• anomalous magnetic moment
• bdt
• g-2
• lead-lead collisions
• tau

I perform a multi-variate analysis on the data using a BDT algorithm, in order to extract the value of the anomalous magnetic moment of the tau lepton, aτ, and the signal strength through the optimization of both signal selection and background rejection. The aim of this thesis is to test these performances on real data, provided by the ATLAS collaboration, and to compare the limits on aτ with those obtained by ATLAS and by the other experiments of LHC and LEP. The final limits are extracted through profile likelihood fits performed on the pT distribution of the muon or electron from tau decay, using, for the aτ fit, a template morphing technique with different non-zero values of aτ, parameterizing the BSM effects and, for the signal strength fit, the SM fixed value aτ = 0. The data analyzed have been collected from lead-lead collisions taken in 2018 Runs of LHC. The total data corresponds to an integrated luminosity of 1.44 nb−1 with a center of mass energy of 5.02 TeV/n. In particular, the analysis focuses on the process of τ -pair production from photon-photon interactions coming from ultra-peripheral collisions (UPC) of the lead nuclei, as the double photon-lepton vertexes that appear in this process makes it very sensitive to changes in the aτ value.