Gerasimov-Drell-Hearn sum rule and related integrals

Abstract

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.

Electroproduction of neutral pions in the Hall A at the Jefferson Laboratory; Electroproduction de pions neutres dans le Hall A au Jefferson Laboratory

“…The r 04 00 is compatible within the error bars with the model we injected in the simulation. The errors estimation of the density matrix element r 5 1,−1 are better than 0.1 in every bin, that means the sensitivoty of SCHC violating terms is better than 10 %.…”

“…To this end, we express the virtual cross section in Eq. (1.1) in terms of structure functions as described in the paper of Drechsel and Tiator [5] directly related to bilinear combinations of the CGLN helicity amplitudes [81].…”

“…In [5], D. Drechsel and L. Tiator write the π electroproduction cross section in terms of hadronic tensors. To this end, they express the electroproduction cross section first in terms of leptonic and hadronic currents, using the conventions of Bjorken and Drell [6]:…”

“…The general expression of the 5-fold unpolarized pion electroproduction cross sections is, in the conventions of Drechsel and Tiator [5], and in the One-Photon-ExchangeApproximation (OPEA):…”

“…We also define, within the following conventions of Drechsel and Tiator [5]: ẑ axis along the virtual photon; ŷ = (k i ∧k f )/ sin θ e orthogonal to the leptonic plane;…”