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We report on a search for the radiative decay of Upsilon(1S) to thepseudoscalar mesons eta and etaprime in 21.2 +/- 0.2 times 10^6 Upsilon(1S)decays collected with the CLEO III detector at the Cornell Electron StorageRing (CESR). The eta meson was reconstructed in the three modes eta togamma-gamma, eta to pi+pi-pi0 and eta to 3pi0. The etaprime meson wasreconstructed in the mode etaprime to pi+ pi- eta with eta decaying through anyof the above three modes, and also etaprime to gamma rho, where rho decays topi^+ pi^-.  Five out of the seven sub-modes are found to be virtually background-free. Infour of them we find no signal candidates and in one Upsilon(1S) togamma-etaprime, etaprime to pi+ pi- eta, eta to pi+pi-pi0 there are two goodsignal candidates, which is insufficient evidence to claim a signal. The othertwo sub-modes eta to gamma-gamma and etaprime to gamma rho are backgroundlimited, and show no excess of events in their signal regions. We combine theresults from different channels and obtain upper limits at the 90% C.L. whichare B(Upsilon(1S) to gamma eta) < 1.0 times 10^-6 and B(Upsilon(1S) to gammaetaprime) < 1.9 times 10^-6. Our limits are an order of magnitude tighter thanthe previous ones and below the predictions made by some theoretical models.

Search for Radiative Decays of Upsilon(1S) into eta and eta'