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Search for di-muon decays of a light scalar Higgs boson in radiative Y(1S) decays

We search for di-muon decays of a low-mass Higgs boson ($A^0$) in the fully reconstructed decay chain of $Υ(2S,3S) \to \pipiΥ(1S)$, $Υ(1S) \to \g A^0$, $A^0 \to \mumu$. The $A^0$ is predicted by several extensions of the Standard Model (SM), including the Next-to-Minimal Supersymmetric Standard Model (NMSSM). NMSSM introduces a \CP-odd light Higgs boson whose mass could be less than 10 \gevcc. The data samples used in this analysis contain $92.8 \times 10^6$ $Υ(2S)$ and $116.8 \times 10^6$ $Υ(3S)$ events collected by the \babar\ detector. The $Υ(1S)$ sample is selected by tagging the pion pair in the $Υ(2S, 3S) \to π^+π^-Υ(1S)$ transitions. We find no evidence for $A^0$ production and set 90% confidence level (C.L.) upper limits on the product branching fraction $\mathcal{B}(Υ(1S) \to \g A^0) \times \mathcal{B}(A^0 \to \mumu)$ in the range of $(0.28 - 9.7)\times 10^{-6}$ for $0.212 \le m_{A^0} \le 9.20$ \gevcc. We also combine our results with previous \babar\ results of $Υ(2S,3S) \to \g A^0$, $A^0 \to \mumu$ to set limits on the effective coupling ($f_Υ$) of the \b-quark to the $A^0$, $f_Υ^2 \times \mathcal{B}(A^0 \to \mumu)$, at the level of $(0.29 - 40)\times 10^{-6}$ for $0.212 \le m_{A^0} \le 9.2$ GeV/$c^2$.