Top-Assisted Di-Higgs boson Production Motivated by Baryogenesis

We study top-assisted di-Higgs production via $cg \to tH \to thh$, where $h$ is the 125 GeV scalar boson, and $H$ is the $CP$-even heavy Higgs. The context is the two Higgs doublet model without a $Z_2$ symmetry, where the extra Yukawa coupling $\rho_{tc}$ generates $tH$ production, with the extra top Yukawa $\rho_{tt} \simeq 0$ to avoid $gg \to H$ constraints. We find that discovery is possible for $m_H$ around 300 GeV or so at the LHC, but would need finite $h$-$H$ mixing angle $\cos\gamma$ to allow for finite $\lambda_{Hhh}$ coupling, and $\rho_{tc}$ also needs to be not too small. A sizable $\rho_{tc}$ could drive electroweak baryogenesis, which further motivates the search.