Explorations of W Boson-Photon Scattering and Higgs-Scalar Resonance Production with the ATLAS Detector

The Standard Model provides a comprehensive theoretical framework for accurately describing fundamental particles and their interactions, including electromagnetic, weak, and strong interactions. The spontaneous breaking of electroweak symmetry through the Higgs mechanism explains the origin of particle masses, endowing the W and Z bosons with mass while ensuring that the photon remains massless. Vector Boson Scattering (VBS), as a key avenue for indirectly probing electroweak symmetry breaking, offers an opportunity for new physics searches through its sensitivity to quartic gauge boson couplings. The study of Higgs boson self-coupling and its interactions with other new particles is crucial for further understanding the completeness of the Higgs mechanism. The di-Higgs model and extended Higgs models provide the theoretical foundation for this research, facilitating the exploration of new physics phenomena and further revealing the complex nature of the Higgs boson. The Large Hadron Collider (LHC) is the world's largest particle physics experiment platform, which, in 2012, enabled the discovery of the Higgs boson through the ATLAS (A Toroidal LHC Apparatus) and CMS (Compact Muon Solenoid) detectors, completing the final piece of the Standard Model. As one of the two largest multipurpose experiments at the LHC, the ATLAS detector plays a significant role not only in the search for new physics phenomena but also in the precise measurement of Standard Model processes. The detector consists of the inner detector, electromagnetic calorimeter, hadronic calorimeter, and muon spectrometer, with exceptional capabilities in electron, photon, muon, and jet reconstruction, allowing it to maintain high precision in a complex collision environment. The measurement of missing transverse momentum ($E_T^{miss}$) has been enhanced through finer energy calibration and improved background suppression techniques, improving the detection of neutrinos and other weakly interacting particles. Monte Carlo simulation techniques are essential in the ATLAS experiment, ensuring accurate comparisons between experimental data and theoretical predictions, thereby supporting the robustness of the physical analyses. This thesis uses 140 $\text{fb}^{-1}$ of data collected by the ATLAS detector at $\sqrt{s} = 13$ TeV from 2015 to 2018 and presents the first observation within the ATLAS collaboration of the electroweak production of a W boson and a photon in association with two jets, along with a differential cross-section measurement. The measurement is conducted in an enhanced VBS phase space to improve sensitivity to WW$\gamma\gamma$ couplings. The process demonstrates high sensitivity to quartic gauge boson couplings through the vector boson scattering mechanism, providing a stringent experimental test for electroweak symmetry breaking in the Standard Model. The event selection requires one electron or muon, missing transverse momentum, at least one photon, and two jets. The use of neural network-based multivariate techniques significantly improves the discrimination between electroweak $W\gamma jj$ production and the background. Complex and diverse background estimation is a major challenge in this analysis, with data-driven methods used to accurately estimate and analyze errors for fake photons from mis-reconstructed jets, electrons, or muons, as well as background from pile-up vertices. After combining theoretical and experimental uncertainties, the observed significance of the electroweak $W\gamma jj$ process exceeds 6 standard deviations, consistent with the expected significance of 6.3 standard deviations. The fiducial and differential cross sections are measured in a fiducial phase space close to the detector acceptance, with results that are consistent within uncertainties with leading-order Standard Model predictions from \textsc{MadGraph5+Pythia8} and \textsc{Sherpa}. These results are used to constrain new physics effects based on effective field theory (EFT). This result is utilized to constrain new physics effects based on effective field theory, revealing that $p_T^{jj}$) is the observable most sensitive to tensor operators, while $p_T^l$ is the observable most sensitive to mixed scalar operators. Notably, the constraints on the $f_{T3}$ and $f_{T4}$ operators represent the first results published at the LHC. The second physics analysis in this thesis is a search for a resonance decaying into a scalar particle and a Higgs boson in the final state with two bottom quarks and two photons, specifically investigating the process $X \to S(\to b\bar{b})H(\to \gamma\gamma)$. This analysis is also based on 140 $\text{fb}^{-1}$ of data collected by the ATLAS detector at $\sqrt{s} = 13$ TeV, covering the $X$ mass range from 170 GeV to 1000 GeV and the $S$ mass range from 15 GeV to 500 GeV. Due to the boosted $S$ particle decaying into two $b$ quarks, often reconstructed as a single $b$ quark, the analysis is divided into two categories: 2 $b$-tagged and 1 $b$-tagged, corresponding to the reconstruction of two and one $b$ quarks, respectively. High-performance parameterised neural networks enhance signal purity, and in the 2 $b$-tagged category, interpolation techniques based on Lorentz transformations enable continuous sensitivity measurements across the $(m_X, m_S)$ plane, optimizing the signal-to-background ratio across different parameter spaces. Although no significant excess over the background expectation is observed, upper limits on the product of the signal cross-section and branching ratio at each mass point were set by the analysis at the 95\% confidence level, ranging from 39 fb to 0.09 fb. The most significant deviation occurs at $(m_X, m_S) = (575, 200)$ GeV, with a local significance of 3.5 standard deviations and a global significance of 2.0 standard deviations. For the $(m_X, m_S) = (650, 90)$ GeV mass point, CMS previously reported a local (global) significance of 3.8 (below 2.8) standard deviations for an excess, while this analysis shows consistency with the background-only hypothesis and set an upper limit of 0.2 fb on the signal cross-section at 95% CL.