On the Decay Rate of the Charged Pion

Abstract

The Goldberger-Treiman relation between the pion decay amplitude and the axial vector coupling constant in β-decay is shown to be plausible if the divergence of the axial vector current is a highly non-singular operator (i.e., one that emphasizes low frequencies). Such a situation is probably realized, for example, in a renormalizable theory for which this operator is proportional to the conventional pion field. Some other possible consequences of the low-frequency character of the operator are mentioned.

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