The enhancement of the decay Upsilon(1D) -> eta Upsilon(1S) by the axial anomaly in QCD

It is shown that the rates of the decays Upsilon(1^3D_1) -> eta Upsilon(1S) and Upsilon(1^3D_2) -> eta Upsilon(1S) should be comparable to and likely exceed that of the recently discussed in the literature two-pion transition Upsilon(1D) -> pi pi Upsilon(1S). The reason for this behavior is that the discussed eta transitions are enhanced by the contribution of the anomaly in the flavor singlet axial current in QCD.