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

Abstract

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 solitonlike excitations of the sigma models. Diffractive hadron-hadron scattering appears primarily due to exchange of longitudinal flux between partons.