An improved description of the $Z$-boson mass lineshape, and a first joint analysis of electroweak parameters and parton distribution functions with the ATLAS experiment at the LHC

The work reported in this thesis is presented in two parts. The first is focused on the study of a newly proposed calibration technique, while the second describes the results of the first combined $m_W$+PDF fits performed in ATLAS. The Liquid Argon electromagnetic calorimeter is calibrated by looking at the mass lineshape of the $Z$-boson in the di-electron channel. Using the event samples corresponding to 2018 measurements, a newly proposed Monte Carlo calibration technique was implemented with the objective of absorbing the remaining disagreement between the mass lineshapes of the measured data and its simulation. The method consists of an electron-by-electron energy resolution correction, parametrised as functions of electron pseudorapidity and transverse momentum. The final fit improved the data-to-MC agreement, improving the $\chi^2$ from 2323 to 122 for 100 degrees of freedom. The same calibration technique was later repeated with special low pile-up runs at $13~\mathrm{TeV}$, studying its impact in the measurement of the mass of the $W$-boson. As part of the minimisation studies implemented for the calibration, a new statistical method was proposed in order to treat discontinuities in a multidimensional $\chi^2$ curve produced by the histogrammed comparison between two samples. The method is based on the parametrisation of the relevant histogram via a continuous functional form, which is used to estimate a $\chi^2$ against the other histogram. This method allows to implement the fit of the 40 parameters used to define the resolution correction. The combined $m_W$ and PDF study aims primarily to determine the correlation between both measurements. The study revolves around the low pile-up inclusive $W$-boson cross sections as a function of lepton transverse momentum ($p_\mathrm{T}^\ell$), used to probe the dependency of $p_\mathrm{T}^\ell$ as a function of $m_W$; for the purpose of this study, pseudodata at $m_W^\mathrm{nom}=80.4~\mathrm{GeV}$ was used instead of real unfolded measurements. The constraining of the PDF part was implemented as an extension of the ATLASpdf21 fit, which only uses ATLAS data (on top of HERA DIS cross sections). Combined studies revealed an important influence of the PDF on the fitted value of $m_W$, leading to shifts of $m_W^\mathrm{fit}$ (with respect to $m_W^\mathrm{nom}$) that depend on the shape of the pseudodata. The final combined $m_W$+PDF fits on pseudodata (which includes all the relevant sources of systematic) retrieved a shift of $\Delta m_W = (-7 \pm 23)~\mathrm{MeV}$ with a global correlation of $\rho_{m_W} \approx 0.39$.