Following our recenty proposed self-consistent mean-field approximation approach, we have done some researches on the chiral phase transition of strong interaction matter within the framework of Nambu-Jona-Lasinio (NJL) model. The chiral susceptibility and equation of state (EOS) are computed in this work for both two-flavor and three-flavor quark matter for contrast. The Pauli-Villars scheme, which can preserve gauge invariance, is used in this paper. Moreover, whether the three-flavor quark matter is more stable than the two-flavor quark matter or not in quark stars is discussed in this work. In our model, when the bag constant are the same, the two-flavor quark matter has a higher pressure than the three-flavor quark matter, which is different from what Witten proposed in his pioneering work.
We study hidden-flavor pentaquarks, $Q\bar Q qqq$, based on a constituent quark-model with a standard quark-quark interaction that reproduces the low-energy meson and baryon spectra. We make use of dynamical correlations between the heavy quarks arising from the Coulomb-like nature of the short-range interaction. A detailed comparison is made with other results in the literature and with experimental data. Our results show a different pattern for open-flavor and hidden-flavor pentaquarks, as suggested by the data. Further implications about the existence of quarkonia bound to nuclei are discus…
A flavor dependent kernel is constructed based on the rainbow-ladder truncation of the Dyson-Schwinger and Bethe-Salpeter equation approach of Quantum Chromodynamics. The quark-antiquark interaction is composed of a flavor dependent infrared part and a flavor independent ultraviolet part. Our model gives a successful and unified description of the light, heavy and heavy-light ground pseudoscalar and vector mesons. For the first time, our model shows that the infrared enhanced quark-antiquark interaction is stronger and wider for the lighter quark.
It is shown that spin polarization with respect to each flavor in three-flavor quark matter occurs instead of the color-flavor locking at high baryon density by using the Nambu-Jona-Lasinio model with four-point tensor-type interaction. Also, it is indicated that the order of phase transition between the color-flavor locked phase and the spin polarized phase is the first order by means of the second order perturbation theory.
We have computed shear viscosity coefficient for hot and dense QCD matter within Polyakov loop extended quark meson(PQM) model for three flavors. Viscosity coefficient is estimated using Boltzmann equation within the relaxation time approximation. Relaxation times for quarks are calculated from elastic scattering of quarks and antiquarks via gluon exchange. Also the mean free paths of strange and light quarks are estimated for this cases. The calculations are performed at finite chemical potential. Thermodynamic properties like energy, pressure, entropy densities are also computed and compared…
We show that the chiral $SU(n)\otimes SU(n)$ flavor symmetry on the null-plane severely restricts the sea quarks in the baryon octet. It predicts large asymmetry for the light sea quarks $(u,d,s)$, and universality and abundance for the heavy sea quarks. Further it is shown that existence of the heavy sea quarks constrained by the same symmetry reduces the theoretical value of the Ellis-Jaffe sum rule substantially.
The possible formation of tensor condensates originated from a tensor-type interaction between quarks is investigated in the three-flavor Nambu-Jona-Lasinio model including the Kobayashi-Maskawa-'t Hooft interaction, which leads to flavor mixing. It is shown that independent two tensor condensates appear and a tensor condensate related to the strange quark easily occurs by the effect of the flavor mixing compared with one related to light quarks. Also, it is shown that the tensor condensate related to the strange quark appears at a slightly smaller chemical potential if the Kobayashi-Maskawa-'…
This study is performed with the aim of gaining insights into the possible applicability of the quark-hadron continuity concept, not only in the idealized case of three-flavor symmetric quark matter, but also for the transition from neutron matter to two-flavor quark matter. A key issue is the continuity between neutron superfluidity and a corresponding superfluid quark phase produced by $d$-quark pairing. Symmetry arguments are developed and relevant dynamical mechanisms are analyzed. It is pointed out that the $^3P_2$ superfluidity in dense neutron matter has a direct analogue in the $^3P_2$…
The phase diagram of strongly interacting matter at non-zero temperature and baryon chemical potential is calculated within a 3-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. …
New relations between the quark spin-flavor contents of the nucleon and axial weak coupling constants are obtained in the chiral quark model with both SU(3) and U(1)-breaking effects. Using the nonsinglet spin combinations, $Δ_3$ and $Δ_8$, all spin-flavor observables are functions of only one parameter $a$ $-$ probability for the chiral pionic fluctuation. The upper and lower bounds of these observables are given. The optimal range of $a$, determined by NMC data $\bar d-\bar u$, gives a constraint to the cutoff of the chiral quark field theory. The model predictions are in good agreement with…
We show that the chiral $SU(n)\otimes SU(n)$ flavor symmetry on the null-plane severely restricts the sea quarks in the baryon octet. It predicts large asymmetry for the light sea quarks $(u,d,s)$, and universality and abundance for the heavy sea quarks. Further it is shown that existence of the heavy sea quarks constrained by the same symmetry reduces the theoretical value of the Ellis-Jaffe sum rule substantially.
