Effective chiral lagrangian from QCD at nonzero chemical potential

Abstract

We start from the euclidean QCD action for gluons and massless quarks with N_c colours at finite baryon chemical potential μ_B and zero temperature. For μ_B of the order of external momenta o(p) we derive an euclidean effective real chiral lagrangian at finite μ_B, up to and including o(pˆ4), in terms of Goldstone Bosons (GB), in the large N_c limit, including gluon contributions. Our effective action generalizes non-trivially the one obtained for μ_B = 0 by previous authors, and it includes new μ_B -dependent terms. In particular, a topological term μ_B N_B is found, N_B being the baryon number in terms of GB fields with the correct normalization factor. Physical implications of the remaining μ_B -dependent terms are discussed briefly.