Study of the $K^{+} \to e^{+} \nu_{e}\gamma$ decay with the NA62 experiment

The present thesis is focused on the measurement of the form factors of the K + → e + ν e γ decay ( K e 2 γ ) with data collected by the NA62 experiment in 2007 during a preliminary phase of data taking, dedicated to a precision test of lepton flavour universality. For this phase, the NA62 collaboration used the pre-existing apparatus of the NA48/2 experi- ment. The measurement of the form factors is a test for the e ff ective theories of strong interaction at low energies as the Chiral Perturbation Theory (ChPT) and the Light Front Quark Model (LFQM). The only kinematic configuration accessible to the analysis is the structure-dependent configuration in which the photon is emitted preferentially with positive helicity (SD + term). The measurement of the K e 2 γ form factors is obtained by analysing 11170 recon- structed K e 2 γ ( SD + ) candidates with 4% background contamination, about ten times the statistics collected by earlier experiments. The final result of the analysis, assuming ChPT at O ( p 6 ) ,is: F V (0) + F A (0) = 0 . 127 ± 0 . 002 stat ± 0 . 010 syst λ =0 . 60 ± 0 . 05 stat ± 0 . 39 syst The LFQM prediction of the form factors was also tested but it was found to be completely inconsistent with data.