Measurements of charged kaon semileptonic decay branching fractions K±-> π0μ±ν and K±-> π0e±ν and their ratio

Measured ratios of decay rates for R-Ke3/K2 pi, RK mu 3/K2 pi and R-K mu 3/Ke3 are presented. These measurements are based on K-+/- decays collected in a dedicated run in 2003 by the NA48/2 experiment at CERN. The results obtained are R-Ke3/K2 pi = 0.2496 +/- 0.0009( stat) +/- 0.0004(syst) and R-K mu 3/K2 pi = 0.1637 +/- 0.0006( stat) +/- 0.0003(syst). Using the PDG average for the K-+/-->pi(+/-)pi(0) normalisation mode, both values are found to be larger than the current values given by the particle data book and lead to a larger magnitude of the vertical bar V-us vertical bar CKM element than previously accepted. When combined with the latest particle data book value of vertical bar V-ud vertical bar, the result is in agreement with unitarity of the CKM matrix. In addition, a new measured value of R-K mu 3/Ke3 = 0.656 +/- 0.003( stat) +/- 0.001( syst) is compared to the semi-empirical predictions based on the latest form factor measurements.