Generalized Drell-Hearn-Gerasimov Sum Rule at Order {\cal O}(p^4) in Chiral Perturbation Theory

TL;DR

This paper computes the forward spin-dependent photon-nucleon Compton amplitudes at next-to-leading order in chiral perturbation theory to analyze the generalized Drell-Hearn-Gerasimov sum rule's behavior at low momentum transfer.

Contribution

It provides a detailed calculation of the sum rule at order {}(p^4) in chiral perturbation theory, revealing a rapid Q^2 variation.

Findings

Sum rule varies rapidly with Q^2 at low energies.

Next-to-leading order calculations improve understanding of spin-dependent amplitudes.

Results suggest deviations from simple dimensional analysis predictions.

Abstract

We calculate the forward spin-dependent photon-nucleon Compton amplitudes $S_1$ and $S_2$ as functions of photon energy $\nu$ and mass $Q^2$ at the next-to-leading (${\cal O}(p^4)$) order in chiral perturbation theory, from which we extract the contribution to a generalized Drell-Hearn-Gerasimov sum rule at low $Q^2$. The result indicates a much rapid $Q^2$ variation of the sum rule than a simple dimensional analysis would yield.