Some electromagnetic properties of the nucleon from Relativistic Chiral Effective Field Theory

Abstract

Considering the magnetic moment and polarizabilities of the nucleon we emphasize the need for relativistic chiral EFT calculations. Our relativistic calculations are done via the forward-Compton-scattering sum rules, thus ensuring the correct analytic properties. The results obtained in this way are equivalent to the usual loop calculations, provided no heavy-baryon expansion or any other manipulations which lead to a different analytic structure (e.g., infrared regularization) are made. The Baldin sum rule can directly be applied to calculate the sum of nucleon polarizabilities. In contrast, the GDH sum rule is practically unsuitable for calculating the magnetic moments. The breakthrough is achieved by taking the derivatives of the sum rule with respect to the anomalous magnetic moment. As an example, we apply the derivative of the GDH sum rule to the calculation of the magnetic moment in QED and reproduce the famous Schwinger's correction from a tree-level cross-section calcualation. As far as the nucleon properties are concerned, we focus on two issues: 1) chiral behavior of the nucleon magnetic moment and 2) reconciliation of the chiral loop and $\Delta$-resonance contributions to the nucleon magnetic polarizability.

Comments: 11 pages, 3 figs.; invited seminar at the 26th Course of the International Erice School of Nuclear Physics: Lepton Scattering and the Structure of Hadrons and Nuclei, Erice, Italy, 16-24 Sep 2004; revision to v3: reference added, typo in Eq. (38) corrected