Constraining 2HDM by Present and Future Muon(g-2) Data

Constraints on the general 2HDM ("Model II") are obtained from the existing $(g-2)_{\mu}$ data including limits on Higgs bosons masses from LEP I data. We consider separately two cases: with a light scalar $h$ and with a light pseudoscalar $A$, assuming ${M_{h}+M_{A}} \ge {M_{Z}}$. The charged Higgs contribution is also included. It is found that already the present $(g-2)_{\mu}$ data improve limits obtained recently by ALEPH collaboration on $\tb$ for the mass of the pseudoscalar below $\mr$ 2 GeV. The improvement in the accuracy by factor 20 in the forthcoming E821 experiment may lead to more stringent, than provided by ALEPH group, limits up to $M_A\sim$ 30 GeV if the mass difference between $h$ and $A$ is $\sim M_Z$. Similar results should hold for a light scalar scenario as well.