Search for new phenomena using three-photon final states in data collected with the ATLAS detector at the Large Hadron Collider

This thesis presents a search for new phenomena using three high-$p_T$ photons in the final state. In some Beyond the Standard Model (BSM) theories, a vector boson, $Z^\prime$, can decay to a pseudoscalar, $a$, and a photon, $\gamma$. The pseudoscalar can then decay into two photons: $Z^\prime \rightarrow a \gamma \rightarrow \gamma \gamma \, \gamma$. In addition, the Standard Model (SM) $Z$ boson can rarely decay into three photons via fermion and boson loops. The branching ratio for this decay is extremely small (order of $10^{-10}$) in the SM, and has not yet been observed, with the best limits for this branching ratio being of order $10^{-6}$. A secondary goal of this analysis is to search for $Z \rightarrow \gamma \gamma \gamma$ as a test of the SM, and if not observed to set a better limit on this branching ratio. The dataset used for this analysis was collected at the CERN Large Hadron Collider (LHC) during the run period from 2015 to 2018. The proton-proton collision center-of-mass energy was 13\,TeV and the corresponding integrated luminosity recorded by the ATLAS detector was $139\,{\rm fb^{-1}}$.