Probing Lepton Flavour Violation with NA64 Experiment

Neutrino oscillations are evidence of flavor violation of neutral leptons, but such a process has not yet been discovered in the sector of charged leptons. The search for flavor violation of charged leptons is one of the most interesting problems in modern physics. One of the experiments aimed at searching for this process, NA64, is a fixed target experiment at CERN. In the article is discussed the possibility of searching for conversion between charged leptons. Preliminary estimates of the sensitivity of NA64 in electron and muon beams are presented. The probability of observing the process in an experiment based on current statistics is also discussed.