Electromagnetic polarizabilities of the nucleon and properties of the σ-meson pole contribution

The t-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, (α−β)t, can be quantitatively understood in terms of a σ-meson pole in the complex t-plane of the invariant scattering amplitude A1(s, t) with properties of the σ meson as given by the quark-level Nambu–Jona-Lasinio model (NJL). Equivalently, this quantity may be understood in terms of a cut in the complex t-plane where the properties of the σ meson are taken from the ππ → σ → ππ, γγ → σ → ππ andNN̄ → σ → ππ reactions. This equivalence may be understood as a sum rule where the properties of the σ meson as predicted by the NJL model are related to the f0(600) particle observed in the three reactions. In the following we describe details of the derivation of (α− β) making use of predictions of the quark-level NJL model for the σ-meson mass. PACS. 11.30.Rd Chiral symmetries – 11.55.Fv Dispersion relations – 11.55.Hx Sum rules – 13.60Fz Elastic and Compton scattering – 14.65.Bt Light quarks – 14.70.Bh Photons