The branching ratio (BR) for the rare decay eta ->pi(0)gamma gamma was measured with the Crystal Ball multiphoton spectrometer. The result, BR(eta ->pi(0)gamma gamma)=(3.5 +/- 0.7(stat)+/- 0.6(syst))x10(-4), is in agreement with calculations of chiral perturbation theory to third order. We have used a sample of 28 million eta mesons produced at the BNL Alternating Gradient Synchrotron using the pi(-)p ->eta n reaction close to threshold. We detail the intricate extraction of the signal, which has about 1.6 thousand eta ->pi(0)gamma gamma events, from the overwhelming background of eta -> 3 pi(0) decays and from the pi(-)p ->pi(0)pi(0)n reaction.
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