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We show how the Regge trajectory of a resonance can be obtained from its polein a scattering process and analytic constraints in the complex angularmomentum plane. The method is suited for resonances that dominate an elasticscattering amplitude. In particular, from the rho(770) resonance pole inpion-pion scattering, we obtain its linear Regge trajectory, characteristic ofordinary quark-antiquark states. In contrast, the f0(500) pole -the sigmameson- which dominates scalar isoscalar pion-pion scattering, yields anon-linear trajectory with a much smaller slope at the f0(500) mass.Conversely, imposing a linear Regge trajectory for the f0(500), with a slope oftypical size, yields an elastic amplitude at odds with the data. This providesstrong support for the non-ordinary nature of the sigma meson.

Identification of non-ordinary mesons from the dispersive connection between their poles and their Regge trajectories: the f0(500) resonance