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Generalized sum rules for spin-dependent structure functions of the nucleon

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The Drell-Hearn-Gerasimov and Bjorken sum rules are special examples of dispersive sum rules for the spin-dependent structure function [iopmath latex="$G_1(\nu, Q^2)$"] G1(,Q2) [/iopmath] at [iopmath latex="$Q^2 = 0$"] Q2 = 0 [/iopmath] and [iopmath latex="$\infty$"] [/iopmath] . We generalize these sum rules through studying the virtual-photon Compton amplitudes [iopmath latex="$S_1(\nu, Q^2)$"] S1(,Q2) [/iopmath] and [iopmath latex="$S_2(\nu, Q^2)$"] S2(,Q2) [/iopmath] . At small [iopmath latex="$Q^2$"] Q2 [/iopmath] , we calculate the Compton amplitudes at leading order in chiral perturbation theory; the resulting sum rules will be able to be tested against data soon available from the Jefferson Laboratory. For [iopmath latex="$Q^2 \gg\Lambda_{\rm QCD}^2$"] Q2>>QCD2 [/iopmath] , 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- [iopmath latex="$Q^2$"] Q2 [/iopmath] window, we argue that chiral perturbation theory and the twist-expansion alone already provide strong constraints on the [iopmath latex="$Q^2$"] Q2 [/iopmath] -evolution of the [iopmath latex="$G_1(\nu, Q^2)$"] G1(,Q2) [/iopmath] sum rule from [iopmath latex="$Q^2 = 0$"] Q2 = 0 [/iopmath] to [iopmath latex="$\infty$"] [/iopmath] .

Document Type: Miscellaneous

Publication date: January 1, 2001


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