Observation of the Decay K- -> pi- mu+ mu- and Measurements of the Branching Ratios for K+/- -> pi+/- mu+ mu-

Using data collected with the HyperCP (E871) spectrometer during the 1997 fixed-target run at Fermilab, we report the first observation of the decay K- -> pi- mu+ mu- and new measurements of the branching ratios for K+/- -> pi+/- mu+ mu- . By combining the branching ratios for the K+ and K- decays, we measure the ratio (K+/- -> pi+/- mu+ mu-)/(K+/- -> all) = (9.8 +/- 1.0 +/- 0.5)x10^(-8). The CP asymmetry between the K+ and K- decay modes = -0.02 +/- 0.11 +/- 0.04.