Abstract
The Nambu and Gell-Mann-Levy versions of the Goldberger-Treiman relation are compared by going to the chiral conservation limit and then passing to the physical problem of partial chiral conservation. Using current algebra we show that the Adler-Weisberger sum rule is rigorously correct in the chiral limit for both cases. In the Nambu caseFA is renormalized in the chiral limit. Going to the physical situation then further increasesFAin Nambu’s case to about 1.5, but simply gives back the A-W value of about 1.2 in the Gell-Mann-Levy case. On this basis, present theory favours the Gell-Mann-Levy over the Nambu interpretation.
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