The single-flavor excluded-volume model based on the effective size of baryons reproduces the hard-soft density evolution of the equation of state (EoS) required by the recent studies of GW170817. This phenomenological model basically realizes the concept of quarkyonic matter which is introduced from large-$N_{c}$ gauge theory for dense matter. Enhanced nucleon interactions and dynamically generated quark degrees of freedom can reproduce the hard-soft evolution of the EoS. In this paper, we extend the excluded-volume model to a three-flavor system by considering electromagnetic charge and poss…
We summarize and discuss some of the experimental and theoretical results on heavy flavor, quarkonia, and electro-weak probes presented at Quark Matter 2012.
A new Monte Carlo model of jet quenching in nuclear collisions, CUJET1.0, is applied to predict the jet flavor dependence of the nuclear modification factor for fragments {\it $f=π,D,B,e^-$} from quenched jet flavors {\it $g,u,c,b$} in central collisions at RHIC and LHC. The nuclear modification factors for different flavors are predicted to exhibit a novel level crossing pattern over a transverse momentum range $5< p_T< 100$ GeV which can test jet-medium dynamics in quark gluon plasmas.
We study the hierarchy of the coefficients in the 1/Nc expansion for the negative parity L=1 excited baryons from the perspective of the constituent quark model. This is related to the problem of determining the spin-flavor structure of the quark interaction. The most general two-body scalar interaction between quarks contains the spin-flavor structures $t_1^a t_2^a, \vec s_1\cdot \vec s_2$ and $ \vec s_1\cdot \vec s_2 t_1^a t_2^a$. We show that in the limit of a zero range interaction all these structures are matched onto the same hadronic mass operator $S_c^2$, which gives a possible explana…
The role of the strange quark mass for the phase structure of QCD at non-vanishing densities is studied by employing a recently developed self-consistent truncation scheme for the Dyson-Schwinger equations of the quark propagators in Landau gauge. Hereby the medium modification of the effective quark interaction by the polarization of gluons is implemented. Taking into account this effect results in significantly smaller dynamical quark masses at the Fermi surface. Due to this reduction the color-flavor locked phase is always the preferred color-superconducting phase at zero temperature and fo…
The phase diagram at finite temperature and density is investigated in the framework of the Polyakov linear sigma model (PLSM) with three light quark flavors in the mean field approximation. It is found that in the PLSM, the three phase transitions, i.e, the chiral restoration of $u,d$ quarks, the chiral restoration of $s$ quark, and the deconfinement phase transition are independent. There exists two-flavor quarkyonic phase at low density and three-flavor quarkyonic phase at high density. The critical end point (CEP) which separating the crossover from the first-order line in the PLSM model i…
We investigate the symmetry property and the stability of dibaryons containing two strange quarks and one heavy flavor with $I=\frac{1}{2}$. We construct the wave function of the dibaryon in two ways. First, we directly construct the color and spin state of the dibaryon starting from the four possible SU(3) flavor state. Second, we consider the states composed of five light quarks, and then construct the wave function of the dibaryon by adding one heavy quark. The stability of the dibaryon against the strong decay into two baryons is discussed by using variational method in a constituent quark…
We match the non-relativistic quark model, with both flavor dependent and flavor independent effective quark-quark interactions, to the spin-flavor operator basis of the 1/Nc expansion for the L=1 non-strange baryons. We obtain analytic expressions for the coefficients of the 1/Nc operators in terms of radial integrals that depend on the shape and relative strength of the spin-spin, spin-orbit and tensor interactions of the model, which are left unspecified. We obtain several new, parameter-free relations between the seven masses and the two mixing angles that can discriminate between differen…
We investigate the unpolarized pion and kaon fragmentation functions, employing the nonlocal chiral-quark model, which manifests the nonlocal interactions between the quarks and pseudoscalar mesons, considering the explicit flavor-SU(3)-symmetry breaking in terms of the current-quark masses. Moreover, we study the quark-distribution functions, derived from the fragmentation ones with the Drell-Yan-Levi relation. Numerical results are evaluated to higher Q^2 by the DGLAP evolution and compared with the empirical data. The ratios between the relevant valance quark-distribution functions are also…
Electric and color neutral solutions, and the critical conditions for the formation of gapless color superconductors, are investigated in $K^0$ condensed color-flavor locked quark matter for nonzero strange quark mass. We show that as the strange quark mass increases, gapless modes for up-strange quark pairing occur first, followed by down-strange quark pairing. The behavior of the gaps, the dispersion relations, and the thermodynamic potential are all found as functions of the strange quark mass on the basis of a Nambu Jona-Lasinio type model. To a high degree of accuracy, they are presented …
The structure of the phase diagram of strongly interacting matter at moderate densities is calculated within a 3-flavor NJL-type quark model with realistic quark masses. We focus on the influence of the selfconsistently determined effective strange quark mass on the color-flavor unlocking phase transition.
