The non-ordinary Regge behavior of the $f_0(500)$ meson

TL;DR

This paper reviews how the Regge trajectories of mesons can be derived from their pole properties, revealing that the lightest scalar meson $f_0(500)$ has a non-linear, non-ordinary trajectory unlike the typical linear one of the $ ho(770)$.

Contribution

It introduces a dispersive formalism to extract Regge trajectories from resonance poles, highlighting the non-ordinary nature of the $f_0(500)$ meson.

Findings

The $ ho(770)$ has an ordinary linear Regge trajectory with a universal slope.

The $f_0(500)$ exhibits a non-linear, smaller-slope Regge trajectory.

This difference indicates the non-ordinary nature of the $f_0(500)$ meson.

Abstract

We review how the Regge trajectory of an elastic resonance can be obtained just from its pole position and coupling, by means of a dispersive formalism. This allows to deal correctly with the finite widths of resonances in Regge trajectories. For the $\rho(770)$ meson this method leads to the ordinary linear Regge trajectory with a universal slope. In contrast, for the $f_0(500)$ meson, the resulting Regge trajectory is non-linear and with much smaller slope. This is another strong indication of the non-ordinary nature of the lightest scalar meson.