Temperature dependence of gluon and quark condensates as from linear confinement

Abstract

The gluon and quark condensates and their temperature dependence are investigated within QCD premises. The input for the former is a gauge invariant gg kernel made up of the direct (D), exchange (X) and contact(C) QCD interactions in the lowest order, but with the perturbative propagator k^-2 replaced by a non-perturbative k^-4 form obtained via two differentiations: μ²∂²_m (m² + k²)^-1, (μ a scale parameter), and then setting m = 0, to simulate linear confinement. Similarly for the input qq̅ kernel the gluon propagator is replaced by the above k^-4 form. With these 'linear' simulations, the respective condensates are obtained by looping up the gluon and quark lines in the standard manner. Using Dimensional regularization (DR), the necessary integrals yield the condensates plus temperature corrections, with a common scale parameter μ for both. For gluons the exact result is <GG<= 36μ⁴π^-3α_s(μ²)[2-γ-4π²T²/(3π²)] Evaluation of the quark condensate is preceded by an approximate solution of the SDE for the mass function m(p), giving a recursive formula, with convergence achieved at the third iteration. Setting the scale parameter π equal to the universal Regge slope 1GeV², the gluon and quark condensates at T = 0 are found to be 0.586Gev⁴ and (240-260MeV)³ respectively, in fair accord with QCD sum rule values. Next, the temperature corrections (of order T² for both condensates) is determined via finite-temperature field theory a la Matsubara.