QCD Evolution of Superfast Quarks

Recent high-precision measurements of nuclear deep inelastic scattering at high x and moderate 6 < Q$^2$ < 9GeV$^2$ give a rare opportunity to reach the quark distributions in the {\it superfast} region, in which the momentum fraction of the nucleon carried by its constituent quark is larger than the total fraction of the nucleon at rest, x>1. We derive the leading-order QCD evolution equation for such quarks with the goal of relating the moderate-Q$^2$ data to the two earlier measurements of superfast quark distributions at large 60 < Q$^2$ < 200~GeV$^2$. Since the high-Q$^2$ measurements gave strongly contradictory estimates of the nuclear effects that generate superfast quarks, relating them to the high-precision, moderate-Q$^2$ data through QCD evolution allows us to clarify this longstanding issue. Our calculations indicate that the moderate-Q$^2$ data at $x\lesssim 1.05$ are in better agreement with the high-Q$^2$ data measured in (anti)neutrino-nuclear reactions which require substantial high-momentum nuclear effects in the generation of superfast quarks. Our prediction for the high-Q$^2$ and x>1.1 region is somewhat in the middle of the neutrino-nuclear and muon-nuclear scattering data.