The symmetry energy characterizes the isospin dependent part of the equation of state of isospin asymmetric strong interaction matter and it plays a critical role in many issues of nuclear physics and astrophysics. In this talk, we briefly review the current status on the determination of the symmetry energy in nucleon (nuclear) and quark matter. For nuclear matter, while the subsaturation density behaviors of the symmetry energy are relatively well-determined and significant progress has been made on the symmetry energy around saturation density, the determination of the suprasaturation density behaviors of the symmetry energy remains a big challenge. For quark matter, which is expected to appear in dense matter at high baryon densities, we briefly review the recent work about the effects of quark matter symmetry energy on the properties of quark stars and the implication of possible existence of heavy quark stars on quark matter symmetry energy. The results indicate that the $u$ and $d$ quarks could feel very different interactions in isospin asymmetric quark matter, which may have important implications on the isospin effects of partonic dynamics in relativistic heavy-ion collisions.
The existence of the five-quark Fock states for the intrinsic charm quark in the nucleons was suggested some time ago, but conclusive evidence is still lacking. We generalize the previous theoretical approach to the light-quark sector and study possible experimental signatures for such five-quark states. In particular, we compare the $\bar d - \bar u$ and $\bar u + \bar d - s -\bar s$ data with the calculations based on the five-quark Fock states. The qualitative agreement between the data and the calculations is interpreted as evidence for the existence of the intrinsic light-quark sea in the…
We generalize the approach of Brodsky {\it et al.} for the intrinsic charm quark distribution in the nucleons to the light-quark sector involving intrinsic $\bar u, \bar d, s$ and $\bar s$ sea quarks. We compare the calculations with the existing $\bar d - \bar u$, $s + \bar s$, and $\bar u + \bar d - s -\bar s$ data. The good agreement between the theory and the data is interpreted as evidence for the existence of the intrinsic light-quark sea in the nucleons. The probabilities for the $|uudu\bar{u}>$, $|uudd\bar{d}>$ and $|uuds\bar{s}>$ Fock states are also extracted.
This article reviews our current understanding of how the internal quark structure of a nucleon bound in nuclei differs from that of a free nucleon. We focus on the interpretation of measurements of the EMC effect for valence quarks, a reduction in the Deep Inelastic Scattering (DIS) cross-section ratios for nuclei relative to deuterium, and its possible connection to nucleon-nucleon Short-Range Correlations (SRC) in nuclei. Our review and new analysis (involving the amplitudes of non-nucleonic configurations in the nucleus) of the available experimental and theoretical evidence shows that the…
We present a field theoretical description of quarkyonic matter consisting of quark, nucleon and ghost fields coupling to mesonic degrees of freedom. The ghosts are present to cancel over-counting of nucleon states that are Pauli blocked by the quark Fermi sea. Such a theory becomes an effective field theory of nucleons at low baryon density, and as such will reproduce nucleonic matter phenomenology. This theory can accommodate chiral symmetry restoration and the dynamical generation of a shell of nucleons at the Fermi surface. It is valid for finite temperature and density. In such a theory, …
We apply the single quark transition model to resonance transition amplitudes extracted from photo-and electroproduction data. We use experimental data on the S11(1535) and D13(1520) nucleon resonances to extract the amplitudes for the electromagnetic transition from the nucleon ground state to the [70,1-] SU(6)xO(3) supermultiplet, and make predictions for the transition amplitudes of all other states associated with the [70,1-]. We find suprisingly good agreement with the data.
I review some recent developments in the study of quark flavor distributions in the nucleon, including (i) valence quark distributions and the quark-hadron duality prediction for the x -> 1 d/u ratio (ii) sea quark asymmetries and electromagnetic form factors (iii) strange quarks in the nucleon.
We explore further applications of the twist-two quark interference fragmentation functions introduced earlier. We show that semi-inclusive production of two pions in the current fragmentation region in deep inelastic scattering of a longitudinally polarized electron on a longitudinally polarized nucleon can provide a probe of the valence quark spin (or helicity difference) distribution in the nucleon.
Semi-inclusive deep inelastic lepton scattering off few-nucleon systems is investigated assuming that virtual boson absorption occurs on a hadronic cluster which can be either a two-nucleon correlated pair or a six-quark bag. In both cases the relevance of nuclear effects on forward and backward nucleon emissions is illustrated and the differences expected in the energy distribution of the emitted nucleons are analyzed both at x>1 and x<1.
We present a model of baryonic matter which contains free constituent quarks in addition to bound constituent quarks in nucleons. In addition to the common linear sigma-model we include the exchange of vector-mesons. The percentage of free quarks increases with baryon density but the nucleons resist a restoration of chiral symmetry.
In this contribution, we discuss the spin and flavor content of the proton in the framework of the unquenched quark model, and address the role of valence and sea quarks in the nucleon.
We propose a new model of the nucleon in which quark-diquark configurations immersed in a pion cloud are treated in a manner consistent with Poincaré invariance. With suitably chosen parameters, the computations employing this model reproduce the measured electromagnetic form factors and the quark-spin contribution to the total nucleon angular momentum.
