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Space-Time Analysis of High-Energy Scattering
Phys. Rev. D 7, 488 – Published 15 January, 1973
DOI: https://doi.org/10.1103/PhysRevD.7.488
Abstract
We present a phenomenological space-time analysis of high-energy scattering. For a two-body process , the off-shell amplitude [, , , , ] is written in terms of its Lehmann-Symanzik-Zimmermann correlation function . The properties of in the -limit (, with , , and fixed) and in the -limit (, , , and fixed) are translated into space-time properties of . By combined use of the assumed Regge -limit behavior, scaling -limit behavior, as well as of the assumed Regge small- -limit behavior , we determine the form of in the interesting space-time regions to be as and near the light cone (LC) , with as . This latter property of is shown to uniquely correspond to having quark-hadron amplitudes with Regge behavior, at least in quark models for light-cone operator-product expansions. The large- behavior of is determined from the assumed Regge behavior of the pole-dominance approximation to , and we again find a large-() behavior of in this region. The emerging picture is simply summarized by setting with near the LC. The only important space-time regions for high-energy scattering are the regions , which is shown to determine the moving Regge poles, and , which is shown to give rise to a fixed-pole behavior if and only if . We also consider the high-energy limit of semiweak exclusive processes, and show that, contrary to existing claims, such processes need not scale.
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