Di-Higgs Production in the $4b$ Channel and Gravitational Wave Complementarity

We present a complementarity study of gravitational waves and double Higgs production in the $4b$ channel, exploring the gauge singlet scalar extension of the SM. This new physics extension serves as a simplified benchmark model that realizes a strongly first-order electroweak phase transition necessary to generate the observed baryon asymmetry in the universe. In calculating the signal-to-noise ratio of the gravitational waves, we incorporate the effect of the recently discovered significant suppression of the gravitational wave signals from sound waves for strong phase transitions, make sure that supercooled phase transitions do complete and adopt a bubble wall velocity that is consistent with a successful electroweak baryogenesis by solving the velocity profiles of the plasma. The high-luminosity LHC sensitivity to the singlet scalar extension of the SM is estimated using a shape-based analysis of the invariant $4b$ mass distribution. We find that while the region of parameter space giving detectable gravitational waves is shrunk due to the new gravitational wave simulations, the qualitative complementary role of gravitational waves and collider searches remain unchanged.