Il Nuovo Cimento A (1965-1970)

, Volume 58, Issue 3, pp 553–588 | Cite as

Compositeness and elementarity in theories with crossing

  • J. C. Le Guillou


It is shown that in anS-matrix with crossing, criteria of compositeness based on the vanishing of renormalization constants can be applied in a consistent way, allowing us to study the crucial dependence of the left-hand singularities on the degree of elementarity of the exchanged particles. Then, using both field theory andS-matrix approaches, we solve a paradox about an «impossibility», stated several times in the literature, of distinguishing between elementarity and compositeness of two baryons in two crossed channels: on the contrary, we exhibit different physical interpretations for distinct domains of the parameters values, at the boundary of which the amplitude undergoes critical change. We discriminate the various cases where each particle is either elementary or composite; when only one of these two baryons is («chain» or «ladder») composite, its mass is always the heaviest one. Next, we discuss and compare in our explicit model theZ=0, strong coupling limit and reciprocal bootstrap approaches, together with a discussion of approximations currently used in theN/D calculations. The vanishing of bothZ, while keeping finite the coupling constants, implies a characteristic symmetry in the theory.


Composite Particle Renormalization Constant Strong Coupling Limit Elastic Approximation Fermi Coupling 
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Сложность и элементарность в теориях с кроссингом


Показывается, что вS-матрице с кроссингом критерий сложности, основанный на обращении в нуль перенормировочных констант, может быть применен последовательным образом, позволяюшим нам изучить критическую зависимость левосторонних сингулярностей от степени элементарности элементарных частиц. Затем, используя и теорию поля и подходS-матрицы, мы разрешаем парадокс о «невозможности», отмеченной несколько раз в литературе, различения элементарности и сложности двух барионов в двух поперечных каналах: наоборот, мы указываем различные физические интерпретации для отдельных областей величин параметров, на границе которых амплитуда притерпевает критическое изменение. Мы различаем различные случаи, где каждая частица либо является элементарной, либо сложной: когда только один из этих двух барионов является («цепочным» или «лестничным») сложным, причем, его масса всегда является наибольшей. Затем мы обсуждаем и сравниваем в нашей точной моделиZ=0, предел сильной связи и приближения взаимного бутстрепа, вместе с обсужжением приближений, обычно используемых вN/D вычислениях. Обращение в нуль обоихZ, хотя константы связи остаются «конечными», означает характеристическую симметрию в теории.


Si dimostra che, in una matriceS con incrocio, si possono applicare in modo coerente criteri di composizione basati sull’annullarsi delle costanti di rinormalizzazione, permettendoci di studiare la cruciale dipendenza delle singolarità di sinistra dal grado di elementarità delle particelle scambiate. Poi, usando sia la teoria dei campi che gli approcci con la matriceS, si risolve un paradosso su una «impossibilità», affermata parecchie volte nella letteratura sull’argomento, di distinguere fra l’elementarità e la composizione di due barioni in due canali incrociati: al contrario si offrono differenti interpretazioni fisiche per distinti domini dei valori dei parametri, ai cui bordi le ampiezze subiscono un cambiamento critico. Si discriminano i vari casi in cui ciascuna particella è o elementare o composta; quando uno solo di questi due barioni è composto («a catena» o «a scalini»), la sua massa è sempre quella maggiore. Poi si discutono e si confrontano nel nostro modello esplicito gli approcci del limite dell’accoppiamento forte,Z=0, e del bootstrap reciproco, e si discutono anche le approssimazioni correntemente usate nei calcoli diN/D. L’annullarsi di entrambi gliZ, mentre si mantengono finite le costanti di accoppiamento, implica una caratteristica simmetria della teoria.


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Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • J. C. Le Guillou
    • 1
    • 2
  1. 1.Laboratoire de Physique Théorique Associé au CNRSInstitut Henri PoincaréParis
  2. 2.Laboratoire de Physique Atomique et MoléculaireCollège de FranceParis

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