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 $pp \rightarrow W^\pm/Z \rightarrow H^{\pm}/H A$ and $pp \rightarrow h \rightarrow AA$ 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 $pp \rightarrow W^\pm/Z \rightarrow H^{\pm}/Z A$ processes. And $pp \rightarrow h \rightarrow AA$ process covers similar parameter space. All processes can surpass the current limits.