Identification of non-ordinary mesons from the dispersive connection between their poles and their Regge trajectories: The f{sub 0}(500) resonance

• Published in: Physics letters. B 2014-02, Vol.729
• Main Authors: Pelaez, J. R., Londergan, J. T., Nebreda, J., Szczepaniak, Adam P.
• Format: Article
• Language: English
• Subjects: Light scalar mesons; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Regge theory
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2013.12.061

We show how the Regge trajectory of a resonance can be obtained from its pole in a scattering process and analytic constraints in the complex angular momentum plane. The method is suited for resonances that dominate an elastic scattering amplitude. In particular, from the {rho}(770) resonance pole in {pi}{pi} scattering, we obtain its linear Regge trajectory, characteristic of ordinary quark–antiquark states. In contrast, the f{sub 0}(500) pole—the sigma meson—which dominates scalar isoscalar {pi}{pi} scattering, yields a nonlinear trajectory with a much smaller slope at the f{sub 0}(500) mass. Conversely, imposing a linear Regge trajectory for the f{sub 0}(500), with a slope of typical size, yields an elastic amplitude at odds with the data. This provides strong support for the non-ordinary nature of the sigma meson.