Precise measurement of semileptonic kaon decay rates with NA62

An important tool for exploring the limits of the Standard Model is the measurement of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix with a very high precision. One of the possible unitarity relations is vertical stroke V_ud vertical stroke ²+ vertical stroke V_us vertical stroke ²+ vertical stroke V_ub vertical stroke ²=1 whose uncertainty is dominated by the precision on vertical stroke V_us vertical stroke. The vertical stroke V_us vertical stroke element is accessible by measuring the decay rate of semileptonic decays of the kaon (K_l3 = K^± → π⁰l^±ν with l = e,μ). These decay rates can be determined both in experiment and in theory to a very high degree of accuracy. Secondly, a stringent constraint can be given on new physics by measuring the ratio R = Γ(K_μ3)/Γ(K_e3), which is used to test the lepton universality. The NA62 collaboration acquired data in 2007 at the CERN SPS. This talk will give an overview of the decay rate analysis of the collected data. The selection of signal decays, suppression of background decays, comparison between data and Monte Carlo simulation, and a preliminary result is discussed.