Probing Type-I 2HDM light Higgs in the top-pair-associated diphoton channel

Motivated by the possible 95 GeV diphoton excess, we investigate the capability of the Type-I Two-Higgs-Doublet Model (2HDM-I) to explain this signal under current theoretical and experimental constraints. Using full Monte Carlo (MC) simulations for the process of $pp \to t(\to W^+ b)\bar{t}(\to W^- \bar{b})h(\to \gamma\gamma)$, we evaluate the discovery potential of a 95 GeV Higgs boson at future colliders. Direct Higgs searches strongly constrain the parameter $\alpha$, excluding the region with $\alpha \lesssim 0.95$. Monte Carlo results indicate that a minimum cross section of 0.3 fb is required to achieve a $5\sigma$ signal statistical significance at the HL-LHC with $L = 3~\mathrm{ab}^{-1}$. For the same luminosity, HE-LHC and FCC-hh require 0.67 fb and 2.36 fb, respectively. At the 14 TeV HL-LHC with an integrated luminosity of $3~\mathrm{ab}^{-1}$, parameter regions with $\sin(\beta-\alpha) \gtrsim 0.4$ and $\sin(\beta-\alpha) \gtrsim 0.25$ can be probed at the $5\sigma$ and $2\sigma$ significance levels, respectively. At the 27 TeV HE-LHC with $L = 10~\mathrm{ab}^{-1}$, the sensitivity improves to $\sin(\beta-\alpha) \gtrsim 0.25$ ($5\sigma$) and $\gtrsim 0.15$ ($2\sigma$). For the 100 TeV FCC-hh with $L = 30~\mathrm{ab}^{-1}$, even regions with $\sin(\beta-\alpha) \gtrsim 0.1$ or $\sin(\beta-\alpha) \lesssim -0.05$ can be covered at the $5\sigma$ level. Parameter regions near $\sin(\beta-\alpha) \approx 0$ remain challenging to probe in the diphoton channel, even with increased energy or luminosity.