Generalized Gerasimov-Drell-Hearn Sum Rule for the Proton-Neutron Difference in Chiral Perturbation Theory

Applications of the chiral expansion to generalize the Gerasimov-Drell-Hearn sum rule for finite $Q^2$ are discussed. The observation of several authors that the corrections to the leading order contributions are large and limit the applicability to a very small range in $Q^2$, are valid when considering the sum rule for protons and neutrons, separately. When using the proton-neutron difference, the chiral expansion may be valid to considerably higher momentum transfers where hadronic degrees of freedom at large distances may connect up with quark and gluon degrees of freedom. This could mark the first time that nucleon structure is decribed by fundamental theory from large to small distances.