Quark matter in QC<Subscript>2</Subscript>D

Results are presented from a numerical study of lattice QCD with gauge group SU(2) and two flavors of Wilson fermion at non-zero quark chemical potential μ ≫ T. Studies of the equation of state, the superfluid condensate, and the Polyakov line all suggest that in addition to the low-density phase of Bose-condensed diquark baryons, there is a deconfined phase at higher quark density in which quarks form a degenerate system, whose Fermi surface is only mildly disrupted by Cooper pair condensation.     

Diquark condensation in dense adjoint matter

We study SU(2) lattice gauge theory at non-zero chemical potential with one staggered quark flavor in the adjoint representation. In this model the fermion determinant, although real, can be both positive and negative. We have performed numerical simulations using both hybrid Monte Carlo and two-step multibosonic algorithms, the latter being capable of exploring sectors with either determinant sign. We find that the positive determinant sector behaves like a two-flavor theory, with the chiral condensate rotating into a two-flavor diquark condensate for , implying a superfluid ground state. Good agreement is found with analytical predictions made using chiral perturbation theory. In the ‘full’ model there is no sign of either onset of baryon density or diquark condensation for the range of chemical potentials we have considered. The impact of the sign problem has prevented us from exploring the true onset transition and the mode of diquark condensation, if any, for this model. Received: 28 September 2001 / Published online: 23 November 2001     

Mass spectrum of diquarks and mesons in the color–flavor locked phase of dense quark matter

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential μ. We investigate the effective action of meson and diquark fields both at sufficiently large values of μ>μ_c≈  330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μ_c). In the latter case all nine pseudoscalar mesons are Nambu–Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400–500 MeV for not too large values of μ>μ_c. PACS 11.30.Qc; 12.38.-t; 12.39.-x     

Critical behavior in the dense planar Nambu--Jona-Lasinio model

We present results of a Monte Carlo simulation of a (2+1)-dimensional Nambu-Jona-Lasinio model. In the vacuum phase, the diquark condensate vanishes linearly as a function of diquark source j as expected, but simulations in a region with nonzero baryon density suggest a power-law scaling infinity j(alpha) and hence a critical system for all mu > mu(c). There is no signal for superfluidity. Comparisons are drawn with the pseudogap phase in cuprate superconductors. We also measure the dispersion relation E(k) for fermionic excitations, and find results consistent with a sharp Fermi surface. Any gap Delta is constrained to be much less than the constituent quark mass scale Sigma(0).     

Bound diquarks and their Bose–Einstein condensation in strongly coupled quark matter

We explore the formation of diquark bound states and their Bose–Einstein condensation (BEC) in the phase diagram of three-flavor quark matter at nonzero temperature, T, and quark chemical potential, μ  . Using a quark model with a four-fermion interaction, we identify diquark excitations as poles of the microscopically computed diquark propagator. The quark masses are obtained by solving a dynamical equation for the chiral condensate and are found to determine the stability of the diquark excitations. The stability of diquark excitations is investigated in the T–μ$T\text{–}\mu$ plane for different values of the diquark coupling strength. We find that diquark bound states appear at small quark chemical potentials and at intermediate coupling strengths. Bose–Einstein condensation of non-strange diquark states occurs when the attractive interaction between quarks is sufficiently strong.     

Chiral soliton model vs. pentaquark structure for Θ(1540)

The exotic baryon Θ⁺(1540 MeV) is visualized as an expected (iso) rotational excitation in the chiral soliton model. It is also argued as a pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast these two points of view; observe the similarities and differences between the two pictures. Collective excitation, the characteristic of chiral soliton model, points toward small mixing of representations in the wake ofSU (3) breaking. In contrast, constituent quark models prefer near ‘ideal’ mixing, similar to ω-φ mixing.     

