Single eta production in heavy quarkonia: breakdown of multipole expansion

Abstract

The $\eta$ production in the $(n,n^{\prime })$ bottomonium transitions ${\rm Y}(n)\to {\rm Y}(n^{\prime })\eta ,$ is studied in the method used before for dipion heavy quarkonia transitions. The widths ${\Gamma }_{\eta }(n,n^{\prime })$ are calculated without fitting parameters for $n=2,3,4,5,n^{\prime }=1$. Resulting ${\Gamma }_{\eta }(4,1)$ is found to be large in agreement with recent data. Multipole expansion method is shown to be inadequate for large size systems considered.

Comments: 12 pages, 1 figure