Remarks on the decays chi_{bJ}^\prime -> omega Upsilon

The recently observed by CLEO cascade decays Upsilon(3S) -> gamma chi_{bJ}^\prime -> gamma omega Upsilon are discussed. It is shown that within the nonrelativistic description of bottomonium in the heavy b quark limit, the ratio of the rates of the transitions chi_{bJ}^\prime -> omega Upsilon with J=1 and J=2 should be given by the ratio of the corresponding S wave phase space factors. As a result, the rate of the observed cascade transitions through the chi_{b2}^\prime resonance should be close to that through the chi_{b1}^\prime. It is suggested that the ratio of the discussed cascade rates can also be tested by measuring a simple angular correlation.

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