Investigations on the Foundation and Possible Modifications of the Gerasimov-Drell-Hearn Sum Rule

Abstract

All derivations of the GDH sum rule are presented and discussed in detail, focussing particularly on the validity of the underlying assumptions. Several tests of the sum rule within perturbative models are reviewed. Various possible sources of modifications of the sum rule are examined. With respect to the current-algebra derivation, the crucial role of the infinite-momentum limit is pointed out. A derivation is presented that exhibits the infinite-momentum limit as its last step, opening the prospect of studying its legitimacy within perturbative models. Adopting the Weinberg-Salam model as a testing ground, it is shown that a modification due to an anomalous charge-density commutator is remedied owing to the infinite-momentum limit. This finding is confirmed upon considering $t$-channel exchange of axial-vector mesons. Several other aspects of possible sources of modifications are investigated. Evolving the GDH sum rule to non-zero photon virtualities $Q^2$, it is argued that different generalizations of the GDH integral, which coincide both at $Q^2=0$ and at large $Q^2$, may considerably deviate from one another at intermediate $Q^2$. The limits $Q^2\to0$ and $Q^2\to\infty$ are investigated beyond leading terms. The contribution of the pion-nucleon final state to inclusive electroproduction is analyzed.