Single eta production in heavy quarkonia: breakdown of multipole expansion

TL;DR

This paper investigates eta meson production in heavy quarkonium transitions, revealing that the multipole expansion method fails for large systems, with calculations aligning well with recent experimental data.

Contribution

It demonstrates the breakdown of the multipole expansion approach in describing eta production in heavy quarkonia transitions for large systems.

Findings

Calculated eta transition widths without fitting parameters.

Found large eta widths consistent with recent data.

Showed multipole expansion is inadequate for large quarkonium systems.

Abstract

The $\eta$ production in the $(n,n')$ bottomonium transitions $\Upsilon (n) \to \Upsilon (n') \eta, $ is studied in the method used before for dipion heavy quarkonia transitions. The widths $\Gamma_\eta(n,n')$ are calculated without fitting parameters for $n=2,3,4,5, n'=1$. 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.