The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon

Abstract

The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal principles as causality, unitarity, and gauge invariance, these sum rules provide a unique testing ground to study the internal degrees of freedom that hold the system together. The present article reviews these sum rules for the spin-dependent cross sections of the nucleon by presenting an overview of recent experiments and theoretical approaches. The generalization from real to virtual photons provides a microscope of variable resolution: At small virtuality of the photon, the data sample information about the long range phenomena, which are described by effective degrees of freedom (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at the larger virtualities. Through a rich body of new data and several theoretical developments, a unified picture of virtual Compton scattering emerges, which ranges from coherent to incoherent processes, and from the generalized spin polarizabilities on the low-energy side to higher twist effects in deep inelastic lepton scattering.

Electromagnetic excitation of nucleon resonances

“…This structure can be compared with QCD inspired quark models and, in recent years, more and more also with lattice QCD calculations [65,66,67,68]. Moreover, the nucleon transition form factors provide an essential input for dispersive calculations of both sum rules and two-photon corrections to electron scattering [69,70,71,72,73].…”

The Spin Structure of ³He and the Neutron at Low Q²: A Measurement of the Generalized GDH Integrand

“…The cross section can also be written equivalently as a cross section for the absorption of a virtual photon, which involves four partial cross sections [18,19]:…”

“…The sum rule's significance is that it relates static properties of the particle's ground state to dynamic properties of all its excited states. It also divulges that a non-zero anomalous magnetic moment requires that a particle have a finite size and hence an excitation spectrum [19]. Consequently, the discovery that the nucleon had a large anomalous magnetic moment provided a strong indication that the nucleon has an intrinsic structure and is not a point-like particle.…”

Two-photon physics

“…These relations can then be expanded in energy to obtain the SRs for the different static properties introduced in eqs. (2), (3). In this way we obtain the Baldin SR [6,7]:…”

“…Impressive experimental programs to measure these photoabsorption cross-sections for the nucleon have recently been carried out at ELSA and MAMI (for a review see ref. [3]). Such measurements provide an empirical test of the GDH SR, and can be used to generate phenomenological estimates of electromagnetic polarizabilities via related SRs.…”