We show that a general two-Higgs-doublet model with a very light $\mathrm{CP}$-odd scalar (A) can be compatible with the $\rho$ parameter, $\mathrm{Br}\left(\overrightarrow{b}s\gamma \right),$ $R_b{,A}_b,$ $(g-{2)}_{\mu }$ of the muon, $\mathrm{Br}\left(\overrightarrow{{\rm Y}}A\gamma \right),$ and the direct search via the Yukawa process at CERN LEP. For its mass around 0.2 GeV, the muon $(g-{2)}_{\mu }$ and $\mathrm{Br}\left(\overrightarrow{{\rm Y}}A\gamma \right)$ data require $\tan \beta$ to be about 1. Consequently, A can behave like a fermiophobic $\mathrm{CP}$-odd scalar and predominantly decay into a $\gamma \gamma$ pair, which registers in detectors of high energy collider experiments as a single photon signature when the momentum of A is large. We compute the partial decay width of $\overrightarrow{Z}\mathrm{AAA}$ and the production rate of $f\overline{f}\to \mathrm{ZA}\overrightarrow{A}Z+$ $“\gamma \gamma ,”$ $f^{\prime }\overline{f}\to W^{\pm }A\overrightarrow{A}{W}^{\pm }+$ $“\gamma \gamma ,”$ and $f\overline{f}\to H^{+}{H}^{-}\to W^{+}{W}^{-}A\overrightarrow{A}{W}^{+}{W}^{-}+$ $“\gamma \gamma ”$ at high energy colliders such as LEP, Fermilab Tevatron, CERN LHC, and future Linear Colliders. Other production mechanisms of a light A, such as $g\overrightarrow{g}\overrightarrow{h}A\overrightarrow{A}$ $“\gamma \gamma ,”$ are also discussed.

• Received 27 March 2001

DOI:https://doi.org/10.1103/PhysRevD.64.055004