Color Superconducting Phase Transition Research Articles

Enhancement of dilepton production rate and electric conductivity around the QCD critical point

Abstract We investigate whether the soft mode that becomes massless at the QCD critical point (CP) causes an enhancement of the dilepton production rate (DPR) and electric conductivity around the CP through modification of the photon self-energy using the two-flavor Nambu–Jona-Lasinio model. The modification is described by the so-called Aslamazov–Larkin, Maki–Thompson, and density of states terms, which have been taken into account in our previous study on the DPR near the color-superconducting phase transition, with a replacement of the diquark modes with the soft mode of the QCD CP. We show that the coupling of photons with the soft modes brings about an enhancement of the DPR in the low-invariant-mass region and the conductivity near the CP, which would be observable in relativistic heavy-ion collisions.

Color superconductivity in a self-consistent NJL-type model

In this paper, the NJL-type model is used to investigate the color superconductivity. The four-fermion interactions of the NJL-type model are Fierz-transformed into two different classes, i.e., the quark-antiquark and the quark-quark interaction channels, associated with the chiral symmetry breaking and color superconductivity respectively. We conclude that the weighting factor between quark-antiquark and quark-quark interaction channels has significance on the phase structure when the mean-field approximation is employed, and the baryon number density gives a tight constraint on the weighting factor of quark-antiquark interaction channels. Besides, the susceptibilities show that the color superconducting phase transition is of the second-order and takes place before the chiral crossover transition as quark number density increases. In the end, we study the critical temperatures ${T}_{c}$ of the color superconductivity and it agrees with the perturbative result of diquark condensate $\mathrm{\ensuremath{\Delta}}\ensuremath{\approx}0.57{T}_{c}$.

Functional renormalization group approach to color superconducting phase transition

We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar SU(Nc) gauge theories by calculating the β function of the gauge coupling in arbitrary dimension d based on two different regularization schemes. We find that in d = 3, due to gluon fluctuation effects, the β function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.

Neutrality of a magnetized two-flavor quark superconductor

We investigate the effect of electric and color charge neutrality on the two-flavor color superconducting (2SC) phase of cold and dense quark matter in presence of constant external magnetic fields and at moderate baryon densities. Within the framework of the Nambu-Jona-Lasinio (NJL) model, we study the inter-dependent evolution of the quark's BCS gap and constituent mass with increasing density and magnetic field. While confirming previous results derived for the highly magnetized 2SC phase with color neutrality alone, we obtain new results as a consequence of imposing charge neutrality. In the charge neutral gapless 2SC phase (g2SC), a large magnetic field drives the color superconducting phase transition to a crossover, while the chiral phase transition is first order. At larger diquark-to-scalar coupling ratio $G_D/G_S$, where the 2SC phase is preferred, we see hints of the Clogston-Chandrasekhar limit at a very large value of the magnetic field ($B\sim 10^{19}$G), but this limit is strongly affected by Shubnikov de Haas-van Alphen oscillations of the gap, indicating the transition to a domain-like state.

Two- and three-color two-quark states in warm, dense quark matter

We study the Gaussian fluctuations of the two-flavor, meson-diquark bosonized NJL model for two and three colors at the color superconducting phase transition. The analysis is based on analytical properties of the polarization matrix. Pionic fluctuations are shown to be stabilised in the 2SC phase compared to the two-color result where they are right on threshold.

Effects of a multi-quark interaction on color superconducting phase transition in an extended NJL model

We study the interplay of the chiral and the color superconducting phase transition in an extended Nambu–Jona-Lasinio model with a multi-quark interaction that produces the nonlinear chiral–diquark coupling. We observe that this nonlinear coupling adds up coherently with the ω2 interaction to either produce the chiral–color superconductivity coexistence phase or cancel each other depending on its sign. We discuss that a large coexistence region in the phase diagram is consistent with the quark–diquark picture for the nucleon whereas its smallness is the prerequisite for the applicability of the Ginzburg–Landau approach.

PHASE TRANSITION IN STRANGE QUARK MATTER WITH DENSITY DEPENDENT QUARK MASS

We investigate the color superconducting phase transition in strange quark matter at zero temperature considering the density dependence of quark masses. At high densities, it is well known that cold quark matter is a color superconductor with favorable phase being the color flavor locked (CFL). We analyze the phase transition between the initially strange quark matter (SQM) and the CFL phases. The quark masses are parametrized with the baryon number density nB in the dense system.

Fermionic Collective Modes in QGP near Critical Temperatures

We investigate the quark spectrum in the quark-gluon plasma phase near color superconducting (CS) and chiral phase transitions. Owing to the precursory soft modes of the phase transitions, there appear novel excitaion spectra: In the CS transition, the quark matter shows non-Fermi liquid behavior and leads to the pseudogap in the density of states of quarks. In the chiral transition, three collective excitations appear in the quark spectrum.

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

We show how the quasiparticle picture of quarks changes near but above the critical temperature Tc 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.

