Perturbative odderon in the dipole model

Abstract

We show that, in the framework of Mueller's dipole model, the perturbative QCD odderon is described by the dipole model equivalent of the BFKL equation with a Codd initial condition. The eigenfunctions and eigenvalues of the odderon solution are the same as for the dipole BFKL equation and are given by the functions E n,ν and χ(n, ν) correspondingly, where the C-odd initial condition allows only for odd values of n. The leading high-energy odderon intercept is given by α odd − 1 = 2 αs Nc π χ(n = 1, ν = 0) = 0 in agreement with the solution found by Bartels, Lipatov and Vacca. We proceed by writing down an evolution equation for the odderon including the effects of parton saturation. We argue that saturation makes the odderon solution a decreasing function of energy.

Pomeron fan diagrams in perturbative QCD

“…For this special odderon solution, the pomeron→two-odderon vertex becomes similar to the triple pomeron vertex. It is this special odderon solution which appears in the generalizations of the BK-equation [15,16]. Our more general version (3.10), on the other hand, allows to inlcude also other three-gluon solutions, such as the one found in [20,21] with intercept slightly below one.…”

“…Since the structure of this odderon is practically identical to the pomeron, it became possible to radically simplify vertices for both pomeron →two odderon and odderon → odderon+pomeron transitions, which actually reduce to the triple pomeron form. This allowed to easily derive the coupled system of evolution of the pomeron and odderon including both transitions [15,16]. This system was analyzed in [26] where the angular dependence introduced by the pomeron→two odderon transition (POO) was drastically simplified.…”

“…The integral equation for D 4 can be written as 15) where the momentum dependent part of the kernel K 4←2 has the form: Formally we could solve (2.15) by…”

“…Next, for the inhomogeneous terms T 1 + T 2 + T 3 we note that -formally -we could solve the integral equation (4.13) by introducing the Green's function G 6 : in rapidity space we put 15) and (4.13) can be solved by…”

Small-xQCD evolution of2nWilson line correlator: The weak field limit

“…This corresponds to investigating multi-particle production in the kinematic region where the produced particles have transverse momenta higher than the saturation scale in the problem. It has been shown that in this limit the evolution equation for the dipole is the well-known BFKL equation [14], whereas the evolution equation for the odderon and quadrupole reduces to the BJKP equation for the energy dependence of a state of 3 or 4 Reggeized gluons [15][16][17] (see also [18] for a nice discussion of gluon Reggeization). It should be noted that this problem has also been investigated using a dual approach known as the KLWMIJ equation [19].…”