# Threshold Effects in Heavy Quarkonium Spectroscopy and Decays

## TL;DR

This paper explores how threshold effects influence heavy quarkonium spectroscopy and decays, comparing models to distinguish pure quarkonium states from exotic states with continuum components.

## Contribution

It introduces a novel coupled-channel model based on the Unquenched Quark Model that addresses convergence issues and differentiates between quarkonium and exotic states.

## Key findings

- The coupled-channel model successfully describes $ ext{chi}_c(2P)$ as mixed states with molecular components.
- It characterizes $ ext{chi}_b(3P)$ as nearly pure bottomonium states.
- Potential applications to decay amplitude calculations are discussed.

## Abstract

The possible importance of threshold effects in heavy quarkonium spectroscopy is discussed. The starting point is the calculation of the spectrum of heavy quarkonium-like states with self-energy/threshold corrections. Two different approaches are compared: I) The Unquenched Quark Model (UQM); II) A novel coupled-channel model, based on the UQM formalism. The latter provides a possible solution to the long-standing problem of convergence in UQM calculations; it also makes it possible to distinguish between states which are almost pure quarkonia and exotic states, characterized by non-negligible threshold (or continuum) components in their wave functions. The UQM-based coupled-channel model is used to study the $\chi_{\rm c}(2P)$ and $\chi_{\rm b}(3P)$ multiplets: $\chi_{\rm c}(2P)$'s are described as charmonium-like states with non-negligible molecular-type components in their wave functions, $\chi_{\rm b}(3P)$'s as almost pure bottomonia. Other possible applications of the UQM and the UQM-based coupled-channel model formalisms to the calculation of other observables, like the strong decay amplitudes, are also discussed.