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This thesis is focused on the study of the Z -> µ+ µ- process. This process is quite interesting. From the detector performance point of view, it can be used to measure from data muon trigger and reconstruction eﬃciencies. To extract these eﬃciencies, in the past three years I developed and optimized a method, called Tag&Probe, using Monte Carlo simulation. In the past few months, with the ﬁrst ATLAS data, it allowed to measure the muon eﬃciencies from data for the ﬁrst time. A data sample of 1.3 pb^-1 of integrated luminosity has been used and the results have been compared with the MC expectations.
The eﬃciencies estimation is also relevant for the cross-section measurement of all processes involving muons. In fact, when comparing the measured cross-section from data with the theoretical expectations, one has to correct for the detector ineﬃciencies, which at the start-ip are not perfectly reproduced in the simulation. In this thesis, these muon eﬃciencies have been used for a ﬁrst data/MC comparison of the Z -> µ+ µ- cross-section, both inclusive and diﬀerential as a function of the jet multiplicity.