Partially Conserved Currents and Weak Form Factors

A modification of the Goldberger-Treiman relations (for G_A and for the induced pseudoscalar G_P) is obtained by assuming, in addition to the hypothesis of partially conserved axial-vector currents, that the matrix element of the axial-vector current between two nucleon states is dominated by the A₁(1080) and π. This yields a more detailed structure of the weak form factors. The result is discussed. Extending this line of thought to the case of strangeness-changing currents, which we assume to be "partially conserved," we obtain corresponding expressions for the strangeness-changing induced scalar and pseudoscalar form factors. A relation is obtained relating the induced scalar coupling to the K_l3 form-factor ratio ξ=f_-(0) / f₊(0). These results are useful in a detailed study of the Cabibbo theory. A value for the K_l3 parameter ξ is obtained by combining our results with the soft-pion current-algebra result of Callen and Treiman. It ranges from -0.15 to -0.10, depending on the experimental value of f_K / f_π.