Interplay of quark and meson degrees of freedom in near-threshold states: A practical parametrisation for line shapes

TL;DR

This paper introduces a versatile parametrisation for near-threshold state line shapes that respects unitarity and analyticity, enabling comprehensive data analysis of coupled-channel systems including various decay channels.

Contribution

It presents a general, nonperturbative formula for coupled-channel line shapes, applicable to multiple reactions and channels, demonstrated through fitting bottomonium Zb states data.

Findings

Zb(10610) is consistent with a virtual state

Zb(10650) is consistent with a resonance

Good fit to experimental data across channels

Abstract

We propose a practical parametrisation for the line shapes of near-threshold states compatible with all requirements of unitarity and analyticity. The coupled-channel system underlying the proposed parametrisation includes bare poles and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting formulae are general enough to be used for a simultaneous analysis of the data in all available production and decay channels of the (system of) state(s) under consideration for a quite wide class of reactions. As an example, we fit the experimental data currently available for several decay channels for the charged $Z_b^{(\prime)}$ states in the spectrum of bottomonia and find a good overall description of the data. We find the present data to be consistent with the $Z_b(10610)$ as a virtual state and with the $Z_b(10650)$ as a resonance, both residing very close to the $B\bar{B}^*$ and $B^*\bar{B}^*$ threshold, respectively.