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We construct an effective action for QCD by expanding the quark determinantin powers of the chemical potential at finite temperature in the case ofmassless quarks. To cut the infinite series we adopt the Weinberg powercounting criteria. We compute the minimal effective action (~p^4), expanding inthe external momentum, which implies the use of the hard thermal loopapproximation. Our main result is a gauge invariant expression for the phasetheta of the functional determinant in QCD, and recovers dimensional reductionin the high-temperature limit. We compute, analytically, <theta^2> in the rangeof p << 2 pi T, including perturbative and nonperturbative contributions, thelatter treated within the mean field approximation. Implications for latticesimulations are briefly discussed.

Weinberg power counting and the quark determinant at small chemical potential