Three-loop Debye mass and effective coupling in thermal QCD

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Abstract

We determine the three-loop effective parameters of the dimensionally reduced theory of EQCD as matching coefficients to full QCD. The mass parameter $\mE$ is interpreted as the high temperature, perturbative contribution to the Debye screening mass of chromo-electric fields and enters the pressure of QCD at the order of $g^7$. The effective coupling $\gE$ can be used to compute the spatial string tension of QCD. However, we suspect that the effective coupling $\gE$ obtains through renormalization contributions from higher order operators that have not yet been taken into account. Therefore our result reflects the (still divergent) contribution from the super-renormalizable EQCD Lagrangian. In addition, we present a new method for computing tensor sum-integrals and provide a generalization to the known computation techniques of spectacles-type sum-integrals.

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