Nonplanar Couplings in the Triple-Regge Vertex

Abstract

Recently zeros have been found at ${\ensuremath{\alpha}}_{V}(0)=2\ensuremath{\alpha}(t)\ensuremath{-}1,2\ensuremath{\alpha}(t)\ensuremath{-}2,\dots{}$ in the triple-Regge vertex involving ${\ensuremath{\alpha}}_{V}(0)\ensuremath{-}\ensuremath{\alpha}(t)\ensuremath{-}\ensuremath{\alpha}(t)$. 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 ${\ensuremath{\alpha}}_{V}(0)=2\ensuremath{\alpha}(t)\ensuremath{-}2,2\ensuremath{\alpha}(t)\ensuremath{-}4,\dots{}$ but not at ${\ensuremath{\alpha}}_{V}(0)=2\ensuremath{\alpha}(t)\ensuremath{-}1,2\ensuremath{\alpha}(t)\ensuremath{-}3,\dots{}$. In particular, the zero involving the triple-Pomeranchukon coupling at $t=0$ is not present.