Trajectory Function of the Bare Pomeron in the Higher Rank Cylinder Amplitude

Abstract

By the use of an explicit parametrization for the planar triple reggeon coupling, the slope and intercept of the bare pomeron are calculated for the second rank cylinder amplitude of the possible finite energy correction.In the dual topological unitarization scheme, the leading Regge singularity of the cylinder is identified as the bare pomeronY-91 The slope-intercept relationship of the cylinder singularity has originally been evaluated by Bishari 91 for a naive cylinder model with substantial j-plane cut contamination. From the phenomenological point of view, the numerical results of Ref. 9) are very reasonable. From the theoretical point of view, however, the cylinder amplitude is free of j-plane cuts so long as the planar amplitude correctly satisfies the pole-to-pole bootstrap condition. 21 · 41 As is generally known, u · 21 · 41 the planar analyticity provides us with the most crucial constraint on the cylinder singularity. Consequently it may be of physical importance to examine the trajectory function of the bare pomeron for the cylinder amplitude which is built just by the planar sewing method. 21 · 41In the present short communication, this is performed for the second rank cylinder amplitude of the possible finite energy correction which has recently been proposed by the present authors. 41 Use is made of an empirical parametrization for the t-dependence of the planar triple reggeon coupling which has been adopted in Ref. 9).Leading and nonleading triple reggeon couplings, g (t; t, +, t, -) and g (t; t 1 +, t 1 -), are parametrized, respectively, as follows : 91 1-J [-] g, =g(t; t, +, t,-)) where a[a] is the planar leading [nonleading] reggeon and ac,l =a (t1 +)+a (t~-) -1. It is evident that the dual nonsensezero structure is automatically guaranteed in Eq. (1). As has often been argued, the planar analyticity plays a central role in building up the cylinder and requires the planar bootstrap constraint!) · 41 · 91 where (3) and N corresponds to the internal SU(N) symmetry. Linearity of a and a is taken for granted in the standard manner. It is of great use to remember the O'Donovantype integration 101 (4) by guest on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from