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
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Accepted: 15 September 2006
Published online: 12 October 2006
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.
PACS: 11.55.Fv Dispersion relations – / 11.55.Hx Sum rules – / 13.60.Fz Elastic and Compton scattering – / 14.70.Bh Photons –
© Società Italiana di Fisica and Springer-Verlag, 2006