Summary
A very simple derivation of a complete set of sum rules implied by crossing symmetry on partial-wave amplitudes is given. This set is shown to be equivalent to the Balachandran-Nuyts crossing relations for partial-wave amplitudes. Many applications to dynamical models are proposed and discussed, and it is shown in particular that the Padé treatment of theλϕ 4 theory for ππ scattering yields extremely good agreement with crossing symmetry.
Riassunto
Si ricava in modo semplice un insieme completo di regole di somma che derivano dalla simmetria incrociata delle ampiezze d’onda parziali. Si dimostra che questo insieme è equivalente alle relazioni incrociate di Balachandran-Nuyts per ampiezze d’onda parziali. Si propongono e si discutono molte applicazioni a modelli dinamici e si dimostra in particolare che il trattamento di Padé della teoriaλϕ 4 per lo scattering ππ fornisce un buon accordo con la simmetria incrociata.
Резюме
Приводится очень простой вывод полной системы правил сумм, предполагающих кроссинг-симметрию парциальных амплитуд. Показывается, что эта система эквивалентна поперечным соотношениям Балачандрана-Нуитса для парциальных амплитуд. Предлагаются и обсуждаются различные приложения к динамическим моделям, и, в частности, показывается, что интерпретация Падэ теорииλϕ 4 для ππ рассеяния приводит к очень хорошему согласию с кроссингсимметрией.
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Basdevant, J.L., Cohen-Tannoudji, G. & Morel, A. Crossing-symmetry constraints on partial-wave amplitudes and their physical content. Nuovo Cimento A (1965-1970) 64, 585–602 (1969). https://doi.org/10.1007/BF02721662
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DOI: https://doi.org/10.1007/BF02721662