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

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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Correspondence to J. Bernstein.

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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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