Boosting Sensitivity to $HH\to b\bar{b}\gamma \gamma$ with Graph Neural Networks and XGBoost

In this paper, we explore the use of advanced machine learning (ML) techniques to enhance the sensitivity of double Higgs boson searches in the $HH\to b\bar{b}\gamma \gamma$ decay channel at $\sqrt{s}=$ 13.6 TeV. Two ML models are implemented and compared: a tree-based classifier using XGBoost, and a geometrical-based graph neural network classifier (GNN). We show that the geometrical model outperform the traditional XGBoost classifier improving the expected 95% CL upper limit on the double Higgs boson production cross-section by 28%. Our results are compared to the latest ATLAS experiment results, showing significant improvement of both upper limit and Higgs boson self-coupling (${\kappa }_{\lambda }$) constraints.