Summary
Using the dual-resonance model of Kikkawa and Sato, we calculate the contributions of the one-closed-loop graph to the electromagnetic form factor and the virtual-Compton-scattering amplitude of theI=1,I 3=1, 0+ meson. It will be shown that the resulting form factors behave like 1/(−t) ast → −∞, and the virtual-Compton-scattering amplitudeA (see eq. (4.2)) satisfies the Bjorken’s scaling law and has the fixed-pole structure required by the Fubini-Gell-Mann sum rule. Obviously this model is gauge invariant.
Riassunto
Facendo uso del modello della risonanza duale di Kikkawa e Sato si calcolano i contributi dei diagrammi con un’ansa chiusa al fattore di forma elettromagnetico e all’ampiezza dello scattering di Compton virtuale del mesoneI=1,I 3=1, 0+. Si mostra che i fattori di forma risultanti si comportano come 1/(−t) quandot → 0, e che l’ampiezza dello scattering di Compton virtualeA (vedi eq. (4.2)) soddisfa la legge di scala di Bjorken e la struttura di polo fisso richiesta dalla regola di somma di Fubini-Gell-Mann. Ovviamente questo modello è invariante di gauge.
Реэюме
Испольэуя модель дуальных реэонансов Киккава и Сато, мы вычисляем вклады графика с одной эамкнутой петлей в злектромагнитный форм-фактор и амплитуду виртуального комптоновского рассеяния для меэонаI=1,I 3= 1, 0+. Будет покаэано, что полученные форм-факторы ведут себя, как 1/(−t) при t → −∞, и амплитуда виртуального комптоновского рассеяния A удовлетворяет эакону подобия Бьёркена и имеет структуру с фиксированным полюсом, что требуется согласно правилу сумм Фубини-Гелл-Манна. Эта модель является калибровочноинвар иантной.
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Literatur
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This paragraph had its origin in a discussion with Profs.J. Iizuka andZ. Maki. I would like to thank them for this helpful discussion.
T. Muta andY. Simizu: Kyoto University preprint, to be published;H. B. Nielsen andL. Susskind: CERN preprint, Ref. TH. 1230-CERN.
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This article was originally submitted toLettere al Nuovo Cimento on 16th October, 1970, and then resubmitted toIl Nuovo Cimento, according to the advice of the referee.
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Niégawa, A. Form factor and virtual-compton-scattering amplitude in the kikkawa-sato model (Dual-resonance model of hadron with gauge bosons). Nuov Cim A 4, 883–903 (1971). https://doi.org/10.1007/BF02731525
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DOI: https://doi.org/10.1007/BF02731525