Search for New Heavy Gauge Bosons in $\sqrt{s}=13$~TeV $pp$ Collisions with the ATLAS Detector

In this thesis, the search for a new heavy charged gauge boson, namely the $W^{\prime}$, in the context of the Sequential Standard Model is described. The study presented here focuses on $ W^{\prime}$ decays to an electron and a neutrino. The analysis utilises 36.1~fb\textsuperscript{-1} of $\sqrt{s} = 13$~TeV proton-proton ($pp$) collision data recorded using the ATLAS detector over the 2015 and 2016 data taking periods at the Large Hadron Collider at CERN. The transverse mass, $m_{T}$, is used as the search variable and is analysed over the region $150 < m_{T}< 6000$~GeV. The $ m_{T}$ spectrum for selected $ W^{\prime}$ candidates is compared to the Standard Model expectation, which is quantified using a combination of simulated Standard Model predictions with state-of-the-art theory corrections, and data-driven methods. No significant excess is observed above the Standard Model, therefore statistical techniques are adopted in order to obtain limits on the production and decay of this new gauge boson. A frequentist framework widely used in the ATLAS community is adapted for the statistical analysis presented here, in a departure from the Bayesian tools historically used for this analysis. Frequentist tools are used to set a 95\% CL lower limit on the $ W^{\prime}_{SSM}$ transverse mass of 5.1~TeV. \par A novel reinterpretation of $ W^{\prime}\rightarrow\ell\ell$ and $ Z^{\prime}\rightarrow\ell\nu$ results in the context of a Heavy Vector Triplet model is also presented. Using the newly adapted frequentist statistical tools, combined $V^{\prime}\rightarrow\ell\ell/\ell\nu$ resonances with masses below 4.67~TeV are excluded at 95\%~CL. A full combination of these results with those obtained from searches for diboson resonances ($VV+VH$) is described, with final two-dimensional limits set in two coupling planes (based on the couplings to fermions and the Higgs boson). The resulting exclusion limits are compared to indirect limits from various EW fits (including LEP), proving to provide more stringent constraints over the majority of the tested parameter space.