Constraining the two Higgs doublet model by present and future(g−2)μdata

Constraints on the general two Higgs doublet model (“model II”) are obtained from the existing $(g-{2)}_{\mu }$ data including limits on Higgs boson masses from CERN LEP I data. We consider two scenarios: with a light scalar $h$ and with a light pseudoscalar $A$, assuming $M_h{+M}_A>~M_Z$ (the charged Higgs boson contribution is also included). We evaluate separately the 95% C.L. bands for positive and for negative contributions, relevant for a light scalar and a light pseudoscalar scenario, respectively. It is found that already the present $(g-{2)}_{\mu }$ data improve limits obtained recently by the ALEPH Collaboration on $\tan \beta$ for the mass of the pseudoscalar below $\lesssim$2 GeV. The improvement in the accuracy by a factor of 20 in the forthcoming E821 experiment may lead to more stringent limits than provided by the ALEPH group, up to $M_A$∼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.