Topological Glueball Contributions to the Cylinder

Abstract

Possible glueball contributions originated from the overlapping cluster configuration at the cylinder are studied in the dual topological unitarization. Two high-lying vacuum trajectories are obtained. One is the bare pomeron and the other has the same trajectory function as that of the phenomenological P'. It is argued that the result does not correspond to the cOIlventional P+ f scheme. 271 In the liNe expansion of QCD, the graph of the leading nonplanar term has a cylindrical shape with no quark loops. Color confinement hypothesis then leads us to expect the possible existence of glueballs as intermediate states in the q{j annihilation channel of this cylindrical amplitude. 1) Planar loop corrections convert the liNe cylinder into the so-called cylinder in the dual topological unitarization (DTU).2) The typical result of DTU is that the cylinder singu­ larities are obtained just through the cylinder renormalization of the planar poles. 3 ) It is improbable, however, that the insertion of quark loops extinguishes the glueball states which are inherent in the cylindrical topology. This suggests a possibility that the cylinder could generate its own singularity as a consequence of the glueball effect.4)~8) Therefore, it is important to examine whether physically acceptable pictures are realized when the cylinder retains the glueball contribution. The purpose of the present note is to investigate this problem in DTU. Especially, not only the intercept but the slope of the cylinder trajectories is examined in detail. In the following discussion, the glueball effect is intro­ duced through the overlapping cluster configuration in the s-channel cylinder discontinuity. 9) The effective random walk formalism recently proposed by Tan 10) is adopted as a calculative machinery. This formalism is fairly adequate to an investigation of the transverse structure of the multiperipheral (MP) process. Let us briefly introduce the effective random walk formalism. The standard MP integral equation for the reggeon-particle (Rp) amplitude in the J -plane reads