PARTIAL CONSERVATION OF AXIAL-VECTOR CURRENT, DYNAMICAL THEORY, AND DISPERSION-RELATIONS

Forward dispersion relations are used to test a dynamical theory of πN interaction based on the use of the divergence of the axial-vector current as the canonical pion field, the notion of the σ commutator, and the assumption that the seagull term in the Low expansion of the scattering amplitude is purely isoscalar. Most of the parameters of the dynamical theory have been fixed by an earlier work on low-energy S-wave phase shifts. The theory is used to calculate the scattering lengths and the amplitude C̄(±)(0,0) used as subtraction constants. These values and f2=0.0725, fixed mainly by the Goldberger-Treiman relation, are then used in the forward dispersion relations to yield values of cross-section integrals J, I(+), and I(-). The test consists of comparing these values with those obtained from the usual dispersion-theoretic analysis of scattering data. The theory passes the test satisfactorily. This success, coupled with the earlier successes in fitting the low-energy phase shifts and the C̄(+)(0,t<0) amplitudes for small t, provides very strong support for the present theory. © 1979 The American Physical Society.