Bethe Ansatz for QCD Pomeron ∗

The equivalence is found between high–energy QCD in the generalized leading logarithmic approximation and the one-dimensional Heisenberg magnet. According to Regge theory, the high energy asymptotics of hadronic scattering amplitudes are related to singularities of partial waves in the complex angular momentum plane. In QCD, the partial waves are determined by nontrivial two-dimensional dynamics of the transverse gluonic degrees of freedom. The “bare” gluons interact with each other to form a collective excitation, the Reggeon. The partial waves of the scattering amplitude satisfy the BetheSalpeter equation whose solutions describe the color singlet compound states of Reggeons – Pomeron, Odderon and higher Reggeon states. We show that the QCD Hamiltonian for reggeized gluons coincides in the multi–color limit with the Hamiltonian of XXX Heisenberg magnet for spin s = 0 and spin operators the generators of the conformal SL(2,C) group. As a result, the Schrodinger equation for the compound states of Reggeons has a sufficient number of conservation laws to be completely integrable. A generalized Bethe ansatz is developed for the diagonalization of the QCD Hamiltonian and for the calculation of hadron-hadron scattering. Using the Bethe Ansatz solution of high–energy QCD we investigate the properties of the Reggeon compound states which govern the Regge behavior of the total hadron-hadron cross sections and the small−x behavior of the structure functions of deep inelastic scattering. The paper is based on talks delivered at CERN (May 94), Princeton Univ. (June 94) and at the 2nd Workshop on Small−x and Diffractive Physics at the Tevatron, Fermilab (Sept 94) On leave from the Laboratory of Theoretical Physics, JINR, Dubna, Russia