The future probe of the light Higgs boson pair production

In this work we study the light Higgs scenario in the framework of two Higgs doublet model (2HDM). In this case the heavier CP-even Higgs boson $H$ in 2HDM is the SM-like Higgs with 125 GeV mass and a CP-even Higgs boson $h$ lighter than 125 GeV exhibits in the spectrum. We find that this scenario exists in the alignment limit of $\sin(\beta-\alpha)\simeq 0$ and is still allowed by the global fit of the 125 GeV Higgs and the direct searches for $H\to hh$ and $h\to \gamma\gamma$. The case of $M_h<M_H/2$ is highly constrained as the exotic decay mode $H\to hh$ is kinematically allowed. We focus on the $M_h>M_H/2$ case and simulate the pair production of the light Higgs boson at the LHC. The pair production is sensitive to the soft $\mathbb{Z}_2$ symmetry breaking term $m_{12}$ in the 2HDM potential through the Higgs self-couplings. We find that the future high-luminosity LHC can discover the $b\bar{b}\gamma\gamma$ signal in the region of $\tan\beta\lesssim 1$ and $0<m_{12}<100$ GeV allowed by the theoretical constraints.