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Il Nuovo Cimento (1955-1965)

, Volume 36, Issue 2, pp 488–508 | Cite as

Meson-baryon resonances inU3U3 symmetry. — II

  • I. S. Gerstein
  • K. T. Mahanthappa
Article

Summary

The assignment of theJ = 3+/2 meson-baryon resonances to the 45 dimensional representation of Schwinger’sW3 symmetry is considered; mass formulae for the 27-plet and the octet have been obtained. We discuss the various possibilities of assigning charges to the fundamental triplets in this theory and the possibilities of constructing particle states from them. The mass operator is discussed and we show that the single requirement of no mixing in a certain representation is sufficient to yield Gell-Mann-Okubo mass formulae; this requirement imposes the condition that the mass operator transform like a unitary singlet plus the neutral component of a unitary octet. Clebsch-Gordan coefficients involving some nonoctet representations ofSU3 using the phase convention of de Swart, are tabulated in the appendix.

Riassunto

Si esamina l’assegnazione delle risonanze mesone-barione alla rappresentazione 45-dimensionale della simmetriaW di Schwinger; si sono ottenute le formule delle masse del 27-pletto e dell’ottetto. Si discutono le varie possibilità di assegnare in questa teoria le cariche ai tripletti fondamentali e le possiblità di costruire con loro stati di particelle. Si discute l’operatore di massa e si dimostra che esigere l’assenza di mescolanza in una certa rappresentazione è sufficiente a dare la formula della massa di Gell-Mann-Okubo; questa richiesta impone la condizione che l’operatore di massa si trasformi in un singoletto unitario più la componente neutra di un ottetto unitario. Nell’appendice sono tabulati i coefficienti di Clebsch-Gordan inerenti ad alcune rappresentazioni di non-ottetto dell’SU3 servendosi della eonvenzione di fase di de Swart.

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Copyright information

© Società Italiana di Fisica 1965

Authors and Affiliations

  • I. S. Gerstein
    • 1
  • K. T. Mahanthappa
    • 1
  1. 1.Department of PhysiosUniversity of PennsylvaniaPhiladelphia

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