A practical parametrization for line shapes of near-threshold states

TL;DR

This paper introduces a self-consistent, analytically parametrized approach for modeling near-threshold quarkonium-like states, ensuring unitarity and analyticity, and effectively describing experimental data for specific charged states.

Contribution

It presents a novel analytical parametrization method for near-threshold states that handles multiple channels nonperturbatively, improving data analysis accuracy.

Findings

Successfully describes data for Z_b(10610) and Z_b(10650) states

Provides a unified framework compatible with unitarity and analyticity

Enables combined analysis of multi-channel experimental data

Abstract

Numerous quarkonium(like) states lying near $S$-wave thresholds are observed experimentally. We propose a self-consistent approach to these near-threshold states compatible with unitarity and analyticity. The underlying coupled-channel system includes a bare pole and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting analytical parametrization is ideally suited for a combined analysis of the data available in various channels that is exemplified by an excellent overall description of the data for the charged $Z_b(10610)$ and $Z_b(10650)$ states.