Search for Dimuon Decays of a Light Scalar Boson in Radiative TransitionsΥ→γA0

We search for evidence of a light scalar boson in the radiative decays of the $\mathit{{\rm Y}}(2S)$ and $\mathit{{\rm Y}}(3S)$ resonances: $\mathit{{\rm Y}}(2S,3S)\to \gamma A^0$, $A^0\to {\mu }^{+}{\mu }^{-}$. Such a particle appears in extensions of the standard model, where a light $CP$-odd Higgs boson naturally couples strongly to $b$ quarks. We find no evidence for such processes in the mass range $0.212\le m_{A^0}\le 9.3\mathrm{GeV}$ in the samples of $99\times {10}^6$ $\mathit{{\rm Y}}(2S)$ and $122\times {10}^6$ $\mathit{{\rm Y}}(3S)$ decays collected by the BABAR detector at the SLAC PEP-II $B$ factory and set stringent upper limits on the effective coupling of the $b$ quark to the $A^0$. We also limit the dimuon branching fraction of the ${\eta }_b$ meson: $\mathcal{B}({\eta }_b\to {\mu }^{+}{\mu }^{-})<0.9\%$ at 90% confidence level.