Properties of quark matter governed by quantum chromodynamics (I). The screened charge

Abstract

A genuine screened charge (coupling) is constructed for quark matter, subject to a flavour constraint, governed by quantum chromodynamics. This is achieved by (i) working in the Coulomb gauge and (ii) using an unambigous renormalization prescription (formulated in terms of the Lie differential equations) to overcome the problems of the previous attempts. Since we must standardize with the vacuum QCD running (experimental) coupling constant at some asymptotic spacelike momentum transfer, | p 0| , it is ensured that the matter contribution is negligible at this point by the condition, μ⪡| p 0| , where μ is the matter (flavour) chemical potential. The screened charge (coupling) has the expected property of merging with the vacuum QCD running coupling constant in the ultraviolet ( p 2 → ∞) and going to zero in the infrared ( p 2 → 0) , indicative of complete screening above a critical value of μ (or density) = μ c . The critical length scale at which the screened charge diverges is well below the vacuum QCD scale length, Λ, and screening always renders the screened charge smaller than its vacuum QCD counterpart. This gives greater access to the long-distance phenomena besides providing a better (see paper II) expansion parameter for perturbative calculations. The richer physical content of the screened charge is pointed out. The quark mass is included and taken to be renormalized on-shell.