Quantum field theory provides the foundation for understanding fundamental interactions through gauge theories. While the Standard Model successfully describes numerous subatomic processes, it remains incomplete, lacking explanations for gravity, dark matter, and other open questions, driving the search for new physics.

This thesis presents two analyses using datasets from the ATLAS experiment, including the full Run-2 and partial Run-3 proton–proton collision data. The electroweak ttWj (ttWj EW) analysis studies tW scattering at a centre-of-mass energy of 13 TeV, utilising an integrated luminosity of 140.1 fb^-1. Background contributions are constrained through data-driven methods. This work provides the first experimental direct constraints on the ttWj EW process, establishing an observed (expected) upper limit at the 95% confidence level (CL_s) of 250 (232) fb, compared to the Standard Model prediction of 47.7 fb. Furthermore, a Standard Model Effective Field Theory (SMEFT) interpretation constrains the two dimension-6 operators relevant to ttWj EW production, highlighting the interplay between ttWj EW and ttZ processes in resolving parameter space degeneracies.

The X → SH → bbγγ search explores a new scalar boson X decaying into a Higgs boson H and a lighter scalar S, with S → bb and H → γγ. Combining the ATLAS Run-2 and partial Run-3 datasets, the analysis sets expected 95% upper limits (CL_s) on the signal strength ranging from 0.09 to 7.6 - representing a 19 ~ 60% improvement over the ATLAS Run-2 results published in 2024 (JHEP 11 (2024) 047). This enhancement is primarily driven by additional Run-3 data and an improved b-tagging algorithm, particularly benefiting the low-mass region.

With the ongoing ATLAS Run-3 and the upcoming High-Luminosity LHC, increasing data availability will improve precision tests of the Standard Model and sensitivity to new physics. In particular, SMEFT studies will benefit from higher statistics, allowing for stronger constraints on Higgs, fermion, and vector boson interactions.