NA48/2 final results on charged semileptonic kaon decays and $|V_{(us)}|$, NA48 measurements of the $K\mu3$ form factors from $K_{L}$ decays

Measured ratios of decay rates for $\Re_{Ke3/K2π}, \Re_{K\mu3/K2\pi}$ and $\Re_{K\mu 3/Ke3}$ are presented, based on $K^{\pm}$ decays collected in a dedicated run in 2003 by the NA48/2 experiment at CERN. The results obtained are $\Re_{Ke3/K2\pi} = 0.2470 \pm 0.0009_{stat} \pm 0.0004_{syst}$ and $\Re_{K\mu3/K2\pi} = 0.1637 \pm 0.0006_{stat} \pm 0.0003_{syst}$. Using the PDG average for the $K^{\pm} \rightarrow \pi^{\pm}\pi^{0}$ normalisation mode, both values are found to be larger than the current values given by the Particle Data Book [1] and lead to a larger magnitude of the $|V_{us}|$ element in the CabibboKobayashi-Maskawa (CKM) matrix than previously accepted. When combined with the latest Particle Data Book value of $|V_{ud}|$[1], the result is in agreement with unitarity of the CKM matrix. In addition, a new measured value of $Re_{K\mu3/K2\pi} = 0.663 \pm 0.003_{stat} \pm 0.001_{syst}$ is compared to the semi-empirical predictions based on the latest form factor measurements. The $K\mu 3$ form factors have been measured from a sample of $K_{L}$ decays in a dedicated run in 1999 by the NA48 experiment at CERN. Studying the Dalitz plot density, using the linear form factor approximation, a measurement was made of $\lambda_{+} = (26.7 \pm 0.6_{stat} \pm 0.8_{sys}) \times 10^{−3}$ and $\lambda_{0} = (11.7 \pm 0.7_{stat} \pm 1.0_{sys} \times 10^{−3}$ . Measurements were also made using the quadratic parameterisation, the pole parameterisation and the dispersive parameterisation. The results of all parameterisations will be presented.