Effective chiral lagrangian from QCD at nonzero chemical potential

We start from the euclidean QCD action for gluons and massless quarks with Nc colours at finite baryon chemical potential μB and zero temperature. For μB of the order of external momenta o(p) we derive an euclidean effective real chiral lagrangian at finite μB, up to and including o(p4), in terms of Goldstone Bosons (GB), in the large Nc limit, including gluon contributions. Our effective action generalizes non-trivially the one obtained for μB = 0 by previous authors, and it includes new μB-dependent terms. In particular, a topological term μBNB is found, NB being the baryon number in terms of GB fields with the correct normalization factor. Physical implications of the remaining μB-dependent terms are discussed briefly.