Quasiclassical QCD pomeron

The Regge behaviour of the scattering amplitudes in perturbative QCD is governed in the generalized leading logarithmic approximation by the contribution of the color-singlet compound states of reggeized gluons, The interaction between reggeons is described by the effective hamiltonian, which in the multi-color limit turns out to be identical to the hamiltonian of the completely integrable one-dimensional XXX Heisenberg magnet of non-compact spin s = 0. The spectrum of the color-singlet reggeon compound states, perturbative pomerons and odderons, is expressed by means of the Bethe ansatz in terms of the fundamental Q-function, which satisfies the Baxter equation for the XXX Heisenberg magnet. The exact solution of the Baxter equation is known only in the simplest case of the compound state of two reggeons, the BFKL pomeron. For higher reggeon states the method is developed which allows to find its general solution as an asymptotic series in powers of the inverse conformal weight of the reggeon states. The quantization conditions for the conserved charges for interacting reggeons are established and an agreement with the results of numerical solutions is observed. The asymptotic approximation of the energy of the reggeon states is defined based on the properties of the asymptotic series, and the intercept of the three-reggeon states, the perturbative odderon, is estimated.