T-dependent Dyson-Schwinger equation in IR regime of QCD: the critical point
Center for Academic Excellence on Cosmology & Particle Astrophysics, National Taiwan University, Taipei 106, Taiwan, R.O.C
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The quark mass function in QCD is revisited, using a gluon propagator in the form 1/(k 2 + m g 2) plus , where the second (IR) term gives linear confinement for m g = 0 in the instantaneous limit, μ being another scale. To find we propose a new (differential) form of the Dyson-Schwinger equation (DSE) for , 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 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 p 2 by = , except for Log factors. The limit p 2 = 0 determines . A third limit, p 2 = -m 0 2, defines the dynamical mass m 0 via . After two checks ( MeV and = ), for with MeV, the T-dependent DSE is used in the real time formalism to determine the “critical” index analytically, with the IR term partly serving as the H-field. We find MeV and check the vanishing of and at T c.
© Springer-Verlag, 2005