PION-MASS EXTRAPOLATIONS AND PARTIAL CONSERVATION OF AXIAL-VECTOR CURRENT

It is proposed, as suggested by a recent study, that the observed 10% corrections to the Goldberger-Treiman relation cannot be accounted for on the basis of unsubtracted dispersion relations. To incorporate the possibility of a small subtraction in the matrix elements of the divergence of the axial-vector current, a supersmooth pion field is defined from the weak interactions by iμAμ(+)(x)=(2MgAμ22g)π(+)(x)-Δfπ□π(+)(x), with Δ=1-2MgA2gfπ+0.1 representing the 10% correction. With this definition and the supersmoothness hypothesis the extrapolation of exact current-algebra threshold theorems for weak amplitudes to relate hadron amplitudes is relatively simple and eliminates a major ambiguity in performing such extrapolations in the virtual pion mass. © 1969 The American Physical Society.