Asymptotic Behavior of Electroproduction Amplitudes in Ladder Models

概要

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Asymptotic behavior of single pion electroproduction amplitude is investigated using ladder models in the limit of s and k^2 tending to infinity. Two cases are considered which we shall refer to as the elementary and composite pion models. In the former, Born terms without k^2 dependence dominate the amplitude. In the latter, the amplitude exhibits Regge behavior with its residue function depending upon k^2, e.g. (k^2)^<-2>.(-s/k^2)^<α(t)> when s grows faster than k^2, while it depends upon k^2 only but does not show any Regge-like behavior when k^2 grows faster than s. This fact leads us to the conclusion that there is a large kinematical region where Regge asymptotic behavior does not hold in electroproduction processes. This implies that a higher cutoff is needed to substitute the high energy side of the finite energy sum rule by regge contributions when k^2 increases. In this connection, a suggestion is made on the modified duality between Regge residue functions and resonance excitation form factors instead of Harari's conjecture on the duality.
理論物理学刊行会の論文
1970-12-25