By using the soft pion theorem in the inclusive reactions, soft pions' contribution to the structure function $F_2$ in the nucleon is estimated. It is shown that this contribution produces such a large flavor asymmetry in the light sea quark distributions that it gives about $30\sim 50 %$ of the NMC deficit in the Gottfried sum.
We investigate the symmetry property and construct the wave function of the dibaryon states containing two strange quarks with S=0 in both the flavor SU(3) symmetric and breaking cases. We discuss how the color $\otimes$ isospin $\otimes$ spin states of dibaryon in the symmetry broking case of flavor SU(3) can be extracted from the fully antisymmetric states in flavor SU(3). The stability of the dibaryon against the strong decay into two baryons are then discussed, by using the variational method within a constituent quark model with a confining and color-spin interactions. To compare our resu…
In $\XQM$, a quark can emit Goldstone bosons. The flavor symmetry breaking in the Goldstone boson emission process is used to intepret the nucleon flavor-spin structure. In this paper, we study the inner structure of constituent quarks implied in $\XQM$ caused by the Goldstone boson emission process in nucleon. From a simplified model Hamiltonian derived from $\XQM$, the intrinsic wave functions of constituent quarks are determined. Then the obtained transition probabilities of the emission of Goldstone boson from a quark can give a reasonable interpretation to the flavor symmetry breaking in …
We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
Because the properties of the QCD phase transition and the chiral magnetic effect (CME) depend on the number of quark flavors ($N_{f}$) and quark mass, relativistic heavy-ion collisions provide a natural environment to investigate the flavor features if quark deconfinement occurs. We introduce an initial two-flavor or three-flavor dipole charge separation into a multiphase transport (AMPT) model to investigate the flavor dependence of the CME. By taking advantage of the recent ALICE data of charge azimuthal correlations with identified hadrons, we attempt to disentangle two-flavor and three-fl…
Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. $CP$ violation is maximal in this sense.
It is shown that extremely strong electric fields may be generated at the surface of strange quark matter in the color-flavor locked phase because of the surface effects. Some properties of strange stars made of this matter are briefly discussed.
Considering the density dependence of quark mass, we investigate the phase transition between the (unpaired) strange quark matter and the color-flavor-locked matter, which are supposed to be two candidates for the ground state of strongly interacting matter. We find that if the current mass of strange quark $m_s$ is small, the strange quark matter remains stable unless the baryon density is very high. If $m_s$ is large, the phase transition from the strange quark matter to the color-flavor-locked matter in particular to its gapless phase is found to be different from the results predicted by p…
Enforcing color and electric charge neutrality conditions on the three-flavor color superconducting matter, I derive the explicit form of the quark propagators and the gluon self-energies for the gapless and the ordinary color-flavor-locked phases.
Heavy-quark interactions in the Quark-Gluon Plasma are analyzed in terms of a selfconsistent Brueckner scheme using a thermodynamic $T$-matrix based on a potential model. The interrelations between quarkonium correlators, spectral functions and zero-modes, and open heavy-flavor transport and susceptibilities are elaborated. Independent constraints from thermal lattice QCD can be used to improve predictions for heavy-quark phenomenology in heavy-ion collisions.
