Deep Learning to Improve the Sensitivity of Di-Higgs Searches in the $4b$ Channel

The study of di-Higgs events, both resonant and non-resonant, plays a crucial role in understanding the fundamental interactions of the Higgs boson. In this work we consider di-Higgs events decaying into four $b$-quarks and propose to improve the experimental sensitivity by utilizing a novel machine learning algorithm known as Symmetry Preserving Attention Network (\textsc{Spa-Net}) -- a neural network structure whose architecture is designed to incorporate the inherent symmetries in particle reconstruction tasks. We demonstrate that the \textsc{Spa-Net} can enhance the experimental reach over baseline methods such as the cut-based and the Deep Neural Networks (DNN)-based analyses. At the Large Hadron Collider, with a 14-TeV centre-of-mass energy and an integrated luminosity of 300 fb$^{-1}$, the \textsc{Spa-Net} allows us to establish 95\% C.L. upper limits in resonant production cross-sections that are 10\% to 45\% stronger than baseline methods. For non-resonant di-Higgs production, \textsc{Spa-Net} enables us to constrain the self-coupling that is 9\% more stringent than the baseline method.