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

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.