Asymptotically scale-free theory of large-transverse-momentum processes

It is shown that an ansatz for quark-quark interaction which is asymptotically scale-free has the property that it eliminates cumulative logarithmic modifications of hadronic wave functions and at the same time suppresses certain mechanisms for large-$P_T$ processes which do not appear to be present phenomenologically. A further argument for such an asymptotically scale-free theory is presented, based on considering parton models which give large multiplicities in deep-inelastic current processes.