Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current

It is shown that a partially conserved =0 axial-vector current (_{J_}^A=C_) implies consistency conditions involving the strong interactions alone. The most interesting of these is a relation among the symmetric isotopic-spin pion-nucleon scattering amplitude A^ (+), the pionic form factor of the nucleon K^NN, and the rationalized, renormalized pion-nucleon coupling constant gₑ: {gₑ^2}M=A^{ (+) (=0, ₁=0, k^2=0) }{K^NN (k^2=0) }. [M is the nucleon mass and -k^2 the (mass) ^2 of the initial pion. The final pion is on mass shell; the energy and momentum transfer variables and ₁ are defined in the text. By using experimental pion-nucleon scattering data, we find that this relation is satisfied to within 10%. Consistency conditions involving the and the scattering amplitudes are stated.