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

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 NN → 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.

Properties of the πη, $ \eta{^\prime}$ ,σ, f0(980) and a0(980) mesons and their relevance for the polarizabilities of the nucleon

“…The result given in (49) has been obtained through an application of the LσM and its dynamical version. The justification for using this result in the interpretation of the electromagnetic polarizabilities has been given in [1] and [3] where it has been shown that this result leads to an excellent agreement with experimental data. In order to obtain α t p,n and β t p,n separately use may be made of (α + β) t p,n = 0.…”

“…The meson-nucleon coupling constants are known to be positive quantities whereas the signs of the two-photon couplings of the mesons have partly been uncertain. Recently, it has been shown [1] that the options…”

“…(5.50) and (5.51) in [29]). In the dynamical version of the LσM the meson-quark couplings constants for the π and σ meson are given by [1,2] g = g πqq = g σqq = 2π/ N c = 3.63.…”

“…This means that the σ-meson resonant excited state is located in the unphysical region of the Compton scattering amplitude A 1 (s, t) at positive t. We consider this as an argument in favor of treating the σ-meson contribution to (α − β) t in terms of a pole in the complex t-plane with properties of the σ meson as the particle of the σ field, having a definite mass of m σ = 666.0 MeV [1,2]. However, for the obvious reasons discussed in [1,3] it is equivalent to treat the σ-meson contribution to (α − β) t in terms of a cut in the complex t-plane with properties as obtained for the on-shell σ meson. This equivalence may be formulated in terms of a sum rule, where (α − β) t connects properties of the σ-meson as the particle of the σ field with properties of the on-shell σ meson.…”

“…The theoretical investigations of the t-channel pole contributions carried out in the past [1,3,4] remained incomplete because there were no firm predictions of the signs. Furthermore, there was only vague information on the contributions of the f 0 (980) and a 0 (980) mesons.…”