Upper limit for axion production in radiativeϒdecay

We have used the CUSB detector at the Cornell Electron Storage Ring to study the decays of $\Upsilon \mathrm{}\left(1S\right)\mathrm{}$ and $\Upsilon \mathrm{}\left(3S\right)\mathrm{}$ resonances into a single photon plus a long-lived noninteracting particle. We obtain an upper limit on the branching ratio for $\Upsilon \mathrm{}\left(1S\right)\mathrm{}\to \gamma +X$, where $X$ is undetected. This upper limit is 3.5×${10}^{-4\mathrm{}}$ (90% C.L.) for masses $m_X$ less than 7 GeV. For the $\Upsilon \mathrm{}\left(3S\right)\mathrm{}$ the upper limit is 1.2×${10}^{-4\mathrm{}}$ (90% C.L.) for masses less than 4 GeV. Also, the product of the branching ratios of $\Upsilon \to \gamma +\mathrm{axion}$ and $\frac{J}{\psi }\to \gamma +\mathrm{axion}$ is calculated to be 0.6×${10}^{-9\mathrm{}}$, inconsistent with theoretical predictions.