Direct Production of Light Scalar in the Type-I Two-Higgs-Doublet Model at the Lifetime Frontier of LHC

A light pseudoscalar $A$ in the sufficient large $\tan \beta$ region of type-I two-Higgs-doublet model (2HDM) can be naturally a long-lived particle (LLP). We focus on $H^{\pm }A$, $HA$ and $AA$ pair productions via the electroweak processes mediated by the bosons at the LHC, including $pp\to W^{\pm }\mathrm{/}Z\to H^{\pm }\mathrm{/}HA$ and $pp\to h\to AA$ at the 14 TeV LHC. The possibility of probing $A$ as a LLP at the FASER-2, FACET, MoEDAL-MAPP-2, MATHUSLA is discussed. We find that FASER-2 fails to probe any parameter space within 0.2 GeV $<m_A<$ 10 GeV for all the considered processes. For 130 $<m_{H\pm }=m_H<$ 400 GeV, FACET, MoEDAL-MAPP-2 and MATHUSLA can probe $\tan \beta \lesssim {10}^{4-6}$ for $m_A\lesssim 3$ GeV, and $\tan \beta \lesssim {10}^{6-8}$ for 3 GeV $\lesssim m_A<$ 10 GeV from $pp\to W^{\pm }\mathrm{/}Z\to H^{\pm }\mathrm{/}ZA$ processes. And $pp\to h\to AA$ process covers similar parameter space. All processes can surpass the current limits.