O(4)Symmetry and the Regge Trajectory of the Pion

Abstract

An off-shell generalization of $O\left(4\right)\mathrm{}$ symmetry is developed, which is applicable to unequal-mass reactions involving arbitrary spins. The symmetry breaking at $t\ne 0$ is also investigated. These methods are used to analyze the hypothesis that the pion Regge trajectory has the Toller quantum number $M=1\mathrm{}$ at zero momentum transfer, as seems to be implied by high-energy photoproduction data. We find that if this hypothesis is correct, then the pion trajectory is necessarily quite complicated. The $M=1\mathrm{}$ trajectory must mix with another trajectory. The $\overline{N}N\pi$ vertex function then shows a zero near $t=0\mathrm{}$, in agreement with some fits to high-energy data, but this zero is factorizable. Moreover, a model is exhibited that seems consistent with the hypothesis of partially conserved axial-vector current.