# Dramatic implications of unitarity for meson spectroscopy

## TL;DR

This paper emphasizes the importance of unitarity in meson spectroscopy, showing that traditional Breit-Wigner parametrizations can significantly misrepresent resonance parameters, and introduces unitary models that better explain meson phenomena.

## Contribution

It demonstrates the limitations of Breit-Wigner parametrizations and presents a manifestly unitary model for meson spectroscopy, highlighting significant deviations from traditional methods.

## Key findings

- Breit-Wigner masses can differ from pole masses by nearly 5 MeV for certain resonances.
- Discrepancies are larger for broad scalar mesons like $f_0(500)$ and $K_0^*(700)$.
- Unitary models can explain meson enhancements as non-resonant threshold effects.

## Abstract

An unambiguous definition of meson resonance masses requires a description of the associated phase shifts in terms of a manifestly unitary $S$-matrix and its complex poles. However, the commonly used Breit-Wigner (BW) parametrisations can lead to appreciable deviations. We demonstrate this for a simple elastic resonance, viz. $\rho(770)$, whose pole and BW masses turn out to differ by almost 5 MeV. In the case of the very broad $f_0(500)$ and $K_0^\star(700)$ scalar mesons, the discrepancies are shown to become much larger, while also putting question marks at the listed PDG BW masses and widths. Furthermore, some results are reviewed of a manifestly unitary model for meson spectroscopy, which highlight the potentially huge deviations from static model predictions. Finally, a related unitary model for production amplitudes is shown to explain several meson enhancements as non-resonant threshold effects, with profound implications for spectroscopy.