Very light CP-odd scalar in the Two-Higgs-Doublet Model

We show that a general two-Higgs-doublet model (THDM) with a very light CP-odd scalar (A) can be compatible with the rho parameter, Br(b --> s\gamma), R_b, A_b, (g-2) of muon, Br(Upsilon --> A gamma), and the direct search via the Yukawa process at LEP. For its mass around 0.2 GeV, the muon (g-2) and Br(Upsilon --> A \gamma) data require tan(beta) to be about 1. Consequently, A can behave like a fermiophobic CP-odd scalar and predominantly decay into a photon pair ("gamma gamma"), 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 Z --> A A A and the production rate of f \bar{f} --> Z A A --> Z +"gamma gamma", f^' {\bar f} --> W^{\pm} A A --> W^\pm + "gamma gamma" and f \bar f --> H^+ H^- --> W^+ W^- A A --> W^+ W^- + "gamma gamma" at high energy colliders such as LEP, Tevatron, LHC, and future Linear Colliders. Other production mechanisms of a light A, such as gg --> h --> AA --> "gamma gamma", are also discussed.Comment: Some improvementes, references updated, 3 new figures, one new appendix, abstract and conclusions unchaged. Version to appear in Physical Review