Q²-Dependence of the Drell-Hearn-Gerasimov integral

The energy and four-momentum (Q^2) dependence of the photo-absorption cross section on the proton is calculated for helicity -1/2 and -3/2 states. An effective Lagrangian model is used, formulated in terms of meson and baryon degrees of freedom, which obeys crossing symmetry, unitarity, Lorentz and gauge invariance. The difference in the cross sections for the two helicity states, the Drell-Hearn-Gerasimov integral $I_{DHG}(Q^2)$, is evaluated at different $Q^2$. We find that at small momentum transfer the absolute value of $I_{DHG}(Q^2)$ first increases to reach a maximum at $Q^2 \approx 0.05 GeV^2$ before decreasing at higher $Q^2$.