Quark Virtuality Distribution in Non-perturbative QCD Vacuum

TL;DR

This paper introduces a nonlocal quark virtuality distribution in the QCD vacuum, revealing how quark confinement and asymptotic freedom manifest through the behavior of virtuality across different scales, with implications for non-perturbative QCD and cosmology.

Contribution

It extends quark virtuality to a distribution using nonlocal condensates, providing new insights into QCD vacuum structure and quark confinement mechanisms.

Findings

Quark virtuality decreases with increasing distance x.

Finite virtuality at small x indicates asymptotic freedom.

Results have implications for non-perturbative QCD and cosmological constant studies.

Abstract

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.