Scalar Resonance Contributions to the Dipion Transition Rates of $Î¥(4S,5S)$ in the re-scattering model

Abstract

In order to explain the observed unusually large dipion transition rates of $Υ(10870)$, the scalar resonance contributions in the re-scattering model to the dipion transitions of $Υ(4S)$ and $Υ(5S)$ are studied. Since the imaginary part of the re-scattering amplitude is expected to be dominant, the large ratios of the transition rates of $Υ(10870)$, which is identified with $Υ(5S)$, to that of $Υ(4S)$ can be understood as mainly coming from the difference between the $p$-values in their decays into open bottom channels, and the ratios are estimated numerically to be about 200-600 with reasonable choices of parameters. The absolute and relative rates of $Υ(5S)\toΥ(1S,2S,3S)π^+π^-$ and $Υ(5S)\toΥ(1S)K^+K^-$ are roughly consistent with data. We emphasize that the dipion transitions observed for some of the newly discovered $Y$ states associated with charmonia may have similar features to the dipion transitions of $Υ(5S)$. Measurements on the dipion transitions of $Υ(6S)$ could provide further test for this mechanism.

version to appear in Phys. Rev. D, discussions and references added