Summary
Pole dominance and a Veneziano model for the scattering amplitudes πN→πN, πN→NA1 and πN→Nρ are used to derive the electromagnetic nucleon form factors. The technique is based on a method proposed by Rosner and Suura. Correction terms to the pole-dominance assumption are necessary and therefore included. Their specific form strongly influences the final result. With the simplest assumptions for them the electric form factor contains a dipole term instead of an infinite sequence of poles as encountered in the meson case, and drops off at infinity liket −1. However to get a reasonable magnetic form factor some correction terms have to be modified. As a by-product an expression for the axial form factor is obtained.
Riassunto
Si usano, per ottenere i fattori di forma elettromagnetici del nucleone, la dominanza dei poli ed un modello di Veneziano per le ampiezze di scattering πN→πN, πN→NA1 e πN→Nρ. La tecnica si basa su di un metodo proposto da Rosner e Suura. I termini di correzione all’ipotesi della dominanza dei poli sono necessari e quindi sono inclusi. La loro forma specifica influenza notevolmente il risultato finale. Facendo per essi le ipotesi più semplici il fattore di forma elettrico contiene un termine di dipolo al posto di una successione infinita di poli come avviene nel caso del mesone; il nuovo termine va all’infinito comet −1. D’altra parte, per ottenere un fattore di forma magnetico ragionevole si devono modificare alcuni dei termini di correzione. Un risultato secondario è un’espressione per il fattore di forma assiale.
Реэюме
Для вывода злектромагнитных нуклонных форм-факторов испольэуются полюсная доминантность и модель Венециано для амплитуд рассеяния πN → πN , πN → πA1 и πN → Nρ. Рассматриваемая техника основывается на методй, предложенном Роснером и Суура. Поправочные члены к предположению полюсное доминантности являются необходимыми и позтому они включаются в рассмотрение. Их специфическая форма сильно влияет на окончательный реэультат. При простейщих предположениях относительно зтих членов, злектрический форм-фактор содержит дипольный член вместо бесконечной последовательности полюсов, в том виде как имело место в меэонном случае, и убывает на бесконечности, какt -1. Однако, для получения раэумного магнитного форм-фактора некоторые поправочные члены должны быть видоиэменены. Как побочный продукт получается выражение для аксиального форм-фактора.
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The arbitrariness in getting form factors from Veneziano models has been pointed out byGeffen, ref. (5), in the pion case.
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Konetschny, W., Majerotto, W. Nucleon form factors in the veneziano model. Nuov Cim A 1, 188–201 (1971). https://doi.org/10.1007/BF02722621
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DOI: https://doi.org/10.1007/BF02722621