Virtual Compton scattering off the nucleon at low energies

Abstract

We investigate the low-energy behavior of the four-point Green’s function ${\mathrm{\Gamma }}^{\mathrm{\mu }\nu }$ 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 ${\mathit{q}}^{\prime }$ 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(${\mathit{q}}_{\mathrm{\alpha }}$ ${\mathit{q}}_{\mathrm{\beta }}^{\prime }$), whereas the orders O(${\mathit{q}}_{\mathrm{\alpha }}$ ${\mathit{q}}_{\mathrm{\beta }}$) and O(${\mathit{q}}_{\mathrm{\alpha }}^{\prime }$ ${\mathit{q}}_{\mathrm{\beta }}^{\prime }$) are contained in the low-energy theorem for ${\mathrm{\Gamma }}^{\mathrm{\mu }\nu }$, 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. © 1996 The American Physical Society.