Complete Light Long-Lived Particles searches in Type-I 2HDM

Recently, the study of long-lived particles (LLPs) has attracted increasing attention. In this work, we analyze the full parameter space of the Type-I Two-Higgs-Doublet Model (2HDM) that allows for light long-lived scalar ($H$) and pseudoscalar ($A$) particles. When involving a light beyongd Standard Model (BSM) Higgs, the $\Delta S$ could be the main contribution during the global fit of the oblique parameters, which is different to $\Delta T$ being the main factor for heavy BSM Higgs cases. By imposing theoretical constraints such as vacuum stability and perturbative unitarity, together with current experimental bounds, we summarize a complete region for a potential light $H$ with $\cos(\beta - \alpha) \simeq \frac{1}{\tan \beta}$, light $A$ with $\cos(\beta - \alpha) \simeq \frac{1}{\tan\beta} \frac{2m_H^2 - m_h^2}{m_H^2 - m_h^2}$, and point out the invisible Higgs decay is the most important constraint. We further identify viable regions for LLPs and propose four benchmark regions that simultaneously accommodate a light long-lived particle and explain the $W$ boson mass anomaly. For these benchmarks, we present the reaches of FASER and FASER~2, where FASER~2 improves the sensitivity by approximately two orders of magnitude compared to FASER.