Eur. Phys. J. A (2006) 30: 413-422
https://doi.org/10.1140/epja/i2006-10103-0

Hadron Physics

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

Zweites Physikalisches Institut der Universität Göttingen, Friedrich-Hund-Platz 1, D-37077, Göttingen, Germany

^* e-mail: mschuma3@gwdg.de

Received: 6 June 2006
Accepted: 15 September 2006
Published online: 12 October 2006

Abstract

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 A ₁(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 and N¯ → 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 f ₀(600) particle observed in the three reactions. In the following, we describe details of the derivation of (α - β)^t making use of predictions of the quark-level NJL model for the σ-meson mass.