Scalar Diquark Channel Research Articles

Generalized Beth–Uhlenbeck approach to mesons and diquarks in hot, dense quark matter

An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the Gaussian approximation for the meson and diquark fields and it is given in the Beth–Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson–diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by π in accordance with Levinson’s theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth–Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.

Diquark correlations in baryons on the lattice with overlap quarks

We evaluate baryon wave functions in both the Coulomb and Landau gauges in lattice QCD. These are constructed from quark propagators calculated with the overlap Dirac operator on quenched gauge configurations at $\ensuremath{\beta}=6$. By comparing baryon states that differ in their diquark content, we find evidence for enhanced correlation in the scalar diquark channel, as favored by quark models. We also summarize earlier results for diquark masses in the Landau gauge, casting them in a form more easily compared with subsequent studies.

Phase diagram of quark matter in nonlocal chiral models under color and electric charge neutrality conditions

We consider the phase diagram of two-flavor quark matter under neutron star constraints for the case of two nonlocal, covariant quark models within the mean field approximation. In one of these models (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap, and the corresponding critical temperature at µ = 0, Tc(0) ~ 140 MeV, is in better agreement with recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both models we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a superconducting quark matter (2SC) phase and a mixed 2SC-NQM phase. In most cases, a narrow gapless 2SC phase region is also obtained at finite temperatures.

Relativistic quark matter in light front field theory

We consider correlations in hot and dense quark matter within the framework of light front quantization. We have computed the masses of two-body boundstates M 2 ( T , μ ) in the pionic and scalar diquark channel using a T -matrix approach. The quark interaction is given by a NJL model. The gap equation is generalized to finite temperature T and quark chemical potential μ and we determine the medium dependent quark mass. Further we calculate the critical temperature of two flavor color superconductivity.

Quark-Antiquark and Diquark Condensates in Vacuumin a 2D Two-Flavor Gross–Neveu Model

The analysis based on the renormalized effective potentialindicates that, similar to in the 4D two-flavor Nambu–Jona-Lasinio(NJL) model, in a 2D two-flavor Gross–Neveu model, the interplaybetween the quark-antiquark and the diquark condensates in vacuumalso depends on GS/HS, the ratio of the coupling constants inscalar quark-antiquark and scalar diquark channel. Only the purequark-antiquark condensates exist if GS/HS>2/3, which is justthe ratio of the color numbers of the quarks participating in thediquark and quark-antiquark condensates. The two condensates willcoexist if 0<GS/HS<2/3. However, different from the 4D NJLmodel, the pure diquark condensates arise only at GS/HS = 0 andare not in a possibly finite region of GS/HS below 2/3.

Phase diagram of neutral quark matter in nonlocal chiral quark models

We consider the phase diagram of two-flavor quark matter under neutron star constraints for two nonlocal, covariant quark models within the mean-field approximation. In the first case (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap and a chiral symmetry breaking (CSB) phase transition line which extends 15--20% further into the phase diagram spanned by temperature ($T$) and chemical potential ($\ensuremath{\mu}$). The corresponding critical temperature at $\ensuremath{\mu}=0$, ${T}_{c}(0)\ensuremath{\simeq}140\text{ }\text{ }\mathrm{MeV}$, is in better accordance to recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both Model I and Model II we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a two-flavor superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in most cases there is also a gapless 2SC phase, this occurs in general in a small region at nonzero temperatures, thus its effect should be negligible for compact star applications.

INSTANTON-INDUCED CORRELATIONS IN HADRONS

QCD instantons generate non-perturbative spin- and flavor- dependent correlations between light quarks. We report on the results of a series of studies on the contribution of instantons to the electro-weak structure of light hadrons. We show that the Instanton Liquid Model can reproduce the available data on proton and pion form factors at large momentum transfer, and explain the delay of the onset of the perturbative regime in some exclusive reactions. We provide unambiguous evidence that instantons lead to the formation of a deeply bound scalar, color anti-triplet diquark, with a mass of about 450 MeV. The strong attraction in the [Formula: see text], scalar diquark channel leads to a quantitative description of non-leptonic decays of hyperons and provides a microscopic dynamical explanation of the Δ I = 1/2 rule.

STRUCTURE FUNCTIONS OF THE NUCLEON IN THE QUARK–DIQUARK MODEL AND EXTENSION TO FINITE DENSITY

In this work we use a simple approximation to the relativistic Faddeev description of the nucleon in the framework of the Nambu-Jona-Lasinio (NJL) model. We discuss the flavor dependence of valence quark light-cone momentum distributions, and by comparing with the empirical informations we extract information on the strength of the axial vector diquark correlations. As an extension to finite density, we also discuss the EMC effect in nuclear matter, keeping only the scalar diquark channel in the wave function.

High-Density QCD and Instantons

Instantons generate strong nonperturbative interactions between quarks. In vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300–400MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as ∼100MeV. We provide a systematic treatment of color superconductivity in the instanton model. We show that the structure of the superconductor depends on the number of flavors. In the case of two flavors, we verify the standard scenario, and provide an improved calculation of the mass gap. For three flavors, we show that the ground state is color–flavor locked and calculate the chiral condensate in the high-density phase. We show that as a function of the strange quark mass, there is a sharp transition between the two phases. Finally, we go beyond the mean-field approximation and investigate the role of instanton/anti-instanton molecules, which—in addition to superconducting gap formation—provide a competitive mechanism for chiral restoration at finite density.

Baryons in the NJL model as solutions of the relativistic Faddeev equation

Abstract The relativistic Faddeev equation for three quarks is solved in the SU(2) f × SU(3) c NJL model to get the nucleon and delta states. We truncate the interacting two-body channels to the scalar and axial vector diquark channels, which are expected to be dominant from the non-relativistic analogy. We find that both channels contribute attractively to the nucleon as well as the delta state, and that the principal mechanism for the mass spitting between the nucleon and the delta in this picture is the interaction in the scalar diquark channel, which is not present in the delta state. We show the dependences of the masses of the nucleon and the delta on the specific form of the interaction lagrangian, and derive restrictions on the possible forms of four-fermi interactions.

Faddeev approach to the nucleon in the Nambu-Jona-Lasinio (NJL) model

The nucleon is studied in the NJL model using the Faddeev equation truncated to the scalar diquark channel. We solve the relativistic Faddeev equation numerically, and compare the results with the static approximation. It is shown that in the original NJL model the coupling constant in the scalar diquark channel is too weak to form a bound state. In order to get about the right nucleon mass, this coupling constant should be about 2 3 of that in the pionic q q ̄ channel.