FASER tracker performance and electron energy resolution in the FASER$\nu$ pilot detector

In collider experiments, very light particles are produced in the far-forward direction with small angle relative to the beam axis and can travel a long distance before decaying. The ForwArd Search ExpeRiment (FASER) is aptly located 480 m downstream from the ATLAS interaction point where background is minimal, so optimally positioned to detect very light new particles. Such particles are likely to decay in FASER to two particles, so two-track vertexing can be used to detect these particles. There is an unexplored energy region 350 GeV - 6 TeV in which the neutrino-nucleon charged current cross-section is not yet known. The FASER$\nu$ emulsion detector, positioned just upstream of FASER, will detect collider-produced neutrinos for the very first time. In addition, the interface detector enables track matching between the FASER spectrometer and the FASER$\nu$ emulsion detector, which enables separate cross section measurements for mu neutrinos and antineutrinos. For electron neutrinos, the outgoing electron will initiate an electromagnetic shower, whose profile characteristics will be used to reconstruct the electron's energy. The FASER$\nu$ pilot detector was installed in the TI18 maintenance tunnel in 2018 and collected $12.2\,\mathrm{fb}^{-1}$ of data, mainly from muons originating at the ATLAS IP. These muons initiate knock-on electron EM showers. By clustering these showers and reconstructing their energies, the muon energy spectrum can be validated, as well as the procedure for reconstructing $\nu_e$ energy in FASER$\nu$. This thesis studies performance at simulation level as well as data analysis. The FASER tracker performance is studied. For the FASER$\nu$ emulsion detector, the electron seeding and clustering algorithms are motivated and developed, and the electron energy resolution is presented. For the FASER$\nu$ pilot run, the validated electron clustering algorithm is run on the data samples in the last 29 layers of the FASER$\nu$ pilot detector and the results are compared with the equivalent simulation samples.