Screening of heavy quark free energies at finite temperatureand non-zero baryon chemical potential

We analyze the dependence of heavy quark free energies on the baryon chemical potential μ_b in 2-flavor QCD by performing a 6th order Taylor expansion in the chemical potential which circumvents the sign problem. The bare quark mass at corresponds to a pion mass of about 770 MeV and is thus not in the range of physical quark masses but the quark mass dependence is known to be small above T_c. At N_τ = 4 the lattices are coarse, however, we are using improved (p4 staggered) fermions. The Taylor expansion coefficients of color singlet and color averaged free energies are calculated and from this the expansion coefficients for the corresponding screening masses are determined. We find that for small μ_b the free energies of a static quark-antiquark pair decrease in a medium with a net excess of quarks and that screening is well described by a screening mass which increases with increasing μ_b. The μ_b-dependent corrections to the screening masses are well described by perturbation theory for T ≳ 2T_c. In particular, we find for all temperatures above T_c that the expansion coefficients for singlet and color averaged screening masses differ by a factor 2. PACS. 11.15.Ha, 11.10.Wx, 12.38Gc, 12.38.Mh     

Molecular dynamics simulation for the baryon-quark phase transition at finite baryon density

We study the baryon-quark phase transition in the molecular dynamics (MD) of the quark degrees of freedom at finite baryon density. The baryon state at low baryon density, and the deconfined quark state at high baryon density are reproduced. We investigate the equations of state of matters with different u-d-s compositions. It is found that the baryon-quark transition is sensitive to the quark width.     

Phase transition between three- and two-flavor QCD?

We explore the possibility that QCD may undergo a phase transition as a function of the strange quark mass. This would hint towards models with ”spontaneous color symmetry breaking” in the vacuum. For two light quark flavors we classify possible colored quark-antiquark, diquark and gluon condensates that are compatible with a spectrum of integer charged states and conserved isospin and baryon number. The ”quark mass phase transition” would be linked to an unusual realization of baryon number in QCD₂ and could be tested in lattice simulations. We emphasize, however, that at the present stage the Higgs picture of the vacuum cannot predict a quark mass phase transition - a smooth crossover remains as a realistic alternative. Implications of the Higgs picture for the high-density phase transition in QCD₂ suggest that this transition is characterized by the spontaneous breaking of isospin for nuclear and quark matter. Received: 12 March 2001 / Revised version: 2 April 2003 / Published online: 2 June 2003 RID="a" ID="a" e-mail: C.Wetterich@thphys.uni-heidelberg.de     

Diquark condensate and quark interaction with an instanton liquid

The interaction of light quarks with an instanton liquid is considered at nonzero density of quark/baryon matter in a phase where the diquark condensate is nonzero. It is shown that the inclusion of the relevant perturbation of the instanton liquid leads to an increase in the quark chemical potential μ_c. This in turn induces a considerable growth of the threshold quark-matter density at which one expects the emergence of color superconductivity.     

Instanton liquid at a finite density of quark matter

For the case of finite quark and baryon densities, the interaction of light quarks with an instanton liquid is considered in a phase that involves a nonvanishing chiral condensate. The generating functional is considered in the tadpole approximation, and the behavior of the dynamical quark mass and the behavior of the chiral condensate, as well as the behavior of the instanton-liquid (gluon-condensate) density, which grows slightly with the quark chemical potential, are explored. Arguments are presented in favor of the statement that the quark-density threshold for the emergence of a diquark condensate grows sizably owing to interaction with the instanton liquid.     

Thermodynamics of chiral symmetry at low densities

The phase diagram of two-color QCD as a function of temperature and baryon chemical potential is considered. Using a low-energy chiral Lagrangian based on the symmetries of the microscopic theory, we determine, at the one-loop level, the temperature dependence of the critical chemical potential for diquark condensation and the temperature dependence of the diquark condensate and baryon density. The prediction for the temperature dependence of the critical chemical potential is consistent with the one obtained for a dilute Bose gas. The associated phase transition is shown to be of second order for low temperatures and first order at higher temperatures. The tricritical point at which the second order phase transition ends is determined. The results are carried over to QCD with quarks in the adjoint representation and to ordinary QCD at a non-zero chemical potential for isospin.     

