Anisotropic Admixture in Color-Superconducting Quark Matter

Abstract

The analysis of color-superconducting two-flavor deconfined quark matter at moderate densities is extended to include a particular spin-1 Cooper pairing of those quarks which do not participate in the standard spin-0 diquark condensate. (i) The relativistic spin-1 gap ∆ ′ implies spontaneous breakdown of rotation invariance manifested in the form of the quasi-fermion dispersion law.(ii) The critical temperature of the anisotropic component is approximately given by the relationFor massless fermions the gas of anisotropic Bogolyubov-Valatin quasiquarks becomes effectively gapless and two-dimensional. Consequently, its specific heat depends quadratically on temperature. (iv) All collective Nambu-Goldstone excitations of the anisotropic phase have a linear dispersion law and the whole system remains a superfluid. (v) The system exhibits an electromagnetic Meissner effect.PACS numbers: 12.39. Ki, 12.38.Aw,11.30.Qc Recent investigations suggest that the phase structure of QCD is very rich [1,2]. At low temperatures and high densities strongly interacting matter is expected to be a color superconductor [3]. At asymptotically high densities, where the QCD coupling constant becomes small, this can be analyzed starting from first principles [4,5], whereas at more moderate densities, present (presumably) in the interiors of neutron stars, these methods are no longer justified. In this region the low-energy dynamics of deconfined quark matter is often studied employing effective Lagrangians L eff which contain local or non-local four-fermion interactions, most importantly interactions derived from instantons or on a more phenomenological basis [6,7,8]. The non-confining gluon SU (3) c gauge fields are then treated as weak external perturbations, and neglected in lowest approximation.In this letter we consider the case of two flavors which is most likely relevant at chemical potentials just above the deconfinement phase transition. On physical grounds it is then natural to assume that L eff favors the spontaneous formation of spin-0 isospin singlet Cooper pair condensates [1, 9] δ = ψ T C γ 5 τ 2 λ 2 ψ , where ψ is a quark field, C the matrix of charge conjugation, τ 2 a Pauli matrix which acts in flavor space, and λ 2 a GellMann matrix which acts in color space. Due to the latter SU (3) c is broken down to SU (2) c . This has the following consequences for the physical excitations of the system: (i) Corresponding to the mixing of the colors 1 and 2 there are two Bogolyubov-Valatin quasiquarks for each flavor with the dispersion law EThe energy gap ∆ is the solution of a selfconsistent gap equation and is found to be typically of the order ∼ 100 MeV in model calculations [6,7,8]. ǫ p = p 2 + M 2 , where M is an effective Dirac mass, related to the chiral condensate ψ ψ via a selfconsistency equation [8]. For each flavor there is an unpaired quark of color 3 with the dispersion law ǫ(ii) Because of the spontaneous breaking of SU (3) c down to SU (2) c five of the eight gluons receive a mass (Meissner effect), whereas thre...

Color–flavor unlocking and phase diagram with self-consistently determined strange-quark masses

“…In fact, already for two flavors, one finds that a self-consistent treatment requires the simultaneous consideration of possible expectation values in six different channels, like color dependent quark condensates or densities [24]. For three flavors, there are even more.…”

“…For two flavors this has been done by several authors with different degrees of sophistication [22,23,24]. For three flavors, a first attempt in this direction was made in Ref.…”

General structure of relativistic vector condensation

“…In this case the quarks must pair in a spin one state and a careful analysis has been performed in [9]. Whether this gap occurs or not in practice is a dynamical issue recently investigated in [10].…”

Color Superconductivity in Two- and Three-Flavor Systems at Moderate Densities

“…This interesting possibility has recently been analyzed in Ref. [23] and will be discussed in more detail in Jiří Hošek's contribution [35].…”

“…Other phases have been suggested more recently, like crystalline phases in a small window between the 2SC phase and the CFL phase [18,19] or a CFL phase accompanied by a kaon condensate (CFL + K) [20,21]. In addition, those color or flavor degrees of freedom which do not participate in the "standard" condensates could pair in different, usually more fragile, channels, thus forming additional phases [22,23,24].…”