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On the renormalization of the axial vector coupling constant in β-decay

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Il Nuovo Cimento (1955-1965)

Summary

The models of the axial vector current discussed byGell-Mann andLévy are examined further. Generalized Ward identities are derived for the axial vector weak vertex. It is then shown that in theσ model and the non-linear model the renormalization factor —G A/G may be expressed as a matrix element in the theory of strong interactions. Thus in theσ model, which is renormalizable, —G A/G is finite in every order. Since —G A/G exhibits divergences in the non-linear model, that model is not renormalizable in the usual sense.

Riassunto

Si esaminano ulteriormente i modelli della corrente vettoriale assiale discussi daFeynman, Gell-Mann eLévy. Si derivano identità generalizzate di Ward per il vertice debole del vettore assiale. Si mostra poi che nel modelloσ e nel modello non lineare il fattore di rinormalizzazione —G A/G può essere espresso come un elemento di matrice nella teoria delle interazioni forti. Così nel modelloσ, che è rinormalizzabile, —G A/G è finito in ogni ordine. Poichè —G A/G presenta divergenze nel modello non lineare, questo modello non è rinormalizzabile nel senso usuale.

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References

  1. S. S. Gershtein andJ. B. Zeldovich:Žurn. Ėksp. Teor. Fiz.,29, 698 (1955).

    Google Scholar 

  2. R. P. Feynman andM. Gell-Mann:Phys. Rev.,109, 193 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. M. Gell-Mann andM. Lévy: to be referred to as A. We shall employ the notation of that article and we shall quote equations from it as (A.1) (A.2), etc.

  4. S. Okubo:Nuovo Cimento,13, 292 (1959).

    Article  MathSciNet  Google Scholar 

  5. R. Utiyama, S. Sunakawa andT. Imamura:Progr. Theor. Phys.,8, 77 (1952).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Identities of this type have been studied in the limit of a conserved axial vector current byS. Weinberg (private communication toJ. Bernstein).

  7. S. Weinberg:Phys. Rev.,112, 1375 (1958).

    Article  ADS  MATH  Google Scholar 

  8. M. L. Goldberger andS. B. Treiman:Phys. Rev.,111, 354 (1958).

    Article  ADS  MATH  Google Scholar 

  9. Y. Takahashi:Nuovo Cimento,6, 371 (1957).

    Article  MATH  Google Scholar 

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Bernstein, J., Gell-Mann, M. & Michel, L. On the renormalization of the axial vector coupling constant in β-decay. Nuovo Cim 16, 560–568 (1960). https://doi.org/10.1007/BF02731920

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  • DOI: https://doi.org/10.1007/BF02731920

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