Diquark Channel Research Articles

Diquark properties from full QCD lattice simulations

We study diquarks on the lattice in the background of a static quark, in a gauge-invariant formalism with quark masses down to almost physical mπ. We determine mass differences between diquark channels as well as diquark-quark mass differences. The lightest and next-to-lightest diquarks have “good” scalar, {overline{3}}_F , {overline{3}}_c , JP = 0+, and “bad” axial vector, 6F, {overline{3}}_c , JP = 1+, quantum numbers, and a bad-good mass difference for ud flavors, 198(4) MeV, in excellent agreement with phenomenological determinations. Quark-quark attraction is found only in the “good” diquark channel. We extract a corresponding diquark size of ∼ 0.6 fm and perform a first exploration of the “good” diquark shape, which is shown to be spherical. Our results provide quantitative support for modeling the low-lying baryon spectrum using good light diquark effective degrees of freedom.

Quark-nuclear hybrid equation of state for neutron stars under modern observational constraints

We study a family of equations of state for hybrid neutron star matter. The hybrid EOS are obtained by a Maxwell construction of the first-order phase transition between a hadronic phase described by the relativistic density-functional EOS of the "DD2" class with excluded volume effects and a deconfined quark matter phase modeled by an instantaneous nonlocal version of the Nambu-Jona-Lasinio model in SU(2)$_f$ with vector interactions and color superconductivity. The form factor in the nonlocal quark matter model is fitted to lattice QCD results in the Coulomb gauge. Owing to strong coupling in the vector meson and diquark channels, a coexistence phase of color superconductivity and chiral symmetry breaking occurs. Our results show an approximately constant behavior for the squared speed of sound with values of 0.4 - 0.6 in the density region relevant for neutron star interiors. To simultaneously fulfill the constraints from the Neutron Star Interior Composition Explorer radius measurement for PSR J0740+6620 and tidal deformability from GW170817 it is necessary to consider a $\mu$-dependent bag pressure that mimics confinement.

Early deconfinement of asymptotically conformal color-superconducting quark matter in neutron stars

We present a relativistic density functional approach to color superconducting quark matter that mimics quark confinement by a fast growth of the quasiparticle selfenergy in the confining region. The approach is shown to be equivalent to a chiral model of quark matter with medium dependent couplings. While the (pseudo)scalar sector of the model is fitted to the vacuum phenomenology of quantum chromodynamics, the strength of interaction in the vector and diquark channels is varied in order to provide the best agreement with the observational constraints on the mass-radius relation and tidal deformability of neutron stars modelled with our approach. In order to recover the conformal behavior of quark matter at asymptotically high densities we introduce a medium dependence of the vector and diquark couplings motivated by the non-perturbative gluon exchange. Our analysis signals that the onset of deconfinement to color superconducting quark matter is likely to occur in neutron stars with masses below 1.0 M⊙.

Diquark bound states with a completely crossed ladder truncation

The Bethe-Salpeter equation in the diquark channel is investigated by employing the Dyson-Schwinger method together with the Munczek-Nemirovsky model. The novelty of our study is a resummation of completely crossed ladder diagrams in the Bethe-Salpeter kernel. These diagrams are enhanced due to their color factors in the diquark channel, but not in the meson channel. In our analysis, diquark bound-state solutions exist in the Bethe-Salpeter equation.

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.

Suppression of superconductivity by inhomogeneous chiral condensation in the NJL2 model

We investigate the possibility of spatially inhomogeneous chiral and Cooper, or superconducting, pairing in the (1+1)-dimensional model by Chodos et al. [Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature T and quark number chemical potential μ. In the framework of the Fulde–Ferrel inhomogeneity ansatz for chiral and Cooper condensates, we show that if G1>G2, where G1 and G2 are the coupling constants in the quark–antiquark and diquark channels, then in the (μ, T)-phase diagram the superconducting phase is suppressed by spatially inhomogeneous chiral spiral phase with broken chiral symmetry. In contrast, in the above mentioned original Chodos et al. model, where only the opportunity for homogeneous condensates is taken into account, the superconducting phase is realized at sufficiently high values of μ at arbitrary values of G2>0, including the interval 0<G2<G1.

3 Quark Faddeev Equation in the Nambu-Jona-Lasinio Model

We solve the relativistic Faddeev equation in the Nambu-Jona-Lasinio model numerically in the ladder approximation. The contributions of the scalar and the axial-vector diquark channels to the nucleon state are studied. We calculate the charges and the axial coupling constants of nucleons using Faddeev wave function.

Correlation effects and bound states

Bound states in a simple quark model that are due to correlation effects are analyzed. The confining properties of this model in meson (quark-antiquark and diquark) channels manifest themselves at any quark momenta, and an extra potential field may only enhance the confining effect.

