Electromagnetic polarizabilities of the nucleon and properties of the $\sigma$-meson pole contribution

Abstract

The $t$-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, $(\alpha -\beta {)}^t$, can be quantitatively understood in terms of a $\sigma$-meson pole in the complex $t$-plane of the invariant scattering amplitude $A_1(s,t)$ with properties of the $\sigma$ 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 $\sigma$ meson are taken from the $\pi \pi ->\sigma ->\pi \pi$, $\gamma \gamma ->\sigma ->\pi \pi$ and $N\bar{N}->\sigma ->\pi \pi$ reactions. This equivalence may be understood as a sum rule where the properties of the $\sigma$ 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 $(\alpha -\beta {)}^t$ making use of predictions of the quark-level NJL model for the $\sigma$-meson mass.

References in corpus (10)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• A low-lying scalar meson nonet in a unitarized meson model
• Dispersion relations in real and virtual Compton scattering
• Polarizability of the Nucleon and Compton Scattering
• Signatures of Chiral Dynamics in Low Energy Compton Scattering off the Nucleon
• Ground-State Scalar $\bar{q}q$ Nonet: SU(3) Mass Splittings and Strong, Electromagnetic, and Weak Decay Rates
• The Present Status on sigma and kappa Meson Properties
• Structure of the $\sigma$-meson and diamagnetism of the nucleon
• Compton Scattering by the Nucleon
• $\sigma (600)$ and background in $\pi \pi$ scattering

Cited by in corpus (17)

• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• f0(980) meson as a K bar K molecule in a phenomenological Lagrangian approach
• Strong and radiative decays of the scalars f0(980) and a0(980) in a hadronic molecule approach
• The sigma -> gamma gamma Width from Nucleon Electromagnetic Polarizabilities
• The Quark-Level Linear σ Model
• Electromagnetic polarizabilities and the excited states of the nucleon
• Properties of the ${\pi }^0$, $\eta$, ${\eta }^{\prime }$, $\sigma$, $f_0(980)$ and $a_0(980)$ mesons and their relevance for the polarizabilities of the nucleon
• Dispersion theory of nucleon Compton scattering and polarizabilities
• 2γ-decays of scalar mesons (σ(600), f_0(980) and a_0(980)) in the Nambu-Jona-Lasinio model
• Structure of scalar mesons and the Higgs sector of strong interaction
• Polarizabilities of the nucleon and spin dependent photo-absorption
• Observation of the Higgs Boson of strong interaction via Compton scattering by the nucleon
• Structure of the nucleon and spin-polarizabilities
• Nambu's Nobel Prize, the $\sigma$ meson and the mass of visible matter
• Radiative decays of scalar mesons σ(600), f_0(980) and a_0(980) in the local Nambu-Jona-Lasinio model
• Mass generation via the Higgs boson and the quark condensate of the QCD vacuum
• Obtaining sigma --> gamma gamma Width from Nucleon Polarizabilities