Chasing the two-Higgs doublet model in the di-Higgs production

We investigate the di-Higgs production at the Large Hadron Collider in the two-Higgs doublet model (2HDM). In particular, we study the production of an extra neutral Higgs boson $\phi$ in association with the Standard Model (SM) Higgs boson $h$ in the Higgs alignment limit. We analyze two scenarios where the additional Higgs $\phi$ is CP-even or -odd state with a large top-Yukawa interaction. The leading contribution of this production comes from the top-quark loop-induced gluon-fusion channel $gg \to h\phi$. The measurement of the $h\phi$ production can probe the quartic couplings in the Higgs potential as well as the top-Yukawa couplings. Imposing both theoretical constraints (from the perturbative unitarity and the vacuum stability bounds) and experimental bounds (from the SM Higgs and flavor physics measurements) on the 2HDM parameter space, we calculate the production cross-section of $gg \to h\phi$. Furthermore, we scrutinize these processes in the parameter spaces where the CMS di-tau and di-photon excesses around 100$\,$GeV, and/or the muon $g-2$ anomaly can be accommodated.