Summary
We discuss the canonical light-cone singularities of the vertex function with the aid of the Mellin-transformed DGS representation. We demonstrate that these singularities correctly describe the first two terms in the asymptotic expansion of the momentum space vertex function, both in the scaling limit and in the limit in which one of the current masses goes to infinity while the second is held finite. Moreover, the coefficient function of the leading term in the latter limit is obtained as a smooth limit in the scaling variable of the corresponding function in the scaling limit. Implications for form factors are also pointed out.
Riassunto
Si discutono le singolarità del cono di luce canoniche della funzione di vertice con l’aiuto della rappresentazione trasformata di Mellin DGS. Si dimostra che queste singolarità descrivono correttamente i primi due termini dello sviluppo in serie asintotico della funzione di vertice nello spazio degli impulsi, sia nel caso del limite della trasformazione di scala sia nel caso del limite in cui una delle masse delle correnti tende all’infinito mentre la seconda resta finita. Inoltre, nel secondo caso la funzione dei coefficienti del termine principale si ottiene come un limite spianato nella variabile di scala della corrispondente funzione del limite della trasformazione di scala. Si puntualizzano anche le implicazioni che riguardano i fattori di forma.
Реэюме
Мы обсуждаем канонические сингулярности на световом конусе верщинной функции с помошью преобраэования Меллина для DGS представления. Мы покаэываем, что зти сингулярности привильно описывают первые два члена в асимптотическом раэложении верщинной функции в импульсном пространстве, в пределе подобия и в пределе, в котором одна иэ токовых масс стремится к бесконечности, тогда как вторая остается конечной. Кроме того, в лестничном приближении получается главный член, как плавный предел по переменной подобия соответствуюшей функции в пределе подобия. Также укаэываются следствия для формфакторов.
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Ahmed, M.A. The vertex function and canonical light-cone singularities. Nuov Cim A 20, 655–668 (1974). https://doi.org/10.1007/BF02727458
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DOI: https://doi.org/10.1007/BF02727458