We consider deeply virtual Compton scattering and deep inelastic scattering in presence of Regge exchanges that are part of the non-perturbative quark-nucleon amplitude. In particular we discuss contribution from the Pomeron exchange and demonstrate how it leads to Regge scaling of the Compton amplitude. Comparison with HERA data is given.
We evaluate the nucleon sigma term and in-medium quark condensate in the modified quark-meson coupling model which features a density-dependent bag constant. We obtain a nucleon sigma term consistent with its empirical value, which requires a significant reduction of the bag constant in the nuclear medium similar to those found in the previous works. The resulting in-medium quark condensate at low densities agrees well with the model independent linear order result. At higher densities, the magnitude of the in-medium quark condensate tends to increase, indicating no tendency toward chiral symm…
We utilize a light-front relativistic quark model (LF RQM) to predict the 3q core contribution to the electroexcitation amplitudes for the Delta(1232)P33, N(1440)P11, N(1520)D13, and N(1535)S11 up to Q2= 12GeV2. The parameters of the model have been specified via description of the nucleon electromagnetic form factors in the approach that combines 3q and pion-cloud contributions in the LF dynamics.
In a model where constituent quarks and diquarks interact through quark exchange the Bethe-Salpeter equation in ladder approximation for the nucleon is solved. Quark and diquark confinement is effectively parametrized by choosing appropriately modified propagators. The coupling to external currents is implemented via nontrivial vertex functions for quarks and diquarks to ensure gauge invariance at the constituent level. Nucleon matrix elements are evaluated in a generalised impulse approximation, and electromagnetic, pionic and axial form factors are calculated.
A dynamical investigation of the nucleon-nucleon (NN) interaction by using the resonating group method (RGM) in a chiral SU(3) quark model has been revisited. The considered quark-quark interaction includes, besides the one-gluon exchange (OGE) and the phenomenological confinement potential, the nonet scalar and pseudoscalar meson exchanges derived from the spontaneous SU(3) chiral symmetry breaking. The physical consistency requirement that the wave functions of single baryons satisfy the minimums of the Hamiltonian has been strictly imposed in determination of the model parameters. The calcu…
We demonstrate that there exist two kinds of gauge-invariant decompositions of the nucleon spin, which are physically inequivalent. The quark and gluon orbital angular momenta (OAMs) appearing in one decomposition are basically the canonical OAMs, while the quark and gluon OAMs appearing in another decomposition are called the dynamical OAMs. It is shown that the dynamical OAMs of quarks and gluons in the nucleon can be related to definite high-energy deep-inelastic-scattering observables. On the other hand, we conjecture that the canonical OAMs of quarks and gluon in the nucleon are model-dep…
We develop a rather simple, formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The underlying Bethe-Salpeter equation is transformed into a pair of coupled Salpeter equations. The electromagnetic form factors of the nucleon are calculated in the Mandelstam formalism. We obtain a very good description of all electromagnetic form factors for momentum transfers up to -3 (GeV/c)^2.
We study the short-range nucleon-nucleon interaction in a chiral constituent quark model by diagonalizing a Hamiltonian comprising a linear confinement and a Goldstone boson exchange interaction between quarks. The six-quark harmonic oscillator basis contains up to two excitation quanta. We show that the highly dominant configuration is $\mid s^4p^2[42]_O [51]_{FS}>$ due to its specific flavour-spin symmetry. Using the Born-Oppenheimer approximation we find a strong effective repulsion at zero separation between nucleons in both $^3S_1$ and $^1S_0$ channels. The symmetry structure of the highl…
In analogy to the Altarelli-Parisi equation for the quark and gluon helicity contributions to the nucleon spin, we derive an evolution equation for the quark and gluon orbital angular momenta. The solution of the combined equations yields the asymptotic fractions of the nucleon spin carried by quarks and gluons: $3n_f/(16+3n_f)$ and $16/(16+3n_f)$, respectively, where $n_f$ is the number of active quark flavors. These are identical to the well-known asymptotic partitions of the nucleon momentum between quark and gluon contributions. We show that the axial-anomaly contribution to the quark heli…
In the framework of constituent quark model, the effect of hidden color channels on the nucleon-nucleon ($NN$) interaction is studied. By adjusting the color confinement strength between the hidden color channels and color singlet channels and/or between the hidden color channels and hidden color channels, the experimental data of $S$ to $I$ partial-wave phase shifts of $NN$ scattering can be fitted well. The results show that the hidden color channel coupling might be important in producing the intermediate-range attraction of $NN$ interaction. The deuteron properties and dibaryon candidates …
We apply the approximating chiral quark model. This chiral quark model is based on an effective Lagrangian which the interactions between quarks via sigma and pions mesons. The field equations have been solved in the mean field approximation for the hedgehog baryon state. Good results are obtained for nucleon properties in comparison with original model.
