A light CP-odd Higgs boson and the muon anomalous magnetic moment

We amalgamate the many experimental limits on the $ab\anti b$ coupling of a light CP-odd Higgs boson, $a$, including model-dependence coming from the ratio of the $at\anti t$ to the $a b\anti b$ coupling. We then employ these limits to analyze the extent to which a light $a$ can make a significant contribution to the discrepancy, $\Delta a_\mu$, between the experimentally observed $a_\mu$ and that predicted by the standard model. In a "model-independent" framework and in the context of a general two-Higgs-doublet model this is a significant possibility. In contrast, the minimal supersymmetric model is too strongly constrained (after combining experimental and theoretical input) to allow a CP-odd-$a$ explanation of $\Delta a_\mu$. The next-to-minimal supersymmetric model allows more freedom and the light $a$ of the model could explain the full $\Delta a_\mu$ if $9.2\gev<\ma<12\gev $, or contribute substantially for larger $\ma$, if $\tanb$ is large.