Summary
We study the analyticity in an external-mass variable of a four-point function by looking at simple perturbation theory diagrams. This analyticity information is required in order to apply models like vector-meson dominance and PCAC to two-body scattering amplitudes. A complex singularity is found on the physical sheet but at high energies it moves far from the physical region. The role of these singularities in nuclear shadowing is briefly discussed.
Riassunto
Si studia l’analiticità in una variabile della massa esterna di una funzione di quattro punti tenendo conto di semplici diagrammi della teoria delle perturbazioni. Queste informazioni sull’analiticità sono richieste allo scopo di applicare modelli come la dominanza del mesone vettoriale e la PCAC alle ampiczze di scattering di due corpi. Si trova una singolaritià complessa sul foglietto fisico, ma allc alte energie essa si allontana dalla regione fisica. Si discute brevemente il ruolo di queste singolarità nell’ offuscamento nucleare.
РЕжУМЕ
Мы исследуем аналити чность четырех-точечной фун кции по переменной массе, рассматривая диагра ммы обычной теории возму шений. Эта аналитичсская ин формация требуется, для того чт обы применить модели, полобныё моде ли доминантности векторного меэона и м одели PCAC, к амплитудам двух-частичного расс еяния. На физичсском листе обнаружена ком плексная сингулвух-лярность, но при высок их энергиях она смсща ется далеко от физической области. Вкратце обсуждается роль таких сингулярн остей в ядерном затенении.
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Work supported in part by the National Science Foundation.
U.S. Steel Graduate Fellow.
A.P. Sloan Fellow.
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Sullivan, J.D., Potter, W.T. Analyticity of a scattering amplitude in an external-mass variable. Nuov Cim A 3, 93–115 (1971). https://doi.org/10.1007/BF02912612
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DOI: https://doi.org/10.1007/BF02912612