Il Nuovo Cimento (1955-1965)

, Volume 16, Issue 4, pp 705–726

The axial vector current in beta decay

  • M. Gell-Mann
  • M. Lévy


In order to derive in a convincing manner the formula of Goldberger and Treiman for the rate of charged pion decay, we consider the possibility that the divergence of the axial vector current in β-decay may be proportional to the pion field. Three models of the pion-nucleon interaction (and the weak current) are presented that have the required property. The first, using gradient coupling, has the advantage that it is easily generalized to strange particles, but the disadvantages of being unrenormalizable and of bringing in the vector and axial vector currents in an unsymmetrical way. The second model, using a strong interaction proposed bySchwinger and a weak current proposed byPolkinghorne, is renormalizable and symmetrical betweenV andA, but it involves postulating a new particle and is hard to extend to strange particles. The third model resembles the second one except that it is not necessary to introduce a new particle. (Renormalizability in the usual sense is then lost, however). Further research along these lines is suggested, including consideration of the possibility that the pion decay rate may be plausibly obtained under less stringent conditions.


Allo scopo di dedurre in maniera convincente la formula di Goldberger e Treiman per il tasso di decadimento dei pioni carichi, prendiamo in considerazione la possibilità che la divergenza della corrente vettoriale assiale nel decadimento β sia proporzionale al campo del pione. Si presentano tre modelli della interazione pionenucleone (e della corrente debole) che hanno la proprietà richiesta. Il primo, che si serve dell’accoppiamento di gradiente, ha il vantaggio di poter essere facilmente generalizzato alle particelle strane, ma gli svantaggi di non essere rinormalizzabile e di introdurre le correnti vettoriale e vettoriale assiale in modo asimmetrico. Il secondo modello, che usa un’interazione forte proposta daSchwinger ed una corrente debole proposta daPolkinhorne, è rinormalizzabile e simmetrico fraV edA, ma comporta la postulazione di una nuova particella ed è difficilmente estensibile alle particelle strane. Il terzo modello è simile al secondo salvo che non è necessario introdurre una nuovo particella. (Si perde, tuttavia, la rinormalizzazione nel senso usuale.) Si suggerisce una ulteriore ricerca su queste linee, compresa la considerazione della possibilità che il tasso di decadimento del pione possa ottenersi in modo plausibile con condizioni meno restrittive.


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Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • M. Gell-Mann
    • 1
  • M. Lévy
    • 3
  1. 1.Collège de France and Ecole Normale SupérieureParis
  2. 2.California Institute of TechnologyPasadena
  3. 3.Faculte des SciencesOrsay, and Ecole Normale SupérieureParis
  4. 4.Laboratoire de Physique Théorique et Hautes EnergiesOrsay (Seine et Oise)

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