QCD-like Theories at Finite Baryon Density
J. B. Kogut, M. A. Stephanov, D. Toublan, J. J. M. Verbaarschot, A. Zhitnitsky
TL;DR
The paper develops a symmetry-based, low-energy effective theory for QCD-like theories with pseudoreal fermions at finite baryon density, covering two-color QCD and adjoint QCD. By exploiting the enlarged SU($2N_f$) symmetry and its breaking patterns, it derives the μ-dependent chiral Lagrangian, analyzes vacuum alignment, and computes the masses and dispersions of Goldstone modes as functions of μ and the bare mass m. A second-order phase transition at $μ = m_π/2$ drives diquark Bose condensation, leading to a massless Goldstone mode and a reorganized spectrum with μ-induced mixing, including a linearly dispersing diquark mode signaling superfluid behavior. The work provides quantitative predictions for lattice QCD at nonzero density and insights relevant to real three-color QCD at finite baryon density, linking symmetry, condensation, and spectrum in a controlled effective-field-theory framework.
Abstract
We study QCD-like theories with pseudoreal fermions at finite baryon density. Such theories include two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint color representation. In all such theories the lightest baryons are diquarks. At zero chemical potential $μ$ they are, together with the pseudoscalar mesons, the Goldstone modes of a spontaneously broken enlarged chiral symmetry group. Using symmetry principles, we derive the low-energy effective Lagrangian for these particles. We find that a second order phase transition occurs at a value of $μ$ equal to half the mass of the Goldstone modes. For values of $μ$ beyond this point the scalar diquarks Bose condense and the diquark condensate is nonzero. We calculate the dependence of the chiral condensate, the diquark condensate, the baryon charge density, and the masses of the diquark and pseudoscalar excitations on $μ$ at finite bare quark mass and scalar diquark source. The relevance of our results to lattice QCD calculations and to real three-color QCD at finite baryon density is discussed.