Melting the diquark condensate in two-color QCD: A renormalization group analysis

Abstract

We use a Landau theory and the ǫ-expansion to study the superfluid phase transition of two-color QCD at nonzero temperature, T , and baryonic chemical potential, µ. At low T , and for N f flavors of massless quarks, the global SU(N f )×SU(N f )×U(1) symmetry is spontaneously broken by a diquark condensate down to Sp(N f )×Sp(N f ) for any µ > 0. As the temperature increases, the diquark condensate melts, and at sufficiently large T the symmetry is restored. Using renormalization group arguments, we find that in the presence of the chiral anomaly term there can be a second order phase transition when N f = 2 or N f ≥ 6, while the transition is first order for N f = 4. We discuss the relevance of these results for the emergence of a tricritical point recently observed in lattice simulations.

Chiral Lagrangian and spectral sum rules for dense two-color QCD

“…Although these theories are quite different from QCD in certain respects (e.g., the pattern of chiral symmetry breaking is different from that of real QCD), they also exhibit dynamical phenomena such as diquark condensation that are expected to occur in real QCD, and thus we hope that they can provide us with some clues about the phase structure of real QCD. Recent years have seen substantial progress in the understanding of these QCD-like theories at nonzero temperature and density, both analytically and numerically [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”

Thermodynamics of strong coupling 2-color QCD with chiral and diquark condensates

“…In the present paper, we revisit the thermodynamics of the strong coupling limit of 2-color lattice QCD with staggered fermions with chiral and diquark condensates which was originally studied in [10,11,12]. Our main purpose is to analyze its phase structure and the interplay among the chiral condensate qq , the diquark condensate qq , and the baryon density q † q as functions of T , µ, and m. This would give not only a useful guide to the actively pursued lattice QCD simulations of the same system in the weak coupling [13,14,15] but also give us physical insight into the Bose liquid together with the other knowledge from the instanton liquid model [16], the random matrix model [17], the chiral perturbation theory [18,19], and the renormalization group [20]. This paper is organized as follows.…”

Deformation of a renormalization-group equation applied to infinite-order phase transitions

“…Then, the deformed RGE can be derived when they are d c − ǫ, under the condition that all the coupling constants have a common canonical dimension. This condition is satisfied by various field-theoretical models, e.g., an effective theory of antiferromagnets [6], a model containing several gauge fields [7], a model describing true self-avoiding random walks [8], and a model of nematic elastomers [9]. In Ref.…”

“…up to the common eigenvalue −ǫ. The other eigenvalues divided by ǫ are equal to those of the scaling matrices derived from the new RGE (7), which is computed in Ref. [3].…”

“…However, the derivation presented here is much simpler than the method using Eq. (7). The last example is the RGE in a field-theoretical model for nematic elastomers, proposed in Ref.…”