Lepton universality tests with leptonic kaon decays

The NA62 experiment at CERN aims to use rare kaon decays to search for new phenomena beyond the Standard Model. During the current short term phase (data taking completed in years 2007-8), the ratio $R_K = \Gamma(K^+ \rightarrow e \nu_e (\gamma)) / \Gamma(K^+ \rightarrow \mu \nu_{\mu} (\gamma))$ of leptonic decay rates is studied, which tests the structure of weak interactions and lepton flavour universality. In this paper, the $R_K$ analysis is summarized, and the preliminary result is discussed, based on 59963 $K^+ \rightarrow e \nu_e$ candidates collected in 2007.