The luminosity measurement at the LHC with the ATLAS experiment: upgrade for the LUCID detector for high luminosity-LHC and Z cross section measurement with early Run3-data for luminosity validation

The knowledge of the luminosity is crucial for measuring the cross sections of all physical processes and provides real-time information about the performance of the accelerator. In this thesis, luminosity will be discussed both from a technical point of view and as one of the main systematic uncertainties in physics analysis. In the first part of this thesis, the measurement of luminosity is discussed, starting with a theoretical overview and introducing various experimental techniques. The focus then shifts to the LUCID detector, the primary luminometer of the ATLAS experiment, used during LHC Run-2 (2015–2018) and Run-3 (2022–present). Given the challenging conditions expected in the High-Luminosity LHC, LUCID requires a complete redesign. Three prototypes of the future LUCID have been installed and are currently under tests to evaluate the performances of the new LUCID using data collected in Run-3. In the second part of the thesis, the measurement of the inclusive Z-boson production cross section at a center-of-mass energy of $\sqrt{s}$ = 13.6 TeV is presented, along with its ratio to the W and $t\Bar{t}$ production cross sections, using early ATLAS Run-3 data. This analysis is among the first conducted at the start of each data-taking period, as it allows for checks on detector calibration, alignment, and luminosity measurement via the Z-counting technique and, in this case, testing theoretical predictions at a new center-of-mass energy.