Pomeron-Reggeon relationship according to the topological expansion

Abstract

The nature of the Pomeron and related effects are studied within the framework of Veneziano's topological expansion. At the second, or cylinder, level it is found that no new poles are generated but that first-level (planar) poles with $I=0\mathrm{}$ are shifted by the cylinder, the shifts being in opposite directions for positive and negative charge conjugation. The planar $f$, in particular, is shifted upward and may be interpreted near $t=0\mathrm{}$ as the Pomeron—with couplings lying roughly midway between the ideal mixing of a planar $f$ and an S${\mathrm{U}}_3$ singlet. The Pomeron intercept and couplings (mixing coefficients) together with corresponding intercepts and couplings for $\omega$, $f^{\prime }$, and $\phi$ are semiquantitatively related through a single parameter to the properties of $\rho -A_2$. In the positive-$t$-physical-particle region corresponding relations successfully correlate the breaking of the Iizuka-Okubo-Zweig rule to the $\rho -\omega$ mass difference. Comparison of the cylinder shift in this large-$t$ region to that near $t=0\mathrm{}$ reveals the phenomenon of "asymptotic planarity"—the cylinder perturbation dying out rapidly with increasing $t$. It is pointed out that the small Pomeron slope as well as certain physical effects attributed in field theory to asymptotic freedom are consequences of asymptotic planarity.