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We study di-Higgs production via gluon fusion at the high luminosity LHC inthe presence of new physics, focusing on the $b\bar b\gamma\gamma$ finalstates. Taking a minimal set of three scalar leptoquarks (LQs) with cubic andquartic interactions with the Higgs and choosing four benchmark points with alight LQ, we perform a detailed analysis of differential distributions of thedi-Higgs production cross section, studying the imprints of the new physicsstates running in the loops. Simulating the signal and main backgrounds, westudy the influence of the new physics in differential distributions such asthe invariant mass of the subsystems of final particles, the transversemomentum, and angular variables, finding in particular a resonance peakassociated with the light LQ. It turns out that the angular separation of thephotons, which is correlated with the resonance LQ peak, is a very sensitiveobservable that helps in discriminating the new physics signal from theStandard Model background. We find that for two of our benchmarks discoverycould be reached with 3 ab$^{-1}$, whereas exclusion limits at 95% C.L. couldbe claimed with 0.60-0.75 ab$^{-1}$. For the other two benchmarks that haveheavier LQ masses significances of order 2$\sigma$ are possible for 3ab$^{-1}$. A similar analysis could be applied to other loop-enhanced models.

Double Higgs production at the HL-LHC: probing a loop-enhanced model with kinematical distributions