COLOR SUPERCONDUCTIVITY AT MODERATE BARYON DENSITY

This article focuses on the two-flavor color superconducting phase at moderate baryon density. In order to simultaneously investigate the chiral phase transition and the color superconducting phase transition, the Nambu–Gorkov formalism is extended to treat the quark-antiquark and diquark condensates on an equal footing. The competition between the chiral condensate and the diquark condensate is analyzed. The cold dense charge neutral two-flavor quark system is investigated in detail. Under the local charge neutrality condition, the ground state of two-flavor quark matter is sensitive to the coupling strength in the diquark channel. When the diquark coupling strength is around the value obtained from the Fierz transformation or from fitting the vacuum bayron mass, the ground state of charge neutral two-flavor quark matter is in a thermal stable gapless 2SC (g2SC) phase. The unusual properties at zero as well as nonzero temperatures and the chromomagnetic properties of the g2SC phase are reviewed. Under the global charge neutrality condition, assuming the surface tension is negligible, the mixed phase composed of the regular 2SC phase and normal quark matter is more favorable than the g2SC phase. A hybrid nonstrange neutron star is constructed.

Thermal phase transitions and gapless quark spectra in quark matter at high density

Thermal color superconducting phase transitions in three-flavor quark matter at high baryon density are investigated in the Ginzburg-Landau (GL) approach. We constructed the GL potential near the boundary with a normal phase by taking into account nonzero quark masses, electric charge neutrality, and color charge neutrality. We found that the density of states averaged over paired quarks plays a crucial role in determining the phases near the boundary. By performing a weak coupling calculation of the parameters characterizing the GL potential terms of second order in the pairing gap, we show that three successive second-order phase transitions take place as the temperature increases: a modified color-flavor locked phase (ud, ds, and us pairings) -> a ``dSC'' phase (ud and ds pairings) -> an isoscalar pairing phase (ud pairing) -> a normal phase (no pairing). The Meissner masses of the gluons and the number of gapless quark modes are also studied analytically in each of these phases.

Melting Pattern of Diquark Condensates in Quark Matter

Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. The effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) --> a d-quark superconducting (dSC) phase (ud and ds pairings) --> an isoscalar pairing phase (ud pairing) --> a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are Meissner screened as in the mCFL phase, three out of nine quark quasiparticles are always gapless.

Chiral and Color-Superconducting Phase Transitions with Vector Interaction in a Simple Model

Chiral and Color-Superconducting Phase Transitions with Vector Interaction in a Simple Model

Effects of vector coupling on chiral and color-superconducting phase transitions - interplay among the scalar, pairing and vector interaction

We investigate effects of the vector interaction appearing in chiral effective Lagrangians on the chiral and color superconducting (CSC) phase transitions using Nambu-Jona-Lasinio model. It is shown that the repulsive density-density interaction coming from the vector term enhances competition between the chiral symmetry breaking (κSB) and CSC phase transition: When the vector coupling is increased, the first order transition between the κSB and CSC phase becomes weaker, and the coexisting phase in which both the chiral and color-gauge symmetries are dynamically broken comes to exisit in a wider region in the T- μ plane. We find that the critical line of the first order transition can have two endpoints for an intermediate range of the vector coupling.

2.7 Effects of Vector Coupling on Chiral and Color-superconducting Phase Transitions : interplay among the scalar, pairing and vector interaction

2.7 Effects of Vector Coupling on Chiral and Color-superconducting Phase Transitions : interplay among the scalar, pairing and vector interaction

Chiral and Color-Superconducting Phase Transitions with Vector Interaction in a Simple Model

In the preceding paper(Prog.Theor.Phys.108(2002)929 or hep-ph/0207255), we have shown that the critical line of the first order chiral transition of QCD can have two endpoints. In this addendum, we elucidate the mechanism to realize the two-endpoint structure in the QCD phase diagram and argue the robustness for the appearance of such an interesting phase structure.

Instanton vacuum at finite density of quark matter

We study light quark interactions in the instanton liquid at finite quark/baryon number density analyzing chiral and diquark condensates and investigate the behaviors of quark dynamical mass and both condensates together with instanton liquid density as a function of quark chemical potential. We conclude the quark impact (estimated in the tadpole approximation) on the instanton liquid could shift color superconducting phase transition to higher values of the chemical potential bringing critical quark matter density to the values essentially higher than conventional nuclear one.

Aspects of high density effective theory in QCD

We study an effective theory of QCD at high density in detail, including the finite temperature effects and the leading order correction in $1/\mu$ expansion. We investigate the Cooper pair gap equation and find that the color-flavor locking phase is energetically preferred at high density. We also find the color-superconducting phase transition occurs in dense quark matter when the chemical potential is larger than $250\pm 100~{\rm MeV}$ and the temperature is lower than 0.57 times the Cooper pair gap in the leading order in the hard-dense-loop approximation. The quark-neutrino four-Fermi coupling and the quark-axion coupling receive significant corrections in dense quark matter.