Generalized Sum Rules for Spin-Dependent Structure Functions of the Nucleon

TL;DR

This paper generalizes sum rules for the nucleon's spin-dependent structure functions by studying virtual-photon Compton amplitudes, connecting low and high Q^2 regimes, and providing testable predictions for upcoming experimental data.

Contribution

It introduces a unified framework for sum rules across all Q^2 values using chiral perturbation theory and twist expansion, extending previous special cases.

Findings

Calculated Compton amplitudes at small Q^2 using chiral perturbation theory.

Derived sum rules that can be tested with Jefferson Lab data.

Provided constraints on the Q^2 evolution of the G_1 sum rule.

Abstract

The Drell-Hearn-Gerasimov and Bjorken sum rules are special examples of dispersive sum rules for the spin-dependent structure function G_1(\nu, Q^2) at Q^2=0 and \infty. We generalize these sum rules through studying the virtual-photon Compton amplitudes S_1(\nu, Q^2) and S_2(\nu,Q^2). At small Q^2, we calculate the Compton amplitudes at leading-order in chiral perturbation theory; the resulting sum rules can be tested by data soon available from Jefferson Lab. For Q^2>>\Lambda_{QCD}^2, the standard twist-expansion for the Compton amplitudes leads to the well-known deep-inelastic sum rules. Although the situation is still relatively unclear in a small intermediate-Q^2 window, we argue that chiral perturbation theory and the twist-expansion alone already provide strong constraints on the Q^2-evolution of the G_1(\nu,Q^2) sum rule from Q^2=0 to Q^2=\infty.