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

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.Comment: 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) correcte

The nucleon and Delta-resonance masses in relativistic chiral effective-field theory

We study the chiral behavior of the nucleon and $\Delta$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $\pi N$ and $\pi\Delta$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $\pi N$-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and $\Delta$ masses, while inclusion of the $\pi \Delta$ loops tends to spoil this agreement.Comment: 13 pages, 3 figs, 2 table

Baryon chiral perturbation theory: an update

The issue of consistent power counting in baryon chiral perturbation theory is revisited.Comment: 5 pp, 1 fig; contributed to BARYONS 2010, Osaka, Japan, Dec 7-11, 201

A Statistical Analysis of Hadron Spectrum: Quantum Chaos in Hadrons

The nearest-neighbor mass-spacing distribution of the meson and baryon spectrum (up to 2.5 GeV) is described by the Wigner surmise corresponding to the statistics of the Gaussian orthogonal ensemble of random matrix theory. This can be viewed as a manifestation of quantum chaos in hadrons.Comment: 9 pages, 3 figures, revise

The Delta(1232) Resonance in Chiral Effective Field Theory

I discuss the problem of formulating the baryon chiral perturbation theory ($\chi$PT) in the presence of a light resonance, such as the $\Delta(1232)$, the lightest nucleon resonance. It is shown how to extend the power counting of $\chi$PT to correctly account for the resonant contributions. Recent applications of the resulting chiral effective-field theory to the description of pion production reactions in $\Delta$-resonance region are briefly reviewed.Comment: 8 pages, 8 figs; prepared for the proceedings of the Intl Erice School ``Quarks in Hadrons and Nuclei'', 29th Course, 16--24 Sep 2007, Sicily, Ital