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.