CMSR's for single charged pion photoproduction amplitudes and the role of the gauge invariant Born terms

Abstract

Continuous moment sum rules (CMSR's) for the t-channel single pion photoproduction amplitudes F i (−) ( v, t), i = 1, …, 4, are considered in great detail. Information about the high energy behavior of the amplitudes is extracted from low energy data in terms of an effective Regge pole picture which in most cases turns out to strongly violate certain reasonable postulates about the behavior of pure Regge poles, (idealized Regge pole picture). We ask, whether the deviation of the effective Regge pole picture from the idealized one can be described in terms of fixed poles at J = 0 arising from certain parts of the gauge invariant Born term contributions to the amplitudes. Such a description does work for small | t| in case of the amplitudes F i (−) ( v, t), i = 2, 3, but, as | t| increases, further contributions also become important. Investigation of CMSR's for amplitudes from which appropriate parts of the Born terms have been separated out, leads to a definite finite energy sum rule (FESR) duality scheme where parts of the Born terms ‘build up’ the idealized Regge poles themselves, while other parts give rise to additional contributions on the high energy side of the CMSR's.