Can the two-Higgs-doublet model survive the constraint from the muon anomalous magnetic moment, as suggested?

Requiring the two-Higgs-doublet model II to accommodate the 3σ deviation in the muon anomalous magnetic moment imposes specific constraints on the Higgs spectrum. We analyze the combination of all the relevant available constraints on the model parameter space. The use of constraints from b → sγ, the precision electroweak measurements of R_b, and the → parameter, together with exclusions from direct searches at CERN LEP, gives extremely severe restrictions on the model parameters. That is "almost enough" to destroy the model altogether. The exclusion would be even stronger if the direct searches could be optimized to complement the other constraints, as will be discussed in detail in this work.