Direct production of a light CP-odd Higgs boson at the Tevatron and LHC

We show that the existing CDF L = 630 pb(-1) Tevatron data on pp --> mu(+)mu X- places substantial limits on a light CP-odd Higgs boson a with m(a) 2m(B) produced via gg --> a, even for m(a) > 2m(tau) for which BR(a --> mu(+)mu(-)) is relatively small. Extrapolation of this existing CDF analysis to L = 10 fb(-1) suggests that Tevatron limits on the ab (b) over bar coupling strength in the region m(a) > 8 GeV could be comparable to or better than limits from Upsilon decays in the m(a) < 7 GeV region. We also give rough estimates of future prospects at the LHC, demonstrating that early running will substantially improve limits on a light a ( or perhaps discover a signal). In particular, outside the Upsilon peak region, integrated luminosity of only 5 fb(-1)-20 fb(-1) (depending on m(a) and root s) could reveal a peak in M mu+mu- and will certainly place important new limits on a light a. The importance of such limits in the context of next-to-minimal supersymmetric model Higgs discovery and (g - 2)(mu) are outlined.