Eikonals - from a different point of view

We reopen the old, Abelian problem of t-channel, connected, multiparticle contributions to the eikonal function for quark-quark scattering at ultra-high energies, and ask what might be the resulting forms in non-Abelian QCD. Unless an unexpected, non-Abelian cancellation occurs, there can result a damping of the eikonal contribution to the amplitude at arbitrarily large impact parameter, which violates the condition and spirit of the hadrons' other quarks, treated as spectator particles. A possible resolution of this problem can be accomplished by averaging over the quarks' bound-state, hadronic wave functions, if required effects of sea-quark-pairs and other gluonic structures are displayed. (authors)