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D. Drechsel
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The Gerasimov-Drell-Hearn sum rule and related dispersive integrals connect real and virtual Compton scattering to inclusive photo- and electroproduction. Being based on universal principles as causality, unitarity, and gauge invariance, these relations provide a unique testing ground to study the internal degrees of freedom that hold a system together. The present contribution reviews the spin-dependent sum rules and cross sections of the nucleon. At small momentum transfer, the data sample information on the long range phenomena (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at large momentum transfer (short distance). The rich body of new data covers a wide range of phenomena from coherent to incoherent processes, and from the generalized spin polarizabilities on the low-energy side to higher twist effects in deep inelastic scattering.
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The quantum chromodynamics (QCD) sum rules for the Delta baryons are analyzed by taking into account the finite-width effects, through explicit utilization of the Breit-Wigner shape. We apply a Monte-Carlo based analysis to the traditional and the parity-projected sum rules. The first Delta excitation state is also considered as a sub-continuum resonance and the widths are calculated using the mass values as input.
We present a measurement of the spin-dependent cross sections for the vec{^3He}(vec{e},e)X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.
Using general baryon interpolating fields $J_B$ for $B= N, Xi, Sigma, $ without derivative, we study QCD sum rules for meson-baryon couplings and their dependence on Dirac structures for the two-point correlation function with a meson $iint d^4x e^{iqx} bra 0|{rm T}[J_B(x)bar{J}_B(0)] |{cal M}(p)ket$. Three distinct Dirac structures are compared: $igamma_5$, $igamma_5fslash{p}$, and $gamma_5sigma_{mu u}q^mu p^ u$ structures. From the dependence of the OPE on general baryon interpolating fields, we propose criteria for choosing an appropriate Dirac structure for the coupling sum rules. The $gamma_5sigma_{mu u}q^mu p^ u$ sum rules satisfy the criteria while the $igamma_5$ sum rules beyond the chiral limit do not. For the $igamma_5fslash{p}$ sum rules, the large continuum contributions prohibit reliable prediction for the couplings. Thus, the $gamma_5sigma_{mu u}q^mu p^ u$ structure seems pertinent for realistic predictions. In the SU(3) limit, we identify the OPE terms responsible for the $F/D$ ratio. We then study the dependence of the ratio on the baryon interpolating fields. We conclude the ratio $F/D sim 0.6-0.8$ for appropriate choice of the interpolating fields.
We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<Q^{2}<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which appears to be relatively large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also performed an isospin decomposition of the generalized forward spin polarizability $gamma_{0}$. Although its isovector part provides a reliable test of the calculation techniques of Chiral Perturbation Theory, our data disagree with the calculations.
We are studying the electron scattering process e p to e p gamma in order to obtain information on the genuine virtual Compton scattering (VCS) process gamma^* N to gamma N. In addition to the two kinematical variables of real Compton scattering, e.g. the scattering angle theta and the energy omega of the outgoing photon, the invariant amplitude for VCS depends on a third kinematical variable, which we choose as the absolute value of the three-momentum transfer to the nucleon. The structure-dependent coefficients in the VCS amplitude therefore acquire a momentum dependence and are termed ``generalized polarizabilities of the nucleon in analogy to real Compton scattering. Utilizing the heavy baryon formalism of chiral perturbation theory we present predictions for the momentum dependence of the ``generalized polarizabilities and discuss the VCS response functions to be measured in the scheduled electron scattering experiments.
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