Estimation of the electron charge misidentification background for the same-sign $WW$ measurement with the ATLAS detector at $\sqrt{s}=$ 13 TeV

Electron charge misidentification was the largest source of background in the $ee$ decay channel, and the third-largest background source in the all-inclusive leptonic $\ell\ell$ channel in the ATLAS measurement of electroweak production of same-sign $ W $ boson pairs in proton-proton collisions, made using the partial Run 2 dataset collected during 2015-2016. In this thesis, the sources of the charge misidentification are studied. The contribution of this background to the measurement of the electroweak production of two same-sign $ W $ bosons is then estimated using a data-driven method, based on the full Run 2 dataset, corresponding to an integrated luminosity of 139 fb$^{-1}$ and a center-of-mass energy of $\sqrt{s}=\text{13 TeV}$. The Electron Charge ID Selector, a tool based on a boosted decision tree developed by the Egamma Combined Performance group of the ATLAS Collaboration, is applied to reduce this background. The background contribution in a "$Z$-peak" control region in the $ee$ channel, with the dilepton invariant mass $m_{ee}$ satisfying $|m_{ee} - m_Z| < \text{15 GeV}$, is reduced by a factor of 11. The background yield in the signal region (SR) in the $\ell\ell$ channel is reduced by a factor of 4 and corresponds to $\text{10.3} \pm \text{0.4}\ \text{(stat)}\pm \text{6.7}\ \text{(sys)}$ events using the full Run 2 dataset. To increase the signal yields and to have a unified selection with other decay channels, a possibility for extension of the electron pseudorapidity range in the $ee$ channel to the almost full acceptance of the inner tracking detector ($|\eta|<\text{2.47}$) is checked. In this case, a background yield of $\text{26.2} \pm \text{0.8}\ \text{(stat)}\pm \text{12.2}\ \text{(sys)}$ events is obtained, with a factor of 1.6 signal increase in the $ee$ channel using the full Run 2 dataset.