Renormalization of Regge Trajectories and Singularity Structure in Kikkawa-Sakita-Virasoro—Type Theories

Abstract

An investigation is made of theories which satisfy the duality principle using the Veneziano amplitude as a Born term. In constructing the theory, it is found necessary to average over different ways of assigning the loop momenta to the points of the duality diagram. The Regge-pole terms in the asymptotic behavior are identified, and transcendental equations which express the full renormalization of the leading trajectory are recorded. (It is necessary to assume that the integrals can be so defined that this asymptotic behavior, found in the limit $\mathrm{Re}s\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, continues to be the dominant behavior as $\mathrm{Re}s\ensuremath{\rightarrow}+\ensuremath{\infty}$.) The amplitude is shown to have the Landau-Cutkosky singularity structure corresponding to poles lying on the renormalized leading trajectory. In particular, if low-lying particles on this trajectory are the only stable particles in the theory, the real singularity structure required by unitarity is correctly obtained. It is then possible that the failure in a finite theory of exact factorization for all daughters would not spoil the theory.