Higher Rank Cylinder Amplitude

Abstract

The dual topological unitarization is investigated for the case of any number of planar SU(N) singlet reggeons. In particular, the detailed structure of the cylinder amplitude is fully investigated. The planar bootstrap constraints are derived for the reggeon propagator and the triple reggeon vertex. The cylinder unitarization of planar poles is performed by means of the planar sewing method. The cylinder equation is described in terms of the factorizable kernel of finite rank. We are then led to the following typical properties of the cylinder. First, the cylinder partial wave amplitude is meromorphic in the J-plane. Secondly, extinction of the input SU(N) singlets is guaranteed. Thirdly, the cylinder residue is factorizable at all t. Fourthly, the cylindrical mixing is inevitable for the higher rank kernel. Moreover, the mixing phenomena are examined for the special case of the single daughter contribution. The repulsive [attractive] mixing pattern is expected to be observed between the even [odd] charge conjugation components of the cylindrically renormalized trajectories in the weak cylindrical mixing limit. § l. IntroductionThe dual topological unitarization (DTU) has provided us with a powerful framework in understanding hadron physics. n-sJ The definite topology of the DTU diagrams successfully describes a degree of regularities in hadronic phenomena. This legitimately allows us to construct a perturbation scheme in terms of topological parameters. The discontinuity formulae of the DTU expansion are welldefined.3JThe planar term reads the Born term of the topological perturbation and plays a crucial role in the DTU calculation of the hadronic amplitudes .. The planar amplitude obeys the planar unitarity condition which yields the bootstrap constraint on planar reggeon parameters_<J-aJ This important concept is paraphrased as the planar analyticity. 7 l In the present discussion, the hadronic SU(N) internal symmetry is taken for granted, where JV represents the number of flavors. The cylinder term is obtained by the use of the planar sewing prescription and yields the leading non-planar correction to the SU(N) singlet planar term. The leading reggeon of the cylinder is identified with the bare pomeron without loss of generality.In the standard DTU framework, the cylinder is controlled by a non-singular kernel of rank one. 9 J As a consequence, the cylinder is free from Regge cut contamination and the bare pomeron is given by just the cylinder renormalization at NERL on June 5, 2015 http://ptp.oxfordjournals.org/ Downloaded from