Search for di-muon decays of a low-mass Higgs boson in radiative decays of the \Upsilon(1S)

9 pages, 6 postscript figures, submitted to PRD-RC - See paper for full list of authorsWe search for di-muon decays of a low-mass Higgs boson (A^0) produced in radiative \Upsilon(1S) decays. The \Upsilon(1S) sample is selected by tagging the pion pair in the \Upsilon(2S, 3S) \to \pi^+ \pi^- \Upsilon(1S) transitions, using a data sample of 92.8 \times 10^6 \Upsilon(2S) and 116.8 \times 10^6 \Upsilon(3S) events collected by the \babar\ detector. We find no evidence for A^0 production and set 90% confidence level upper limits on the product branching fraction \mathcal{B} (\Upsilon(1S) \to \gamma A^0) \times \mathcal{B} (A^0 \to \mumu) in the range of (0.28 - 9.7) \times 10^{-6} for 0.212 \le m_{A^0} \le 9.20 GeV/c^2. The results are combined with our previous measurements of \Upsilon(2S,3S) \to \gamma A^0, A^0 \to \mumu to set limits on the effective coupling of the \b-quark to the A^0