Final-state pi pi interactions in Upsilon (3S)--> Upsilon (1S) pi pi.

Abstract

The ${\mathit{m}}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\pi}}}$ spectrum and various angular distributions in \ensuremath{\Upsilon}(3S)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(1S)\ensuremath{\pi}\ensuremath{\pi} are studied including the effects of the \ensuremath{\pi}\ensuremath{\pi} phase shift in the I=L=0 channel using the lowest order amplitude in the pion momentum expansion. Our results are compared with the recent CLEO data, and we find good agreement except for the cos${\mathrm{\ensuremath{\theta}}}_{\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$ distributions. We argue that the cos${\mathrm{\ensuremath{\theta}}}_{\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$ distribution, contrary to other distributions, is sensitive to the higher order corrections in the pion momentum expansion. This argument is supported by using an ansatz for the amplitude which is of higher order in the pion momentum expansion and still satisfies the soft pion theorem.