Comment on the generalized Gerasimov-Drell-Hearn sum rule in chiral perturbation theory Page: 1 of 5

JLAB-PHY-00-03

Comment on the Generalized Gerasimov-Drell-Hearn Sum
Rule in Chiral Perturbation Theory
0 Volker D. Burkerta
0 Thomas Jefferson National Accelerator Facility
(1 Newport News, Virginia, 23606
Abstract
I comment on the application of the chiral expansion to generalize
the Gerasimov-Drell-Hearn sum rule for finite Q2. The observation,
made by several authors, that the corrections to the leading order con-
tributions are large and limit the applicability to a very small range in
Q2 are valid when considering the generalization of the sum rule for
protons and neutrons, separately. However, when using the proton-
neutron difference, the application of chiral perturbation theory may
be expanded to substantially higher Q2
The spin structure of the nucleon has been of central interest for nearly 15
years. Most studies have focused on the deep inelastic regime to measure the
spin structure functions gi(x) and g2(X), and their respective first moments.
In recent years the interest has shifted towards the lower Q2 regime and
the resonance region 1,2, and measurements have been untertaken to study
the transition from the scaling regime to the regime of strong QCD 3,,
These advances in experiments made it urgent to study theoretically the
connection between these different regimes. While perturbative techniques
and higher twist expansion approaches seem appropriate at Q2 > 0.5GeV2
and invariant masses above the resonance region (W > 2.5GeV/c2), new
approaches are needed to study the low Q2 and low W regimes. Numerous
phenomenological models have been constructed to describe the resonance
regime and the transition to the deep-inelastic regime 1,2,6,7,8,9,10 All models
show that the resonance region, especially the A(1232), plays an important
role in the helicity dependence of the inclusive cross section at small Q2. At
Q2 = 0 the sum rule by Gerasimov, Drell, and Hearn " (GDH SR) relates
the energy-weighted integral of the helicity-dependent cross section to the
anomalous magnetic moment of the target nucleon:
IGDH = J 0a112(V) v (2(v) - 32(v)2 1)
Jv 4

1

"e-mail: burkert@jlab.org

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Burkert, Volker D. Comment on the generalized Gerasimov-Drell-Hearn sum rule in chiral perturbation theory, article, March 1, 2000; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc708041/m1/1/ocr/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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