Upper limit for axion production in radiative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ϒ</mml:mi></mml:math>decay

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