Measurement of the branching ratio for the rare decay ${\mathit{K}}_{\mathit{L}}^0$→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$

We have measured the branching ratio for ${\mathit{K}}_{\mathit{L}}^0$→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$ using our full data set obtained during running periods in 1988, 1989, and 1990. The total number of ${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$ candidates after a background subtraction is 707, which represents the largest sample to date of this rare decay mode. Our result is B(${\mathit{K}}_{\mathit{L}}^0$→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$)=(6.86±0.37)×${10}^{\mathrm{-}9}$, which is consistent with earlier results and very near the unitarity bound. The upper limit on B(${\mathit{K}}_{\mathit{L}}^0$→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$) is used to set an upper limit on the real part of the amplitude scrA(${\mathit{K}}_{\mathit{L}}^0$→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$); this is subsequently used to constrain the top quark mass ${\mathit{m}}_{\mathit{t}}$ and the Wolfenstein parameter ρ of the CKM matrix.