Residues of Regge Poles in Different Channels

Abstract

Conservation of the axial-vector current is assumed, together with the soft-$\ensuremath{\pi}$-meson hypothesis and the pole dominance of the vector and the axial-vector current. It is shown that there is a symmetry between the families of the residue functions of Regge poles in the $t$ channel and those in the $u$ channel for the $s$-channel helicity amplitude of the process ${\ensuremath{\rho}}^{+}({h}_{1})+{{A}_{1}}^{+}({h}_{2})\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}({h}^{\ensuremath{'}})+{{A}_{1}}^{+}({h}^{\ensuremath{'}})$. Here ${h}_{i}$ and ${h}^{\ensuremath{'}}$ are the helicities of the particles $\ensuremath{\rho}$ and ${A}_{1}$, and they are restricted to 1 or -1. The direct relation between this symmetry and a Veneziano-type formula is discussed. A relation between the residues of the $\ensuremath{\rho}$ and ${A}_{2}$ Regge poles is also given for the general helicity case.