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