Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Abstract

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, | p 0|, we keep μ ⪡ ¦ p 0¦ , to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at | p 0| and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g inv 2, which is, however, scheme dependent and (ii) g 2( M)/ S( M), where S( M) −1 is the Coulomb propagator, which is scheme independent. The only scheme in which g inv 2 is scheme independent and identical to g 2( M)/ S( M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S −1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.