Finite-Energy Sum Rules and Inelastic Electron Scattering

We use finite-energy sum rules (FESR) to analyze the inelastic-electron-scattering data. We show that the sum of resonances build up a scaling function although each resonance contribution falls off according to a dipole formula. This is achieved by assuming that the dipole mass which enters into the form factor increases when we go to higher resonances. The assumption seems to be confirmed by the data. We also investigate the contribution of the Regge trajectories to the FESR, assuming that they all scale. We find that the equations can be satisfied only if there is another contribution of a $J=0\mathrm{}$ fixed pole. The residue function of the fixed pole is calculated explicitly and compared with that of the fixed pole found at real Compton scattering. The two residue functions are found to have opposite signs.