J. Nebreda

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

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 ρ(770) resonance pole in ππ scattering, we obtain its linear Regge trajectory, characteristic of ordinary quark–antiquark states. In contrast, the f_0(500) pole—the sigma meson—which dominates scalar isoscalar ππ scattering, yields a nonlinear trajectory with a much smaller slope at the f0(500) mass. Conversely, imposing a linear Regge trajectory for the f0(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.

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

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 ρ(770), ƒ_2(1270), ƒ_2(1525) and ƒ_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 ƒ_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.

Regge trajectory of the f0(500) resonance from a dispersive connection to its pole

We report here our results on how to obtain the Regge trajectory of a resonance from its pole in a scattering process by imposing analytic constraints in the complex angular momentum plane. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the ρ (770) and the f0(500) resonances. Whereas for the former we obtain a linear Regge trajectory, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. This provides a strong indication of the non-ordinary nature of the sigma meson.

Non-ordinary nature of the f0(500) resonance from its Regge trajectory

We report our results on how to obtain the Regge trajectory of a resonance from its pole in a scattering process by imposing analytic constraints in the complex angular momentum plane. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the {\rho}(770) and the f_0(500) resonances. Whereas for the former we obtain a linear Regge trajectory, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. Moreover, we 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.

Determination of Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters

We report on our determination of the values of the one and two loop low energy constants appearing in the Chiral Perturbation Theory calculation of th e ππ scattering amplitude. For this we use a precise sum rule determination of scattering lengths a nd slopes that appear in the effective range expansion. In addition we provide new sum rules and the values for these coefficients up to third order in the expansion. Our results when using only t he scattering lengths and slopes of the S, P, D and F waves are consistent with previous determina tions, but seem to require higher order contributions if they are to accommodate the third ord er coefficients of the effective range expansion.