Two-flavor Color Superconducting Phase Research Articles

Emergent QCD Kondo effect in two-flavor color superconducting phase

We show that effective coupling strengths between ungapped and gapped quarks in the two-flavor color superconducting (2SC) phase are renormalized by logarithmic quantum corrections. We obtain a set of coupled renormalization-group (RG) equations for two distinct effective coupling strengths arising from gluon exchanges carrying different color charges. The diagram of RG flow suggests that both of the coupling strengths evolve into a strong-coupling regime as we decrease the energy scale toward the Fermi surface. This is a characteristic behavior observed in the Kondo effect, which has been known to occur in the presence of impurity scatterings via non-Abelian interactions. We propose a novel Kondo effect emerging without doped impurities, but with the gapped quasiexcitations and the residual SU(2) color subgroup intrinsic in the 2SC phase, which we call the 2SC Kondo effect.

Random matrix model for chiral and color-flavor locking condensates

We study the phase diagram of a chiral random matrix model with three quark flavors at finite temperature and chemical potential, taking the chiral and diquark condensates as independent order parameters. Fixing the ratio of the coupling strengths in the quark-antiquark and quark-quark channels applying the Fierz transformation, we find that the color-flavor locked (CFL) phase is realized at large chemical potential, while the ordinary chirally broken phase appears in the region with small chemical potential. We investigate responses of the phases by changing small quark masses in the cases with three equal-mass flavors and with $2+1$ flavors. In the case with three equal-mass flavors, we find that the finite masses make the CFL phase transition line move to the higher-density region. In the case with $2+1$ flavors, we find the two-flavor color-superconducting phase at the medium-density region as a result of the finite asymmetry between the flavors, as well as the CFL phase at the higher-density region.

Formation of quark phases in protoneutron stars: The transition from the two-flavor color-superconducting phase to the normal quark phase

We study the process of formation of quark phases in protoneutron stars. After calculating the phase transition between nucleonic matter and the 2SC phase at fixed entropy and lepton fraction, we show that an unpairing transition between the 2SC phase and the normal quark phase occurs for low lepton fractions. We then calculate the process of diffusion of neutrinos in protoneutron stars and show that for intermediate values of the mass of the star, the deleptonization triggers the phase transition between the two quark phases after a temporal delay of a few seconds. In less massive stars instead only the normal quark phase is formed at the end of the deleptonization stage. We also discuss the possible astrophysical implications of our scenario.

Roles of axial anomaly on neutral quark matter with color superconducting phase

We investigate the effects of the axial-anomaly term with a chiral-diquark coupling on the phase diagram within a two-plus-one-flavor Nambu-Jona-Lasinio model under the charge-neutrality and $\ensuremath{\beta}$-equilibrium constraints. We find that when such constraints are imposed, the new anomaly term plays a quite similar role as the vector interaction does on the phase diagram, which the present authors clarified in a previous work. Thus, there appear several types of phase structures with multiple critical points at low temperature $T$, although the phase diagrams with intermediate-$T$ critical point(s) are never realized without these constraints even within the same model Lagrangian. This drastic change is attributed to an enhanced interplay between the chiral and diquark condensates due to the anomaly term at finite temperature; the $u\mathrm{\text{\ensuremath{-}}}d$ diquark coupling is strengthened by the relatively large chiral condensate of the strange quark through the anomaly term, which in turn definitely leads to the abnormal behavior of the diquark condensate at finite $T$, inherent to the asymmetric quark matter. We note that the critical point from which the crossover region extends to zero temperature appears only when the strength of the vector interaction is larger than a critical value. We also show that the chromomagnetic instability of the neutral asymmetric homogenous two-flavor color-superconducting phase is suppressed and can be even completely cured by the enhanced diquark coupling due to the anomaly term and/or by the vector interaction.

Phase diagram of neutral quark matter: The effect of neutrino trapping

We study the effect of neutrino trapping on the phase diagram of dense, locally neutral three-flavor quark matter within the framework of a Nambu-Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagrams in the plane of temperature and quark chemical potential, as well as in the plane of temperature and lepton-number chemical potential are presented. We show that neutrino trapping favors two-flavor color superconductivity and disfavors the color-flavor-locked phase at intermediate densities of matter. At the same time, the location of the critical line separating the two-flavor color-superconducting phase and the normal phase of quark matter is little affected by the presence of neutrinos. The implications of these results for the evolution of protoneutron stars are briefly discussed.

Pion, σ meson, and diquarks in the two-flavor color-superconducting phase of dense cold quark matter

The spectrum of meson and diquark excitations of dense cold quark matter is investigated within the framework of a Nambu--Jona-Lasinio-type model for light quarks of two flavors. It was found that a first-order phase transition occurs when the chemical potential \ensuremath{\mu} exceeds the critical value ${\ensuremath{\mu}}_{c}=350\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Above ${\ensuremath{\mu}}_{c}$, the diquark condensate $\ensuremath{\langle}\mathit{qq}\ensuremath{\rangle}$ forms, breaking the color symmetry of strong interaction. The masses of \ensuremath{\pi} and \ensuremath{\sigma} mesons are shown to grow with the chemical potential \ensuremath{\mu} in the color-superconducting phase, but the mesons themselves become almost stable particles. Moreover, we have found in this phase an abnormal number of three, instead of five, Nambu-Goldstone bosons, together with a color doublet of light stable diquark modes and a color-singlet heavy diquark resonance with mass $~$1100 MeV. In the color-symmetric phase, i.e., for $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$, a mass splitting of diquarks and antidiquarks is shown to arise if $\ensuremath{\mu}\ensuremath{\ne}0$, contrary to the case of a vanishing chemical potential, in which the masses of antidiquarks and diquarks are degenerate at the value $~$700 MeV.

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

The phase diagram of strongly interacting matter at nonzero temperature and baryon chemical potential is calculated within a three-flavor NJL-type quark model with realistic quark masses. The model exhibits spontaneous chiral symmetry breaking as well as diquark condensation in the two-flavor color-superconducting phase and in the color–flavor-locked phase. We investigate the color–flavor-unlocking phase transition, taking into account self-consistently calculated effective quark masses. We find that it is mainly triggered by a first-order phase transition with respect to the strange-quark mass. It takes place at much higher values of the chemical potential than the transition to the hadronic phase such that we find a relatively large region in the phase diagram where the two-flavor color-superconductor seems to be the most favored state.