Near-integrability and confinement for high-energy hadron-hadron collisions

We investigate an effective Hamiltonian for QCD at large s, in which longitudinal gauge degrees of freedom are suppressed, but not eliminated. In an axial gauge the effective field theory is a set of coupled (1+1)-dimensional principal-chiral models, which are completely integrable. The confinement problem is solvable in this context, and we find the longitudinal and transverse string tensions with techniques already used for a similar Hamiltonian in (2+1)-dimensions. We find some a posteriori justification for the effective Hamiltonian as an eikonal approximation. Hadrons in this approximation consist of partons, which are quarks and soliton-like excitations of the sigma models. Diffractive hadron-hadron scattering appears primarily due to exchange of longitudinal flux between partons.