Higher order heavy quark Green’s functions in Coulomb gauge

The Dyson-Schwinger equation for the 4-point quark Green's functions is studied. In the limit of the heavy quark mass and with the truncation to include only the dressed two point functions for the Yang-Mills sector, we provide an exact solution for the 4-point quark Green's functions, in both quark-antiquark and diquark channels, and show that the corresponding poles relate to the bound state energy of the heavy quark systems. Moreover, a natural separation between physical and unphysical poles in the Green's functions emerges.

INFRARED BEHAVIOR OF THE ATTRACTIVE DI-QUARK CHANNEL IN THE QCD MODEL

We examine the behavior of the attractive di-quark (qq) channel in the infrared region. Conventionally it is considered that the qq channel does not cause the fermion condensation in spite of its attractive interaction, because the quark field is dynamically massive due to the quark–antiquark condensation and the decoupling dynamics is applied. In this paper, we are going to reconsider rigorously the infrared behavior of the qq channel with paying attention to the stability of the effective action. And it is revealed that the behavior is not naively decided by the decoupling dynamics.

T-matrix approach to heavy quark diffusion in the QGP

We assess transport properties of heavy quarks in the quark–gluon plasma (QGP) using static heavy-quark (HQ) potentials from lattice-QCD calculations in a Brueckner many-body T-matrix approach to evaluate elastic heavy-quark–light-quark scattering amplitudes. In the attractive meson and diquark channels, resonance states are formed for temperatures up to ∼1.5T c, increasing pertinent drag and diffusion coefficients for heavy-quark rescattering in the QGP beyond the expectations from perturbative-QCD calculations. We use these transport coefficients, complemented with perturbative elastic HQ gluon scattering, in a relativistic Langevin simulation to obtain HQ p t distributions and elliptic flow (v 2) under conditions relevant for the hot and dense medium created in ultrarelativistic heavy-ion collisions. The heavy quarks are hadronized to open-charm and -bottom mesons within a combined quark-coalescence fragmentation scheme. The resulting single-electron spectra from their semileptonic decays are confronted with recent data on “non-photonic electrons” in 200 A GeV Au–Au collisions at the Relativistic Heavy-Ion Collider (RHIC).

Nonperturbative Heavy-Quark Diffusion in the Quark-Gluon Plasma

We evaluate heavy-quark (HQ) transport properties in a quark-gluon plasma (QGP) within a Brueckner many-body scheme employing interaction potentials extracted from thermal lattice QCD. The in-medium T matrices for elastic charm- and bottom-quark scattering off light quarks in the QGP are dominated by attractive meson and diquark channels which support resonance states up to temperatures of ~1.5T(c). The resulting drag coefficient increases with decreasing temperature, contrary to expectations based on perturbative QCD scattering. Employing relativistic Langevin simulations we compute HQ spectra and elliptic flow in sqrt[s(NN)]=200 GeV Au-Au collisions. A good agreement with electron decay data supports our nonperturbative computation of HQ diffusion, indicative for a strongly coupled QGP.

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>μc≈ 330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μc). 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>μc.

Transversity quark distributions in a covariant quark–diquark model

Transversity quark light-cone momentum distributions are calculated for the nucleon. We utilize a modified Nambu–Jona-Lasinio model in which confinement is simulated by eliminating unphysical thresholds for nucleon decay into quarks. The nucleon bound state is obtained by solving the relativistic Faddeev equation in the quark–diquark approximation, where both scalar and axial-vector diquark channels are included. Particular attention is paid to comparing our results with the recent experimental extraction of the transversity distributions by Anselmino et al. We also compare our transversity results with earlier spin-independent and helicity quark distributions calculated in the same approach.

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 Vacuum in a 3DTwo-Flavor Gross– Neveu Model

The effective potential analysis indicates that, in a 3Dtwo-flavor Gross–Neveu model in vacuum, depending on whetherGS/HP is less or bigger than the critical value 2/3, where GS andHP are respectively the coupling constants of scalarquark-antiquark channel and pseudoscalar diquark channel, thesystem will have the ground state with pure diquark condensates orwith pure quark-antiquark condensates, but never withcoexistence of the two forms of condensates. The similarities anddifferences in the interplay between the quark-antiquark and thediquark condensates in vacuum in the 2D, 3D and 4D two-flavorfour-fermion interaction models are summarized.

Phase Structure of Color Superconductivity and Chiral Restoration

We investigate color superconductivity and chiral symmetry restoration at finite temperature and baryon density in the frame of standard two flavor Nambu–Jona-Lasinio model. We derive the diquark mass in RPA, discuss its constraint on the coupling constant in the diquark channel, and find a strong competition between the two phase transitions when the coupling constant is large enough.

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.