Dispersion relation analysis of neutral pion photoproduction and electroproduction at threshold

Neutral pion photoproduction and electroproduction at threshold is analyzed in the framework of dispersion relations. For this purpose, we evaluate the real threshold amplitudes in terms of Born contributions and dispersion integrals determined by the imaginary parts of the multipoles of the unitary isobar model (MAID) and the phenomenological partial-wave analysis (SAID). The results show considerable cancellations between Born terms and resonance contributions. Good agreement with the data is found for photoproduction. While our dispersion analysis suggests considerable discrepancies for electroproduction, the present state of the experimental multipole analysis at finite ${Q}^{2}$ does not permit drawing conclusions at this time.