The construction of a scalar extension to the Standard Model and the search for a heavy scalar at $\sqrt{s}=13$~TeV with the ATLAS detector

Searches for physics beyond the Standard Model (SM) have always been a focus of the particle physics community, more so since the discovery of a Higgs-like boson ($h$) in 2012. These are typically done using either the top-down or bottom-up methodology. In this thesis, a model is constructed in order to successfully explain a variety of anomalous results from Run 1 and 2 of the Large Hadron Collider (LHC), using a hybrid methodology that iterates between theory and experiment. Initially in 2015, a new heavy scalar boson $H$ was postulated to explain anomalies in the Run 1 LHC data. The result of this early study implied that a heavy scalar boson with a mass around 270~GeV, produced through gluon fusion, could explain these anomalies with a significance of $3\sigma$, with a cross section comparable with that of a heavy Higgs boson as well as a dominant $h$-associated decay mode. Theoretical developments of the model then hinted towards the existence of an additional scalar boson $S$, which acted as this associated decay product. The $S$ boson, with a mass of around 150~GeV, was likely to decay to final states comprising of multiple leptons. The culmination of these studies found that the $H\to Sh$ decay mode was dominant and could be searched for in final states with multiple leptons and $b$-tagged jets at the LHC. In 2017 and 2018, using the input from these initial studies, anomalies in the LHC data were successfully explained by the model, as predicted. It was found that the new physics model improved on the SM description of the data at the level of at least $8\sigma$ with just a single degree of freedom. Should these discrepancies not be resolved, this can be considered as indirect evidence for new physics processes at the LHC, since the current SM tools are unable to provide a reasonable explanation for the anomalies. The potential of correlating this result with a mild excess at 245~GeV in the search for $H$ decaying to four leptons in the ATLAS detector is considered, and future potential developments of the model are discussed.