Temperature dependent Dyson-Schwinger equation in QCD with linear confinement: The Critical point
Journal
Eur. Phys. J.
Journal Volume
C39
Pages
209-218
Date Issued
2004-03
Author(s)
Abstract
The quark mass function Σ(p) in QCD is revisited, using a gluon propagator in the form 1/(k2 + m2g) plus 2μ2/(k2 + mg2)2, where the second (IR) term gives linear confinement for mg = 0 in the instantaneous limit, μ being another scale. To find Σ(p) we propose a new (differential) form of the Dyson-Schwinger equation (DSE) for Σ(p), based on an infinitesimal subtractive renormalization via a differential operator which lowers the degree of divergence in integration on the RHS, by two units. This warrants Σ(p - k) ≈ Σ(p) in the integrand since its k-dependence is no longer sensitive to the principal term (p - k)2 in the quark propagator. The simplified DSE (which incorporates the Ward-Takahashi (WT) identity in the Landau gauge) is satisfied for large p2 by Σ(p) = Σ(0)/(1 + βp2), except for Log factors. The limit p2 = 0 determines Σ0. A third limit, p 2 = -m02, defines the dynamical mass m 0 via Σ(im0) = +m0. After two checks (fπ = 93 ± 1 MeV and 〈qq̄〉 = (280 ± 5 MeV)3), for 1.5 < β < 2 with Σ0 = 300 MeV, the T-dependent DSE is used in the real time formalism to determine the "critical" index γ = 1/3 analytically, with the IR term partly serving as the H-field. We find Tc = 180 ± 20 MeV and check the vanishing of fπ and 〈qq̄〉 at Tc. © Springer-Verlag/Società Italiana di Fisica 2005.
Type
journal article