Advertisement

Il Nuovo Cimento A (1965-1970)

, Volume 47, Issue 2, pp 282–292 | Cite as

Approximate saturation of the algebra of axial currents

  • G. Longhi
Article

Summary

The saturation of the commutation relations of the space components of the axial currents with multiplets ofSU3×SU2W is considered, taking into account possible Schwinger terms. It is shown that the saturation with the states of the56+ multiplet is not consistent with a momentum transfer dependence. This dependence can be obtained, without a renormalization of the staticSU6 results, by adding to the56+ a negative-parity multiplet. Even without specifying this multiplet we can obtain the results 〈r n 2 〉=0, andD/F=3/2 up to first order in the momentum transfer.

Keywords

Commutation Relation Quark Model Positive Parity Axial Current Space Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Приближенное насыщение алгебры аксиальных токов

Резюме

Рассматривается насыщение коммутационных соотношений для пространственных компонент аксиальных токов с мультиплетамиSU3×SU2W, принимая во внимание возможные члены Швингера. Показано, что насыщение посредством состояний мультиплета56+ является несовместимым с зависимостью от передаваемого импульса. Эта зависимость может быть получена путем добавления к56+ мультиплета с отрицательной четностью, без перенормировки результатов статическойSU6. Даже не конкретизируя этот мультиплет, мы можем получить результаты: 〈r n 2 〉=0 иD/F=3/2, которые справедливы вплоть до первого порядка по передаваемому импульсу.

Riassunto

Viene considerata la saturazione delle relazioni di commutazione delle componenti spaziali delle correnti assiali locali mediante multipletti del gruppo collineareSU3×SU2W. Viene mostrato che la saturazione mediante stati della56+ non è consistente con una dipendenza dal trasferimento d'impulso. Si può ottenere tale dipendenza, senza rinormalizzare i risultati della simmetriaSU6, aggiungendo alla56+ un multipletto a parità negativa. Senza specificare tale multipletto è possibile ottenere i risultati 〈r n 2 〉=0,D/F=3/2 fino al primo ordine nel trasferimento d'impulso.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. (1).
    F. Buccella, G. Veneziano, R. Gatto andS. Okubo:Phys. Rev.,149, 1268 (1966).ADSCrossRefGoogle Scholar
  2. (2).
    B. W. Lee:Phys. Rev. Lett.,14, 676 (1965).ADSCrossRefGoogle Scholar
  3. (3).
    The convections used are those ofJ. J. De Swart:Nuovo Cimento,31, 420 (1964) forSU 3, and ofA. R. Edmonds:Angular Momentum in Quantum Mechanics (Princeton, 1957), forSU 2.CrossRefGoogle Scholar
  4. (4).
    H. J. Lipkin andS. Meshkov:Phys. Rev. Lett.,14, 670 (1965).ADSMathSciNetCrossRefGoogle Scholar
  5. (5).
    The notations are those ofJ. J. De Swart:Rev. Mod. Phys.,35, 916 (1963). The method used is the same as showed byR. Gatto, L. Maiani andG. Preparata:Phys. Rev. Lett.,16, 377 (1966), and byG. Altarelli:Nuovo Cimento,45 A, 426 (1966).ADSCrossRefGoogle Scholar
  6. (6).
    The normalization in such thatG ξ is the same as in ref. (2)..G * also is defined n ref. (2)B. W. Lee:Phys. Rev. Lett.,14, 676 (1965)ADSCrossRefGoogle Scholar
  7. (8).
    R. F. Dashen andM. Gell-Mann: preprint CALT-68-65.Google Scholar
  8. (9).
    E. Celeghini andR. Gatto:Nuovo Cimento,43, 219 (1966).ADSCrossRefGoogle Scholar
  9. (10).
    S. L. Adler:Phys. Rev.,143, 1144 (1966).ADSCrossRefGoogle Scholar
  10. (11).
    S. Fubini, G. Segrè andJ. D. Walecka: preprint ITP-199.Google Scholar

Copyright information

© Società Italiana di Fisica 1967

Authors and Affiliations

  • G. Longhi
    • 1
  1. 1.Sezione di FirenzeIstituto Nazionale di Fisica NucleareFirenzeItaly

Personalised recommendations