Muon anomalous magnetic moment, two-Higgs-doublet model, and supersymmetry

The recent measurement of the muon anomalous magnetic moment $a_{\mu }$ shows a $2.6\sigma$ deviation from the standard model value. We show that it puts strong constraints on the parameter space of the two-Higgs-doublet model (2HDM) II. The dominant contribution of the Higgs bosons comes at the two-loop level, and in order to explain the data it favors a pseudoscalar A with a light mass range and a large $\tan \beta .$ At 95% C.L., the upper limit for $m_A$ is 29 (55) (85) GeV for $\tan \beta =30\mathrm{}$ (45) (60), and $\tan \beta$ is bounded below at 17. This is in sharp contrast to the conclusion one draws from considering one-loop Higgs contributions alone. Finally, we also discuss the role of the Higgs contributions in the minimal supersymmetric standard model.