Summary
In a five-particle processa+b→1+2+3, where the invariant mass of 2 and 3 is such that this pair can scatter only elastically in the final state, the conventional production amplitudeT si related easily to a new amplitudeT 23 − which has simpler analyticity properties thanT in relativistic quantum field theory. Concerning the physical interpretation ofT 23 −, its (l, m) partial wave can be consistently regarded as the inelastic scattering amplitude fora+b→1+(one composite particle with angular momentum (l, m)). It is shown thatT 23 − and its absorptive part have analyticity properties in three angular variables which generalize those of the four-particle amplitudes inside the Lehmann ellipses. The problem of deriving dispersion relations forT 23 − is also investigated.
Riassunto
In un processo di cinque particellea+b→1+2+3, in cui la massa invariante di 2 e 3 è tale che questa coppia può avere solo scattering elastico nello stato finale, si può facilmente mettere in relazione l'ampiezza di produzione convenzionaleT con una nuova ampiezzaT 23 − che ha proprietà di analiticità più semplici di quelle diT nella teoria dei campi quantistica relativistica. Riguardo all'interpretazione fisica diT 23 −, la sua onda parziale (l, m) può essere coerentemente considerata come l'ampiezza dello scattering inelastico pera+b→1+(una particella composta con momento angolare (l, m)) Si dimostra cheT 23 − e la sua parte assorbitiva hanno proprietà di analiticità in tre variabili angolari che generalizzano quelle delle ampiezze di quattro particelle entro le ellissi di Lehmann. Si esamina anche il problema della deduzione delle relazioni di dispersione perT 23 −.
Резюме
В пяти-частичном процессеa+b→1+2+3, где инвариантная масса 2 и 3 является такой, что эта пара может рассеиваться только упруго в конечном состоянии, обычная амплитуда рожденияT может быть легко связана с новой амплитудойT 23 −, которая имеет более простые аналитические свойства, чемT в релятивистской квантовой теории поля. Что касается физической интерпретацииT 23 −, то ее парциальную волну (l, m) можно последовательно рассматривать как амплитуду неупругого рассеяния дляa+b→1+(одна составная частица с моментом (l, m)). Показывается, чтоT 23 − и ее абсорбционная часть обладают свойствами аналитичности по трем угловым переменным, которые обобщают свойства четырехчастичных амплитуд внутри эллипсов Лемана. Также исследуется проблема вывода дисперсионных соотношений дляT 23 −.
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Address after 1st October 1971: Division de Física Teorica, Junta de Energia Nuclear, Madrid.
Sponsored by J.E.N. and G.I.F.T., Spain.
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Alvarez-Estrada, R.F. On the analyticity properties of five-particle amplitudes in quantum field theory. Nuov Cim A 13, 1–42 (1973). https://doi.org/10.1007/BF02788905
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DOI: https://doi.org/10.1007/BF02788905