Teiji Kunihiro

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.

Extensive study of phase diagram for charge neutral homogeneous quark matter affected by dynamical chiral condensation: Unified picture for thermal unpairing transitions from weak to strong coupling

Abstract We study the phase structures of charge-neutral quark matter under the β -equilibrium for a wide range of the quark–quark coupling strength within a four-fermion model. A comprehensive and unified picture for the phase transitions from weak to strong coupling is presented. We first develop a technique to deal with the gap equation and neutrality constraints without recourse to numerical derivatives, and show that the off-diagonal color densities automatically vanish with the standard assumption for the diquark condensates. The following are shown by the numerical analyses: (i) The thermally-robustest pairing phase is the two-flavor pairing (2SC) in any coupling case, while the second one for relatively low density is the up-quark pairing (uSC) phase or the color–flavor-locked (CFL) phase depending on the coupling strength and the value of strange quark mass. (ii) If the diquark coupling strength is large enough, the phase diagram is much simplified and is free from the instability problems associated with imaginary Meissner masses in the gapless phases. (iii) The interplay between the chiral and diquark dynamics may bring a non-trivial first order transition even in the pairing phases at high density. We confirm (i) also by using the Ginzburg–Landau analysis expanding the pair susceptibilities up to quartic order in the strange quark mass. We obtain the analytic expression for the doubly critical density where the two lines for the second order phase transitions merge, and below which the down-quark pairing (dSC) phase is taken over by the uSC phase. Also we study how the phase transitions from fully gapped states to partially ungapped states are smeared at finite temperature by introducing the order parameters for these transitions.

Precursor of color superconductivity in hot quark matter

We investigate possible precursory phenomena of color superconductivity in quark matter at finite temperature T with use of a simple Nambu-Jona-Lasinio model. It is found that the fluctuating pair field exists with a prominent strength even well above the critical temperature T_c. We show that the collective pair field has a complex energy located in the second Riemann sheet, which approaches the origin as T is lowered to T_c. We discuss the possible relevance of the precursor to the observables to be detected in heavy ion collisions.

Lattice study of low-lying nonet scalar mesons in quenched approximation

Abstract Using lattice QCD simulation in the quenched approximation, we study the κ meson, which is P 0 3 in the quark model, and compare experimental and other lattice data. The κ is the lowest scalar meson with strangeness and constitutes the scalar nonet. The obtained mass is much higher than the recent experimental value, and therefore the κ ( 800 ) is difficult to consider as a simple two-body constituent-quark structure, and may have another unconventional structure.

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.

Search for the possible S = +1 pentaquark states in quenched lattice QCD

We study spin (1/2) hadronic states in quenched lattice QCD to search for a possible S=+1 pentaquark resonance. Simulations are carried out on 8{sup 3}x24, 10{sup 3}x24, 12{sup 3}x24, and 16{sup 3}x24 lattices at {beta}=5.7 at the quenched level with the standard plaquette gauge action and the Wilson quark action. We adopt a Dirichlet boundary condition in the time direction for the quark to circumvent the possible contaminations due to the (anti)periodic boundary condition for the quark field, which are peculiar to the pentaquark. By diagonalizing the 2x2 correlation matrices constructed from two independent operators with the quantum numbers (I,J)=(0,(1/2)), we successfully obtain the energies of the lowest state and the 2nd-lowest state in this channel. The analysis of the volume dependence of the energies and spectral weight factors indicates that a resonance state is likely to exist slightly above the nucleon-Kaon (NK) threshold in (I,J{sup P})=(0,(1/2){sup -}) channel.

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.

Application of the renormalization-group method to the reduction of transport equations

We first give a comprehensive review of the renormalization-group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and on the importance of the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (or boundary) conditions: the RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. The RG method is applied to derive the Navier–Stokes equation from the Boltzmann equation, as an example of the reduction of dynamics. We work out how to obtain the transport coefficients in terms of the one-body distribution function.