Solving effective field theory of interacting QCD pomerons in the semiclassical approximation

Abstract

Effective field theory of Balitsky, Fadin, Kuraev, and Lipatov (BFKL) pomerons interacting by QCD triple pomeron vertices is investigated. Classical equations of motion for the effective pomeron fields are presented being a minimal extension of the Balitsky-Kovchegov equation that incorporates both merging and splitting of the pomerons and that is self-dual. The equations are solved for symmetric boundary conditions. The solutions provide the dominant contribution to the scattering amplitudes in the semiclassical approximation. We find that for rapidities of the scattering larger than a critical value ${Y}_{c}$ at least two classical solutions exist. Curiously, for each of the two classical solutions with the lowest action the symmetry between the projectile and the target is found to be spontaneously broken, being however preserved for the complete set of classical solutions. The solving configurations at rapidities $Y>{Y}_{c}$ consist of a Gribov field being strongly suppressed even at very large gluon momenta and the complementary Gribov field that converges at high $Y$ to a solution of the Balitsky-Kovchegov equation. Interpretation of the results is given and possible consequences are shortly discussed.