The democracy of quark flavors is a well-motivated flavor symmetry, but it must be properly broken in order to explain the observed quark mass spectrum and flavor mixing pattern. We reconstruct the texture of flavor democracy breaking and evaluate its strength in a novel way, by assuming a parallelism between the Q=+2/3 and Q=-1/3 quark sectors and using a nontrivial parametrization of the flavor mixing matrix. Some phenomenological implications of such democratic quark mass matrices, including their variations in the hierarchy basis and their evolution from the electroweak scale to a superhig…
Some aspects of heavy flavor probes of quark-gluon plasma (QGP) including quarkonia and open heavy flavor D- and B-mesons, aimed to study the properties of QGP, are discussed in this lecture note.
Considering the density dependence of quark masses, we investigate the color-flavor-locked matter and its stability relative to the ( unpaired ) strange quark matter. We find that, when the current mass of strange quark $m_s$ is small, the strange quark matter remains stable for the moderate baryon densities. When $m_s$ is large, the gapless phase of the color-flavor-locked matter is found to be difficult to be stable. A schematic phase diagram of three-flavor quark matter is presented, in which the color-flavor-locked phase region is suppressed in comparison with the previous results.
We suggest a scenario where the three light quark flavors are sequentially deconfined under increasing pressure in cold asymmetric nuclear matter as found, e.g., in neutron stars. The basis for our analysis is a chiral quark matter model of Nambu--Jona-Lasinio (NJL) type with diquark pairing in the spin-1 single flavor (CSL), spin-0 two flavor (2SC) and three flavor (CFL) channels. We find that nucleon dissociation sets in at about the saturation density, n_0, when the down-quark Fermi sea is populated (d-quark dripline) due to the flavor asymmetry induced by beta-equilibrium and charge neutra…
The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This review article is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.
We have studied the lepton and quark mixing patterns which can be derived from the dihedral group $D_n$ in combination with CP symmetry. The left-handed lepton and quark doublets are assigned to the direct sum of a singlet and a doublet of $D_n$. A unified description of the observed structure of the quark and lepton mixing can be achieved if the flavor group $D_n$ and CP are broken to $Z_2\times CP$ in neutrino, charged lepton, up quark and down quark sectors, and the minimal group is $D_{14}$. We also consider another scenario in which the residual symmetry of the charged lepton and up quark…
We study the quark-hadron phase transition by using a three flavor Nambu-Jona-Lasinio model with the Polyakov loop at zero chemical potential, extending our previous work with two flavor model. We show that the equation of state at low temperatures is dominated by pions and kaons as collective modes of quarks and anti-quarks. As temperature increases, mesonic collective modes melt into the continuum of quark and anti-quark so that hadronic phase changes continuously to the quark phase where quark excitations dominate pressure.
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is best suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
Aspects of the quark mixings and flavor changing interactions are investigated in electroweak models with singlet quarks. The effects on the ordinary quark mixing are determined in terms of the quark masses and the parameters describing the mixing between the ordinary quarks q and the singlet quarks Q (q-Q mixing). Some salient features arise in the flavor changing interactions through the q-Q mixing. The unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix within the ordinary quark sector is violated, and the flavor changing neutral currents (FCNC's) appear both in the gauge and scalar cou…
A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a homological flat structure for up-type quarks, down-type quarks, charged leptons and Dirac neutrinos. A $SO(2)_{LR}^f$ flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated CKM mixing for quarks and PMNS for leptons. Since the minimal flavor structure successfully addresses CKM and PMNS even in the mass hierarchy limit, mass hierarchy and flavor mixing are two indep…
I discuss briefly the instabilities of two flavor quark matter, paying attention to the gradient instability which develops in the g2SC phase in the Goldstone $U(1)_A$ sector.
We study a spin-1 single flavor color superconducting phase which results from a color-spin locking (CSL) interaction in two-flavor quark matter. This phase is particularly interesting for compact star cooling applications since the CSL phase may survive under charge neutrality constraints implying a mismatch between up- and down-quark chemical potentials which can destroy the scalar diquark condensate. CSL gaps are evaluated within an NJL model and they are found to be consistent with cooling phenomenology if a density dependent coupling constant is used.
An overview is given of the theoretical developments on heavy quarks and quarkonia in heavy-ion collisions as reported at the "Hard and EM Probes 2018" conference. Specifically, we address progress in the understanding of heavy-flavor diffusion and its hadronization, quarkonium transport and the extraction of quarkonium melting temperatures, energy loss of heavy quarks at high momentum, and their rescattering in small colliding systems.
