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Il Nuovo Cimento (1955-1965)

, Volume 25, Issue 1, pp 193–205 | Cite as

Coupling constants andS-matrix zeros

  • C. H. Albright
  • W. D. McGlinn
Article

Summary

A connection between coupling constants andS-matrix zeros is demonstrated to exist in the case of elastic scattering of neutral, scalar particles. From analyticity and unitarity arguments, the most general solution for a partial-wave phase shift is written in terms of the given discontinuities across the dynamical and inelastic branch cuts. The coupling constants associated with the simple poles follow directly from these phase shift solutions. Under certain conditions, it is shown that the arbitrariness in the solutions can be exhibited entirely by the position and number ofS-matrix zeros. A simple dynamical assumption is introduced as an illustrative example of a possible physical restriction on these zeros, and two coupling constants are calculated with use of very rough approximations.

Riassunto

Si dimostra che, nel caso dello scattering elastico di particelle neutre scalari, esiste un rapporto fra le costanti di accoppiamento e gli zeri della matriceS. Con argomentazioni sull’analiticità e l’unitarietà, si scrive la soluzione più generale per lo spostamento di fase dell’onda parziale in termini delle date discontinuità sui tagli dei rami dinamico ed elastico. Le costanti di accoppiamento associate ai poli semplici discendono direttamente da queste soluzioni dello spostamento di fase. Si dimostra che, in certe condizioni, l’arbitrarietà delle soluzioni può risiedere esclusivamente nella posizione e nel numero degli zeri della matriceS. Si introduce una semplice ipotesi dinamica come esempio illustrativo di una possibile restrizione fisica a questi zeri, e si calcolano due costanti di accoppiamento con approssimazioni molto grossolane.

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    In this connection we point out a preprint byG. Wanders that has come to our attention since this paper was written. Wanders has considered neutral, pseudoscalar meson theory in the static limit and one-meson approximation where crossing symmetry can be handled exactly. He also finds that the arbitrariness of the partial-waveS-matrix solutions lies in the position and number of zeros.Google Scholar

Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • C. H. Albright
    • 1
  • W. D. McGlinn
    • 1
  1. 1.Department of PhysicsNorthwestern UniversityEvanston

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