MODEL FOR PION S-WAVE PHASE SHIFTS FROM CURRENT ALGEBRA AND PARTIAL CONSERVATION OF AXIAL-VECTOR CURRENT

From the algebra of axial-vector charges and divergences, using extensively the principle of pion-pole dominance, we derive a set of sum rules for () S-wave interactions in the isospin-zero channel. In a single-particle approximation, they provide information on the conjectured meson. In the approximation of elastic unitarity, the sum rules take the form of an integral equation for a vertex function ||, which leads to the inequality 0<0< for the () S-wave phase shift 0 in the isospin-zero channel, whenever it is approximately valid. Exact solutions of the approximate integral equation, however, cannot be constructed, and we have to introduce an effective cutoff function as a correction to our approximation of the partial conservation of axial-vector current. The solutions for 0 give a scattering length slightly larger than Weinberg's result and a broad maximum of the phase shift around 700 MeV; its height is sensitive to the cutoff parameter. © 1968 The American Physical Society.