Summary
By using the Veneziano formula for ππ scattering as an approximation to the crossing-symmetricK-matrix, it is possible to obtain a model that satisfies two-body unitarity and is approximately crossing symmetric. The model contains very little freedom, but nevertheless gives good predictions for resonance masses and widths.
Riassunto
Usando la formula di Veneziano per lo scattering ππ come approssimazione alla matriceK a simmetria incrociata, è possibile ottenere un modello che soddisfa l’unitarietà a due corpi e che è approssimativamente a simmetria incrociata. Il modello non consente molta libertà, ma nondimeno fornisce buone previsioni per le masse e le ampiezze delle risonanze.
Реэюме
Благодаря испольэованию формулы Венециано для рассеяния как приближения для кроссинг-симметри чнойК-матрицы, можно получить модель, которая удовлетворяет двух-частичной унитарности и является приблиэительно кроссинг-симметрич ной. Эта модель содержит очень мало свободы, но тем не менее дает хорощие предскаэания для масс и щирин реэонансов.
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References
C. Lovelace:Phys. Lett.,28 B, 264 (1968).
C. Lovelace: CERN preprint TH 1041 (1969).
R. Roskies:Phys. Lett.,30 B, 42 (1969).
P. V. Landshoff andJ. C. Polkinghorne: private communication;S. Humble:Lett. Nuovo Cimento,11, 541 (1969).
J.-G. Cordes:Phys. Rev.,156, 1707 (1967). In this reference,Cordes studies the use of a constant for theV-matrix.
P. N. Dobson:Lett. Nuovo Cimento,16, 751 (1969). In this reference, the freedom in the choice of a left-hand cut for the generalized phase-space function in theK-matrix unitarization is used to incorporate Adler zeros in the unitarized Veneziano model.
Levers andSchwela report much the same violation of the Roskies’ crossing conditions in theK-matrix unitarization when the phase-space function given in ref. (2) is used. SeeR.-G. Levers andD. Schwela:The π-π Veneziano model, positivity and axiomatic analyticity, Bonn preprint 2-73.
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Carpenter, K.M., Negrine, S.M. A crossing-symmetric unitarization of the veneziano amplitude. Nuov Cim A 1, 13–37 (1971). https://doi.org/10.1007/BF02722608
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DOI: https://doi.org/10.1007/BF02722608