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• W2000756830 abstract "We present a phenomenological space-time analysis of high-energy scattering. For a two-body process $a+bensuremath{rightarrow}c+d$, the off-shell amplitude $A(ensuremath{nu}, ensuremath{kappa}, {ensuremath{kappa}}^{ensuremath{'}}, t)$ [$ensuremath{nu}ensuremath{equiv}({p}_{a}+{p}_{c})ifmmodecdotelsetextperiodcenteredfi{}p$, $pensuremath{equiv}{p}_{b}+{p}_{d}$, $ensuremath{kappa}={({p}_{a}+{p}_{c})}^{2}$, $t={ensuremath{Delta}}^{2}={({p}_{c}ensuremath{-}{p}_{a})}^{2}$, ${ensuremath{kappa}}^{ensuremath{'}}=({p}_{a}+{p}_{c})ifmmodecdotelsetextperiodcenteredfi{}ensuremath{Delta}={{p}_{c}}^{2}ensuremath{-}{{p}_{a}}^{2}ensuremath{equiv}{ensuremath{kappa}}_{c}ensuremath{-}{ensuremath{kappa}}_{a}$] is written in terms of its Lehmann-Symanzik-Zimmermann correlation function $mathcal{F}(zifmmodecdotelsetextperiodcenteredfi{}p, zifmmodecdotelsetextperiodcenteredfi{}ensuremath{Delta}, {z}^{2}, t)$. The properties of $A(ensuremath{nu}, ensuremath{kappa}, dots{})$ in the $R$-limit ($ensuremath{nu}ensuremath{rightarrow}ensuremath{infty}$, with $ensuremath{kappa}$, ${ensuremath{kappa}}^{ensuremath{'}}$, and $t$ fixed) and in the $A$-limit ($ensuremath{nu}ensuremath{rightarrow}ensuremath{infty}$, $ensuremath{omega}ensuremath{equiv}ensuremath{-}frac{ensuremath{kappa}}{2ensuremath{nu}}$, ${ensuremath{kappa}}^{ensuremath{'}}$, and $t$ fixed) are translated into space-time properties of $mathcal{F}(z)$. By combined use of the assumed Regge ${ensuremath{nu}}^{ensuremath{alpha}(t)}$ $R$-limit behavior, scaling ${ensuremath{nu}}^{ensuremath{rho}ensuremath{-}2}F(ensuremath{omega})$ $A$-limit behavior, as well as of the assumed Regge small-$ensuremath{omega}$ $A$-limit behavior ${mathrm{lim}}_{ensuremath{omega}ensuremath{rightarrow}0}{mathrm{lim}}_{A}A(ensuremath{nu}, ensuremath{kappa}, dots{})={mathrm{lim}}_{ensuremath{kappa}ensuremath{rightarrow}ensuremath{infty}}{mathrm{lim}}_{R}A(ensuremath{nu}, ensuremath{kappa}, dots{})$, we determine the form of $mathcal{F}(z)$ in the interesting space-time regions to be ${(zifmmodecdotelsetextperiodcenteredfi{}p)}^{ensuremath{alpha}(t)}g(zifmmodecdotelsetextperiodcenteredfi{}ensuremath{Delta}, {z}^{2}, t)$ as $(zifmmodecdotelsetextperiodcenteredfi{}p)ensuremath{rightarrow}ensuremath{infty}$ and ${f}_{ensuremath{rho}}(zifmmodecdotelsetextperiodcenteredfi{}p, zifmmodecdotelsetextperiodcenteredfi{}ensuremath{Delta}, t){({z}^{2})}^{ensuremath{-}ensuremath{rho}}$ near the light cone (LC) ${z}^{2}=0$, with ${f}_{ensuremath{rho}}(ensuremath{lambda}, 0, t)ensuremath{sim}{ensuremath{lambda}}^{ensuremath{alpha}(t)}$ as $ensuremath{lambda}ensuremath{rightarrow}ensuremath{infty}$. This latter property of ${f}_{ensuremath{rho}}$ 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-${z}^{2}$ behavior of $mathcal{F}(z)$ is determined from the assumed Regge behavior of the pole-dominance approximation to $A(ensuremath{nu}, ensuremath{kappa}, dots{})$, and we again find a ${(zifmmodecdotelsetextperiodcenteredfi{}p)}^{ensuremath{alpha}(t)}$ large-($zifmmodecdotelsetextperiodcenteredfi{}p$) behavior of $mathcal{F}(z)$ in this region. The emerging picture is simply summarized by setting $mathcal{F}(z)ensuremath{cong}{f}_{ensuremath{rho}}(zifmmodecdotelsetextperiodcenteredfi{}p, 0, t)g(zifmmodecdotelsetextperiodcenteredfi{}ensuremath{Delta}, {z}^{2}, t)$ with $g(zifmmodecdotelsetextperiodcenteredfi{}ensuremath{Delta}, {z}^{2}, t)ensuremath{sim}{({z}^{2})}^{ensuremath{-}ensuremath{rho}}$ near the LC. The only important space-time regions for high-energy scattering are the regions $zifmmodecdotelsetextperiodcenteredfi{}pensuremath{sim}O(ensuremath{nu})$, which is shown to determine the moving Regge poles, and ${z}^{2}ensuremath{cong}0$, which is shown to give rise to a fixed-pole behavior if and only if $ensuremath{alpha}(t)<ensuremath{rho}ensuremath{-}2$. We also consider the high-energy limit of semiweak exclusive processes, and show that, contrary to existing claims, such processes need not scale." @default.
• W2000756830 created "2016-06-24" @default.
• W2000756830 creator A5080382499 @default.
• W2000756830 date "1973-01-15" @default.
• W2000756830 modified "2023-10-16" @default.
• W2000756830 title "Space-Time Analysis of High-Energy Scattering" @default.
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• W2000756830 doi "https://doi.org/10.1103/physrevd.7.488" @default.
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