Phase of the complex functional determinant in QCD at small chemical potential

We construct an effective action for QCD by expanding the quark determinant in powers of the chemical potential at finite temperature in the case of massless quarks. To cut the infinite series we adopt the Weinberg power counting criterium. We compute the minimal effective action (∼ p), expanding in the external momentum, which implies the use of the Hard Thermal Loop approximation. Our main result is a gauge invariant expression for the phase of the functional determinant in QCD. Implications for lattice simulations are briefly discussed.