Can we discover double Higgs production at the LHC

We explore double Higgs production via gluon fusion in the $b\bar{b} \gamma \gamma $ channel at the high-luminosity LHC using machine learning tools. We first propose a Bayesian optimization approach to select cuts on kinematic variables, obtaining a $30-50$ \% increase in the significance compared to current results in the literature. We show that this improvement persists once systematic uncertainties are taken into account. We next use boosted decision trees (BDT) to further discriminate signal and background events. Our analysis shows that a joint optimization of kinematic cuts and BDT hyperparameters results in an appreciable improvement in the significance. Finally, we perform a multivariate analysis of the output scores of the BDT. We find that assuming a very low level of systematics, the techniques proposed here will be able to confirm the production of a pair of Standard Model Higgs bosons at 5$\sigma$ level with 3 ab$^{-1}$ of data. Assuming a more realistic projection of the level of systematics, around 10\%, the optimization of cuts to train BDTs combined with a multivariate analysis delivers a respectable significance of 4.6$\sigma$. Even assuming large systematics of 20\%, our analysis predicts a 3.6$\sigma$ significance, which represents at least strong evidence in favor of double Higgs production. We carefully incorporate background contributions coming from light flavor jets or $c$-jets being misidentified as $b$-jets and jets being misidentified as photons in our analysis.