}^0$→μe decay and one event, which could not be distinguished from the background, was observed in the fiducial region for the ${\mathit{K}}_{\mathit{L}}^0$→ee decay. The obtained upper limits on the branching ratios at 90% confidence level were B(${\mathit{K}}_{\mathit{L}}^0$→μe)<9.4×${10}^{\mathrm{-}11}$ and B(${\mathit{K}}_{\mathit{L}}^0$→ee)<1.6×${10}^{\mathrm{-}10}$. The branching ratio of the ${\mathit{K}}_{\mathit{L}}^0$→μμ decay was obtained to be [7.9±0.6 (stat ±0.2 (syst)]×${10}^{\mathrm{-}9}$ based on 179 events in the fiducial region. Using 18 events with the effective mass ${\mathit{M}}_{\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$>470 MeV /${\mathrm{c}}^2$ in the ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ sample for the ${\mathit{K}}_{\mathit{L}}^0$→ee decay search, the branching ratio of the ${\mathit{K}}_{\mathit{L}}^0$→${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ decay was estimated to be [6±2 (stat) ±1 (syst)]×${10}^{\mathrm{-}8}$ for ${\mathit{M}}_{\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$>470 MeV/${\mathit{c}}^2$ and [7±3 (stat)±2(syst)]×${10}^{\mathrm{-}8}$ for ${\mathit{M}}_{\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$>480 MeV/${\mathit{c}}^2$.