Kaon identification and Search for Lepton Number Violation in $K^{\pm}$ decay-in-flight experiments at CERN

A search for the Lepton Number Violating decay $K^{\pm} \to \pi^{\pm} \mu^{\pm} \mu^{\pm}$ has been performed using the data collected by the NA48/2 experiment in 2003 and 2004. The signal event selection, the background rejection, the evaluation of the muon identifcation efficiency and the statistical methods used for the data interpretation are presented. Based on $1.8 \times 10 ^{11}$ kaon decays in the fiducial volume and using several models for the signal, upper limits for the branching fraction B($K^{\pm} \to \pi^{\pm} \mu^{\pm} \mu^{\pm}$) of the order of $10^{-10} $ have been obtained for 90%, 95% and 99% confidence levels, improving the previous best limit by one order of magnitude. The Cherenkov differential counter used for kaon identification in the NA62 experiment, equipped with approximately 30% of the photo-detectors, was installed and tested during a Technical Run in 2012. The counter's ability of distinguishing between kaons and pions has been validated via pressure scan procedure. The data collected have been used for evaluating the kaon identification efficiency and time resolution. The extrapolation to the full-sized detector has been also estimated.