Higgs self-coupling measurements using deep learning in the $b\bar{b}b\bar{b}$ final state

Measuring the Higgs trilinear self-coupling $\lambda_{hhh}$ is experimentally demanding but fundamental for understanding the shape of the Higgs potential. We present a comprehensive analysis strategy for the HL-LHC using di-Higgs events in the four $b$-quark channel ($hh \to 4b$), extending current methods in several directions. We perform deep learning to suppress the formidable multijet background with dedicated optimisation for BSM $\lambda_{hhh}$ scenarios. We compare the $\lambda_{hhh}$ constraining power of events using different multiplicities of large radius jets with a two-prong structure that reconstruct boosted $h \to bb$ decays. We show that current uncertainties in the SM top Yukawa coupling $y_t$ can modify $\lambda_{hhh}$ constraints by $\sim 20\%$. For SM $y_t$, we find prospects of $-0.8 < \lambda_{hhh} / \lambda_{hhh}^\text{SM} < 6.6$ at 68% CL under simplified assumptions for 3000~fb$^{-1}$ of HL-LHC data. Our results provide a careful assessment of di-Higgs identification and machine learning techniques for all-hadronic measurements of the Higgs self-coupling and sharpens the requirements for future improvement.