Regge trajectories of ordinary and non-ordinary mesons from their scattering poles

TL;DR

This paper derives Regge trajectories from scattering poles for various mesons, revealing linear trajectories for typical quark-antiquark states and a non-linear, anomalous trajectory for the sigma meson, indicating its non-ordinary nature.

Contribution

It introduces a method to extract Regge trajectories from scattering data, distinguishing between ordinary and non-ordinary mesons based on their trajectory shapes.

Findings

Linear trajectories for $ ho(770)$, $f_2(1270)$, $f_2'(1525)$

Non-linear, small-slope trajectory for $f_0(500)$

Imposing linear trajectory on $f_0(500)$ conflicts with data

Abstract

Our results on obtaining the Regge trajectory of a resonance from its pole in a scattering process and from analytic constraints in the complex angular momentum plane are presented. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the $\rho(770)$, $f_2(1270)$, $f_2'(1525)$ and $f_0(500)$ resonances. Whereas for the first three we obtain linear Regge trajectories, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. We also show that if a linear trajectory with a slope of typical size is imposed for the $f_0(500)$, the corresponding amplitude is at odds with the data. This provides a strong indication of the non-ordinary nature of the sigma meson.