Di-Higgs Production at the LHC

The next major goal of the Large Hadron Collider (LHC) program is to explore
the shape of the Higgs potential by measuring the trilinear Higgs
self-coupling. The most sensitive channel for this endeavor is Higgs pair
production via gluon fusion.

In this talk, I will demonstrate how the presence of new physics can modify
this production mode in two ways: (1) direct resonant production of a heavy
state in the s-channel, and (2) deviations in the Higgs self-coupling due to
the effects of heavy states in radiative corrections. I will show that these
two contributions cannot be analyzed independently — as is often done by
experimental collaborations — highlighting the need for a more refined
resonant analysis that accounts for the non-resonant beyond-the-Standard
Model (BSM) contribution.

To facilitate theoretical predictions in concrete BSM models, I will present
a novel tool, anyHH, for computing the di-Higgs production cross-section at
leading order in QCD for arbitrary scalar extensions of the Standard Model.
Additionally, it incorporates loop corrections to the trilinear couplings,
including full momentum dependence.

Finally, I will discuss the connection between deviations in the Higgs
self-coupling and a strong first-order electroweak phase transition in the
early Universe, a necessary ingredient for electroweak baryogenesis.