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

TL;DR

This paper investigates how scalar resonance re-scattering effects can explain the large dipion transition rates of $ 10870$, showing that differences in decay p-values account for observed rate ratios and aligning with experimental data.

Contribution

It introduces a re-scattering model emphasizing scalar resonance contributions to explain large dipion transition rates in bottomonium states, providing numerical estimates consistent with observations.

Findings

Transition rate ratios estimated to be 200-600

Rates of $ 5S$ transitions align with experimental data

Dipion transition features may be similar across different quarkonium states

Abstract

In order to explain the observed unusually large dipion transition rates of $\Upsilon(10870)$, the scalar resonance contributions in the re-scattering model to the dipion transitions of $\Upsilon(4S)$ and $\Upsilon(5S)$ are studied. Since the imaginary part of the re-scattering amplitude is expected to be dominant, the large ratios of the transition rates of $\Upsilon(10870)$, which is identified with $\Upsilon(5S)$, to that of $\Upsilon(4S)$ 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 $\Upsilon(5S)\to\Upsilon(1S,2S,3S)\pi^+\pi^-$ and $\Upsilon(5S)\to\Upsilon(1S)K^+K^-$ 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 $\Upsilon(5S)$. Measurements on the dipion transitions of $\Upsilon(6S)$ could provide further test for this mechanism.