Nonplanar Couplings in the Triple-Regge Vertex

Abstract

Recently zeros have been found at ${\alpha }_V\mathrm{}\left(0\right)=2\mathrm{}\alpha \mathrm{}\left(t\right)-1,2\mathrm{}\alpha \mathrm{}\left(t\right)-2,\dots$ in the triple-Regge vertex involving ${\alpha }_V\mathrm{}\left(0\right)-\alpha \mathrm{}\left(t\right)-\alpha \mathrm{}\left(t\right)\mathrm{}$. Such zeros were found both in a dual-resonance model and in certain classes of Feynman graphs. We have examined this question in a model of nonplanar Feynman graphs and found zeros at ${\alpha }_V\mathrm{}\left(0\right)=2\mathrm{}\alpha \mathrm{}\left(t\right)-2,2\mathrm{}\alpha \mathrm{}\left(t\right)-4,\dots$ but not at ${\alpha }_V\mathrm{}\left(0\right)=2\mathrm{}\alpha \mathrm{}\left(t\right)-1,2\mathrm{}\alpha \mathrm{}\left(t\right)-3,\dots$. In particular, the zero involving the triple-Pomeranchukon coupling at $t=0\mathrm{}$ is not present.