Algebraic Structure of Superconvergence Relations

Abstract

A general analysis of the matrix element of a vector current in the infinite-momentum frame is given. Use of some simple group-theoretical techniques is shown to be helpful in obtaining a multipole decomposition for the current. The forward-scattering superconvergence relations for vector mesons are then analyzed using these methods. Keeping only $\ensuremath{\Delta}J=0,1$, the first two terms in the multipole expansion, it is shown that these superconvergence relations lead to a covariant, collinear $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$.