Abstract
A current-algebraic result due to Nieh is used to evaluate corrections to the second Weinberg sum rule due to the ${\mathrm{U}}_{A}(1)$ symmetry-breaking effective interactions. The 't Hooft interaction produces the dominant part of the second sum rule breaking terms both in the flavor-singlet and in the flavor-octet channels, whereas the Veneziano-Witten interaction leaves the second sum rule intact. This is a manifestation of the second sum rule's sensitivity to violations of the Feynman--Gell-Mann--Zweig ${\mathrm{U}}_{L}(6)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{R}(6)$ chiral current algebra. These predictions are compared with extant experimental data, tentatively favoring the 't Hooft interaction.
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