Probing Electroweak Phase Transition via Enhanced Di-Higgs Production

We consider a singlet extension of the Standard Model (SM) with a spontaneous $Z_2$ breaking and study the gluon-gluon fusion production of the heavy scalar, with subsequent decay into a pair of SM-like Higgs bosons. We find that an on-shell interference effect can notably enhance the resonant di-Higgs production rate up to 40\%. In addition, consistently taking into account both the on-shell and off-shell interference effects between the heavy scalar and the SM di-Higgs diagrams significantly improves the HL-LHC and HE-LHC reach in this channel. As an example, within an effective field theory analysis in an explicitly $Z_2$ breaking scenario, we further discuss the potential to probe the parameter region compatible with a first order electroweak phase transition. Our analysis is applicable for general potentials of the singlet extension of the SM as well as for more general resonance searches.