Quark Virtuality Distribution in Non-perturbative QCD Vacuum
  We introduce the quark virtuality distribution [$\lambda^{2}_{q}(x)$] as an extenson of the quark virtuality by using nonlocal rather than local quark vacuum condensates. Our results show that the quark virtuality distribution decreases gradually from a finite value to zero as $x$ increases. This clearly indicates that quarks are confined inside hadrons, whereas, as $x$ approaches zero quarks have a finite virtuality, which shows asymptotic freedom of quarks in QCD. The present predictions are important not only for studying the properties of QCD vacuum states, and non-perturbative QCD problems, but also for study of the cosmological constant problem, which we have shown should be treated using nonlocal quark vacuum condensate in the Ghost theory of QCD. 
Zhou Li-juan, Ma Wei-xing, Leonard S. Kisslinger
hep-ph