Summary
A rigorous derivation is given of the asymptotic properties of the one-loop nonplanar amplitude. Boths- andt-channel asymptotic behaviours are investigated. They are controlled by the expected Regge singularities and possible exponentials are ruled out. Thes-channel fixed-angle behaviour is again an exponential. The coefficient ofs in the exponential is exactly half of that obtained for the Born approximation and the planar loop.
Riassunto
In questo lavoro si ottengono — in modo rigoroso — le proprietà asintotiche del diagramma duale con un cappio non planare, associato comunemente al pomerone. I comportamenti ins et sono controllati dalle corrispondenti singolarità di Regge e si escludono possibili comportamenti esponenziali. Il comportamento asintotico ad angolo fisso è un esponenziale con un coefficiente, all’esponente, metà di quello riscontrato per i diagrammi ad albero (approssimazione di Born).
Реэюме
Приводится строгий вывод асимптотических свойств неплоской амплитуды с одной петлей. Исследуется асимптотическое поведение вs иt каналах. Асимптотическое поведение проверяется с помошью ожидаемых сингулярностей Редже. Воэможные зкспоненты исключаются. Поведение вs канале при фиксированном угле по-прежнему является зкспоненциальным. Козффициент приs в зкспоненте составляет ровно половину козффициента, полученного в борновском приближении и для плоской петли.
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References
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This result has also been derived byH. B. Nielsen (private communication) using a simple heuristic argument based on the analogue model.
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V. Alessandrini andD. Amati: unpublished.
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Partially supported by the Swiss National Fund.
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Alessandrini, V., Amati, D. & Morel, B. The asymptotic behaviour of the dual pomeron amplitude. Nuov Cim A 7, 797–823 (1972). https://doi.org/10.1007/BF02728811
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DOI: https://doi.org/10.1007/BF02728811