Vertex counting as a luminosity measure at ATLAS and determination of the electroweak Zjj production cross-section

This thesis presents two analyses of data recorded by the ATLAS detector during proton-proton collisions at the LHC. The first is the implementation of a vertex counting algorithm to measure the luminosity recorded by ATLAS during collisions at a centre-of-mass energy of $\sqrt{s}=$8 TeV in 2012. This comprises a Monte Carlo closure test for validation of the method and its corrections, the calibration of the method using the van der Meer scans performed in 2012 and the application of the method to physics runs. It also includes tests of the internal and external consistency of the algorithm and the potential to use this algorithm to measure the luminosity of data collected during proton-proton collisions at $\sqrt{s}=$13 TeV. \par The second analysis is the measurement of the inclusive and purely electroweak production of dijets in association with a $Z$ boson, performed using the 3.2 $\text{fb}^{-1}$ of data collected during collisions at a centre-of-mass energy of $\sqrt{s}=$13 TeV in 2015. Cross-section measurements are presented for five fiducial regions, each of which has a different sensitivity to the electroweak component of the $Zjj$ production. Data and Monte Carlo predictions are compared and found to be in reasonable agreement for most cases. The electroweak $Zjj$ production cross-section is then extracted in a fiducial region where this contribution is enhanced. This measurement is also in good agreement with the Monte Carlo prediction. These first 13 TeV measurements will set the scene for studies of weak boson fusion, both within the Standard Model and in new phenomena searches, which will become even more important in Run 2 and the future of the LHC due to the electroweak sector not being as constrained yet, compared to the strong sector, and due to the larger enhancements as a result of a higher $\sqrt{s}$, where electroweak physics can be most easily extracted.