Masakiyo Kitazawa

Chiral and color-superconducting phase transitions with vector interaction in a simple model

We investigate effects of the vector interaction on chiral and color superconducting (CSC) phase transitions at finite density and temperature in a simple Nambu-Jona-Lasinio model. It is shown that the repulsive density-density interaction coming from the vector term, which is present in the effective chiral models but has been omitted, enhances the competition between the chiral symmerty breaking (χSB) and CSC phase transition, and thereby makes the thermodynamic potential have a shallow minimum over a wide range of values of the correlated chiral and CSC order parameters. We find that when the vector coupling is increased, the first order transition between the χSB and CSC phases becomes weaker, and the coexisting phase in which both the chiral and color-gauge symmetry are dynamically broken comes to exisit over a wider range of the density and temperature. We also show that there can exist two endpoints, which are tricritical points in the chiral limit, along the critical line of the first order transition in some range of values of the vector coupling. Although our analysis is based on a simple model, the nontrivial interplay between the χSB and CSC phases induced by the vector interaction is expected to be a universal phenomenon and might give a clue to understanding results obtained with two-color QCD on the lattice.

Pre-Critical Phenomena of Two-Flavor Color Superconductivity in Heated Quark Matter Diquark-Pair Fluctuations and Non-Fermi Liquid Behavior

We investigate the fluctuations of the diquark-pair field and their effects on observables above the critical temperature Tc in two-flavor color superconductivity (CSC) at moderate density using a Nambu-Jona-Lasinio-type effective model of QCD. Because of the strongcoupling nature of the dynamics, the fluctuations of the pair field develop a collective mode, which has a prominent strength even well above Tc. We show that the collective mode is actually the soft mode of CSC. We examine the effects of the pair fluctuations on the specific heat and the quark spectrum for T above but close to Tc. We find that the specific heat exhibits singular behavior because of the pair fluctuations, in accordance with the general theory of second-order phase transitions. The quarks display a typical non-Fermi liquid behavior, owing to the coupling with the soft mode, leading to a pseudo-gap in the density of states of the quarks in the vicinity of the critical point. Some experimental implications of the precursory phenomena are also discussed.

How do chiral condensates affect color superconducting quark matter under charge neutrality constraints

We investigate the effects of the dynamical formation of the chiral condensates on color superconducting phases under the electric and color neutrality constraints at vanishing temperature. We shall show that the phase appearing next to the color-flavor locked (CFL) phase down in density depends on the strength of the diquark coupling. In particular, the gapless CFL (gCFL) phase is realized only in a weak coupling regime. We give a qualitative argument on why the gCFL phase in the weak coupling region is replaced by some other phases in the strong coupling, once the competition between dynamical chiral symmetry breaking and the Cooper pair formation is taken into account.

Pseudogap of color superconductivity in heated quark matter

We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the decaying process of quarks near Fermi surface to a hole and the diquark soft mode (qq){sub soft} is responsible for the formation of the pseudogap. Our result suggests that the pseudogap is a universal phenomenon in strong coupling superconductors.

Quark spectrum above but near critical temperature of chiral transition

Abstract We explore the quark properties at finite temperature near but above the critical temperature of the chiral phase transition. We investigate the effects of the precursory soft mode of the phase transition on the quark dispersion relation and the spectral function. It is found that there appear novel excitation spectra of quasi-quarks and quasi-anti-quarks with a three-peak structure, which are not attributed to the hard-thermal-loop approximation. We show that the new spectra originate from the mixing between a quark (anti-quark) and an anti-quark hole (quark hole) caused by a “resonant scattering” of the quasi-fermions with the thermally-excited soft mode which has a small but finite excitation energy.

Novel Collective Excitations and the Quasi-Particle Picture of Quarks Coupled with a Massive Boson at Finite Temperature

Motivated by the observation that there may exist hadronic excitations even in the quark-gluon plasma (QGP) phase, we investigate how the properties of quarks, especially within the quasi-particle picture, are affected by the coupling with bosonic excitations at finite temperature (T ), employing Yukawa models with a massive scalar (pseudoscalar) and vector (axial-vector) boson of mass m. The quark spectral function and the quasi-dispersion relations are calculated at one-loop order. We find that there appears a three-peak structure in the quark spectral function with a collective nature when T is comparable with m, irrespective of the type of boson considered. Such a multi-peak structure was first found in a chiral model yielding scalar composite bosons with a decay width. We elucidate the mechanism through which the new quark collective excitations are realized in terms of the Landau damping of a quark (an antiquark) induced by scattering with the thermally excited boson, which gives rise to mixing and hence a level repulsion between a quark (antiquark) and an antiquark-hole (quark-hole) in the thermally excited antiquark (quark) distribution. Our results suggest that the quarks in the QGP phase can be described within an interesting quasi-particle picture with a multi-peak spectral function. Because the models employed here are rather generic, our findings may represent a universal phenomenon for fermions coupled to a massive bosonic excitation with a vanishing or small width. The relevance of these results to other fields of physics, such as neutrino physics, is also briefly discussed. In addition, we describe a new aspect of the plasmino excitation obtained in the hard-thermal loop approximation.

Stable gapless superconductivity at strong coupling

Abstract We study cross-flavor Cooper pairing in a relativistic system of two fermion species with mismatched Fermi surfaces. We find that there exist gapless phases which are characterized by either one or two gapless nodes in the energy spectra of their quasiparticles. An analysis of the current–current correlator reveals that, at strong coupling, both of these gapless phases can be free of magnetic instabilities. This is in contrast to the weak-coupling case where there are always two gapless nodes and the phase becomes magnetically unstable.

Non-Fermi liquid behavior induced by resonant diquark-pair scattering in heated quark matter

Abstract We show how the quasiparticle picture of quarks changes near but above the critical temperature T c of the color-superconducting phase transition in the heated quark matter. We demonstrate that a non-Fermi liquid behavior of the matter develops drastically when the diquark coupling constant is increased owing to the coupling of the quark with the pairing soft mode: We clarify that the depression and eventually the appearance of a gap structure in the spectral function as well as the anomalous quark dispersion relation of the quark can be understood in terms of the resonant scattering between the incident quark and a particle near the Fermi surface to make the pairing soft mode.

Bose-Einstein Condensation of Diquark Molecules in Three-Flavor Quark Matter

We study the phase diagram of strongly interacting matter with three quark flavors at low and intermediate densities and non-zero temperatures in the framework of an NJL-type model with four-point interactions. At large densities, when the interactions are weak due to asymptotic freedom, quarks form loosely bound Cooper pairs. However, when the density decreases, interactions become stronger and quark Cooper pairs transform smoothly into tightly bound diquark molecules. We find that such molecules are stable at low density and temperature and that they dissociate above a temperature Tdiss of the order of the chiral phase transition temperature Tc ∼ 170 MeV. We also explore the conditions under which these molecules undergo Bose-Einstein condensation (BEC). We find that BEC is only possible if we increase the attractive interaction in the diquark channel to (probably unrealistically) large values.

Precursor of color superconductivity

Abstract We investigate possible precursory phenomena of color superconductivity at finite temperature T with an effective theory of QCD. It is found that the fluctuation of the diquark pair field exists with a prominent strength even well above the critical temperature T c . We show that such a fluctuation forms a collective mode, the corresponding pole of which approaches the origin as T is lowered to T c in the complex energy plane. We discuss the possible relevance of the precursor to the observables to be detected in heavy-ion collisions.