Virtual Compton scattering off the nucleon at low energies

Abstract

We investigate the low-energy behavior of the four-point Green's function $Γ^{μν}$ describing virtual Compton scattering off the nucleon. Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive the leading terms of an expansion of the operator in the four-momenta $q$ and $q'$ of the initial and final photon, respectively. The model-independent result is expressed in terms of the electromagnetic form factors of the free nucleon, i.e., on-shell information which one obtains from electron-nucleon scattering experiments. Model-dependent terms appear in the operator at $O(q_αq'_β)$, whereas the orders $O(q_αq_β)$ and $O(q'_αq'_β)$ are contained in the low-energy theorem for $Γ^{μν}$, i.e., no new parameters appear. We discuss the leading terms of the matrix element and comment on the use of on-shell equivalent electromagnetic vertices in the calculation of ``Born terms'' for virtual Compton scattering.