Spontaneous violation of chiral symmetry in QCD vacuum is the origin of baryon masses and determines baryon magnetic moments and their other static properties

A short review is presented of the spontaneous violation of chiral symmetry in QCD vacuum. It is demonstrated that this phenomenon is the origin of baryon masses in QCD. The value of nucleon mass is calculated, as well as the masses of hyperons and some baryonic resonances, and expressed mainly through the values of quark condensates—, q = u, d, s,—the vacuum expectation values (v.e.v.) of quark field. The concept of v.e.v. induced by external fields is introduced. It is demonstrated that such v.e.v. induced by static electromagnetic field results in quark condensate magnetic susceptibility, which plays the main role in determination of baryon magnetic moments. The magnetic moments of proton, neutron, and hyperons are calculated. The results of calculation of baryon octet β-decay constants are also presented. The text was submitted by the author in English.     

Pion and chiral density waves in a (1 + 1)-dimensional Nambu-Jona-Lasinio model

A (1 + 1)-dimensional massless Nambu-Jona-Lasinio model is investigated in the limit of a large number of colors. The model describes a system with two quark flavors if μ baryon and μ _I isospin chemical potentials occur. The question of whether spatially inhomogeneous chiral and pion condensates can form in a dense quark environment is also examined.     

Phase transitions in dense quark matter in a gravitational field of constant curvature

Abstact The impact of the gravitational field on the formation of quark and diquark condensate in the framework of the extended Nambu-Jona-Lasinio (NJL) model is studied. In the mean field approximation, an expression for the effective potential with regard to a finite temperature and density of quark matter in the static gravitational field of constant curvature is obtained. Original Russian Text ? V.Ch. Zhukovsky, A.V. Tyukov, D. Ebert, 2007, published in Vestnik Moskovskogo Universiteta. Fizika, 2007, No. 3, pp. 68–70.     

Lattice QCD thermodynamic results with improved staggered fermions

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of N _τ =4,6 and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential and present the isentropic equation of state on lines of constant entropy per baryon number.     

Test of the heavy quark–light diquark approximation for baryons with a heavy quark

We check a commonly used approximation in which a baryon with a heavy quark is described as a heavy quark–light diquark system. The heavy quark influences the diquark internal motion reducing the average distance between the two light quarks. Besides, we show how the average distance between the heavy quark and any of the light quarks, and that between the heavy quark and the center of mass of the light diquark, are smaller than the distance between the two light quarks, which seems to contradict the heavy quark–light diquark picture. This latter result is in agreement with expectations from QCD sum rules and lattice QCD calculations. Our results also show that the diquark approximations produces larger masses than the ones obtained in a full calculation.     

A QCD Sum Rule Approach with an Explicit Di-quark Field

We introduce a phenomenological QCD sum rule with an explicit diquark field. We investigate certain configurations of hadrons are expected to have a good diquark structure. The parameters of the model are a diquark mass ${(m_\phi)}$ and condensate ${(\langle \phi^2\rangle)}$ . Assuming that Λ baryons can be represented by a diquark and a spectator quark configuration, we find the sum rule works well for Λ, Λ _c , and Λ _b . We also find a duality relation between the mass and the condensate for which the parameter sets give good Borel curves. To maintain good Borel curve, a smaller diquark condensate is needed for an increased diquark mass. Using these parameter sets, we test the diquark structure in some hadrons which contain both good and bad diquark configurations.     

Nuclear and hadronic reaction mechanisms producing spin asymmetry

We briefly review concept of the quark recombination (QRC) model and a general success of the model. To solve the existing problem, so called anomalous spin observables, in the high energy hyperon spin phenomena, we propose a mechanism; the primarily produced quarks, which are predominantly u and d quarks, act as the leading partons to form the hyperons. Extension of the quark recombination concept with this mechanism is successful in providing a good account of the anomalous spin observables. Another kind of anomaly, the non-zero analysing power and spin depolarization in the Λ hyperon productions, are also discussed and well understood by the presently proposed mechanism. Recently, a further difficulty was observed in an exclusive ΛK ⁺ p production and wel will indicate a possible diagram for resolving it.     

SU (2N f) ⊗ O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as m_q → ∞. Our discussion involves s-wave to s-wave as well as s-wave to p-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying SU (2N_f) ? O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.