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  • Access by Xinjiang University

Space-Time Analysis of High-Energy Scattering

Claudio A. Orzalesi*

  • Department of Physics, New York University, New York, New York 10003

  • *Address after November, 1972: Istituto di Fisica, Università di Parma, Parma, Italy.

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 a+bc+d, the off-shell amplitude A(ν, κ, κ, t) [ν(pa+pc)·p, ppb+pd, κ=(pa+pc)2, t=Δ2=(pcpa)2, κ=(pa+pc)·Δ=pc2pa2κcκa] is written in terms of its Lehmann-Symanzik-Zimmermann correlation function F(z·p, z·Δ, z2, t). The properties of A(ν, κ, ) in the R-limit (ν, with κ, κ, and t fixed) and in the A-limit (ν, ωκ2ν, κ, and t fixed) are translated into space-time properties of F(z). By combined use of the assumed Regge να(t) R-limit behavior, scaling νρ2F(ω) A-limit behavior, as well as of the assumed Regge small-ω A-limit behavior limω0limAA(ν, κ, )=limκlimRA(ν, κ, ), we determine the form of F(z) in the interesting space-time regions to be (z·p)α(t)g(z·Δ, z2, t) as (z·p) and fρ(z·p, z·Δ, t)(z2)ρ near the light cone (LC) z2=0, with fρ(λ, 0, t)λα(t) as λ. This latter property of fρ 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-z2 behavior of F(z) is determined from the assumed Regge behavior of the pole-dominance approximation to A(ν, κ, ), and we again find a (z·p)α(t) large-(z·p) behavior of F(z) in this region. The emerging picture is simply summarized by setting F(z)fρ(z·p, 0, t)g(z·Δ, z2, t) with g(z·Δ, z2, t)(z2)ρ near the LC. The only important space-time regions for high-energy scattering are the regions z·pO(ν), which is shown to determine the moving Regge poles, and z20, which is shown to give rise to a fixed-pole behavior if and only if α(t)<ρ2. 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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