Abstract
We study an approximation to perturbative QCD in which all quarks (active and spectator) move along eikonal lines. These eikonal lines are described by matrix operatorsU defined by time-ordered and path-ordered integrals. All known examples of Bloch-Nordsieck cancellations follow simply from the unitary properties ofU. In particular, when the eikonal lines are space-like, the time-ordering can be omitted and the unitarity ofU is evident. In this model, it is possible to examine rather explicitly the soft and very-soft gluons whose effects must cancel if factorization is hold (to leading twist). We can show such cancellation if there is a smooth continuation from space-like eikonal lines to time-like ones. We give some examples relevant to this conjecture, but we are unable to prove it in general.
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