Near the flavor SU(3) limit, we propose an analytical description for color-flavor-locked-type Bardeen-Cooper-Schrieffer (BCS) phase in the Nambu Jona-Lasinio (NJL) model. The diquark behaviors in light-flavor and strange-flavor-involved channels and Bose-Einstein condensation (BEC) of bound diquark states are studied. When the attractive interaction between quarks is strong enough, a BCS-BEC crossover is predicted in the environment with color-flavor-locked pairing pattern. The resulting Bose-Einstein condensed phase is found to be an intergrade phase before the emergence of the previous-pred…
Within Ginzburg-Landau theory, we study the structure of a magnetic vortex in color-flavor locked quark matter. This vortex is characterized by winding of the SU(3) phase in color-flavor space, as well as by the presence of a color-flavor unlocked condensate in the core. We estimate the upper and lower critical fields and the critical Ginzburg-Landau parameter that distinguishes between type I and type II superconductors.
The Taylor coefficients of flavor diagonal and off-diagonal susceptibilities as well as baryon number, isovector and electric charge susceptibilities are considered within a phenomenological quasiparticle model of the quark-gluon plasma and successfully compared with lattice QCD data for two degenerate quark flavors. These susceptibility coefficients represent sensible probes of baryon density effects in the equation of state. The baryon charge is carried, in our model, by quark-quasiparticle excitations for hard momenta.
Taking the vector kaon-quark interaction into account, we reexamine in detail the neutral kaon condensation in color-flavor locked quark matter. It is found that the pairing phenomena in the quark matter are somewhat influenced by $K^0$ condensation. Different from the previous predictions, we find that the $K^0$ condensed phase might no longer be more stable than the normal phase even if $K^0$ condensation can occur in the color-flavor locked matter.
By means of the functional integral method we show that in the case of the quark-antiquark pairing at zero temperature and zero chemical potential (in the vacuum) the singlet pairing is more preferable than that with the color-flavor locking (CFL)
We present an exact method based on a hyperspherical harmonic expansion to study systems made of quarks and antiquarks of the same flavor. Our formalism reproduces and improves the results obtained with variational approaches. This analysis shows that identical-flavor four-quark systems with non-exotic $2^{++}$ quantum numbers may be bound independently of the quark mass. $0^{+-}$ and $1^{+-}$ states become attractive only for larger quarks masses.
Using DGLAP evolution equation with the corrections of parton recombinations, the flavor asymmetric sea quark distributions in the proton are first extracted from the available experimental data with the global QCD analysis method. Comparisons of our predictions to the CTEQ, MRS, and GRV parton distribution functions for sea quarks are presented. Based on the separation of the flavor symmetric and asymmetric sea, the possible relations between strange quark distribution and symmetric light quark distribution are discussed. The results are used to explain the recent HERMES result of the strange…
Sea quark contents of the octet baryons are investigated by employing an extended chiral constituent quark approach, which embodies higher Fock five-quark components in the baryons wave-functions. The well-known flavor asymmetry of the nucleon sea $\bar{d}-\bar{u}$, is used as input to predict the probabilities of $\bar{u}$, $\bar{d}$ and $\bar{s}$ in the nucleon, $Λ$, $Σ$ and $Ξ$ baryons, due to the intrinsic five-quark components in the baryons wave functions.
A phenomenological ansatz for the flavor-asymmetry of the light sea distributions of the nucleon, based on the Pauli exclusion principle, is proposed. This ansatz is compatible with the measured flavor-asymmetry of the unpolarized sea distributions, $\bar{d}>\bar{u}$, of the nucleon. A prediction for the corresponding polarized flavor-asymmetry is presented and shown to agree with predictions of (chiral quark--soliton) models which successfully reproduced the flavor-asymmetry of the unpolarized sea.
The quark flavor distribution functions of the octet baryons ($N$, $Σ$, $Ξ$ and $Λ$) have been calculated in the chiral constituent quark model ($χ$CQM). In particular, the valence and sea quark flavor distribution functions of the scalar density matrix elements of octet baryons have been computed explicitly. The implications of chiral symmetry breaking and SU(3) symmetry breaking have been discussed in detail for the sea quark asymmetries, fraction of a particular quark (antiquark) present in a baryon, flavor structure functions and the Gottfried integral. The meson-baryon sigma terms $σ_{πB}…