We discuss the electromagnetic form factors, axial form factors, and structure functions of a bound nucleon in the quark-meson coupling (QMC) model. Free space nucleon form factors are calculated using the improved cloudy bag model (ICBM). After describing finite nuclei and nuclear matter in the quark-based QMC model, we compute the in-medium modification of the bound nucleon form factors in the same framework. Finally, limits on the medium modification of the bound nucleon $F_2$ structure function are obtained using the calculated in-medium electromagnetic form factors and local quark-hadron …
An unified scheme for describing both spin and orbital motion in symmetry-breaking chiral quark model is suggested. The analytic results of the spin and orbital angular momenta carried by different quark flavors in the nucleon are given. The quark spin reduction due to spin-flip in the chiral splitting processes is compensated by the increase of the orbital angular momentum carried by the quarks and antiquarks. The sum of both spin and orbital angular momenta in the nucleon is 1/2, if the gluons and other degrees of freedom are neglected. The same conclusion holds for other octet and decuplet …
We develop a formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The underlying Bethe-Salpeter equation is transformed into a pair of coupled Salpeter equations. The space- and timelike electromagnetic form factors of the nucleon are calculated in the Mandelstam formalism for squared momentum transfers up to 3 (GeV/c)^2 above threshold. The model is applied also to the Delta(3/2).
We discuss the flavor asymmetry of the nucleon in an unquenched quark model for baryons in which the effects of quark-antiquark pairs (u anti-u, d anti-d and s anti-s) are taken into account in an explicit form. It is shown that the inclusion of q anti-q pairs leads to an excess of anti-d over anti-u quarks in the proton.
The description of electromagnetic interactions with hadrons from the quark level requires knowledge of the underlying quark-gluon ingredients. I discuss some properties of the quark-photon vertex and quark Compton vertex, along with the role of electromagnetic gauge invariance and vector-meson dominance. A simple parametrization for the quark-photon vertex is given.
We investigate the transverse quark spin densities of the nucleon with the lowest moment within the framework of the SU(3) chiral quark-soliton model, emphasizing the strange quark spin density. Based on previous results of the vector and tensor form factors, we are able to determine the impact-parameter dependent probability densities of transversely polarized quarks in an unpolarized nucleon as well as those of unpolarized quarks in a transversely polarized nucleon. We find that the present numerical results for the transverse spin densities of the up and down quarks are in good agreement wi…
By solving the Schrödinger equation for the three-quark system in the hyperspherical harmonic approach, we have studied the low energy part of the nucleon and $Δ$ spectra using a quark-quark interaction which reproduces the nucleon-nucleon phenomenology. The quark-quark hamiltonian considered includes, besides the usual one-gluon exchange, pion and sigma exchanges generated by the chiral symmetry breaking. The baryonic spectrum obtained is reasonable and the resulting wave function gives consistency to the ansatz used in the two baryon system.
Quark-model nucleon-nucleon and hyperon-nucleon interactions by the Kyoto- Niigata group are applied to the hypertriton calculation in a new three-cluster Faddeev formalism using the two-cluster resonating-group method kernels. The most recent model, fss2, gives a reasonable result similar to the Nijmegen soft-core model NSC89, except for an appreciable contributions of higher partial waves.
On the basis of the non-perturbative Heisenberg's quantization scheme and using some simplifications and assumptions the reduction from the gluon-quark Lagrangian to a scalar-fermion Lagrangian is made. The corresponding field equations have a regular spherically symmetric solution which can be interpret as a simplified model of nucleon. Some properties of such "nucleon" are discused: the presence of a mass gap and spin $\neq \hbar /2$. The mass gap describes the difference between the "nucleon" and the "nucleon" without quark field (a scalar glueball). The presence of spin $\neq \hbar /2$ can…
We examine isospin breaking in the nucleon wave functions due to the $u - d$ quark mass difference and the Coulomb interaction among the quarks, and their consequences on the nucleon electroweak form factors in a nonrelativistic constituent quark model. The mechanically induced isospin breaking in the nucleon wave functions and electroweak form factors are exactly evaluated in this model. We calculate the electromagnetically induced isospin admixtures by using first-order perturbation theory, including the lowest-lying resonance with nucleon quantum numbers but isospin 3/2. We find a small ($\…
We construct the quark-antiquark scattering kernels of Bethe-Salpeter equation from the quark self-energy directly under two specific forms of quark-gluon vertices. The quark dressed tensor vertex is then calculated within this consistent framework and rainbow-ladder(RL) approximation. After employing a simplified nucleon model, the nucleon tensor charge can be defined with the tensor vertex. We then compute the tensor charge with the bare tensor vertex and the dressed vertices obtained in this framework and in RL approximation. The obtained results are consistent with the lattice QCD calculat…
The in-medium behavior of the nucleon spectral density including self-energies is revisited within the framework of QCD sum rules. Special emphasis is given to the density dependence of four-quark condensates. A complete catalog of four-quark condensates is presented and relations among them are derived. Generic differences of such four-quark condensates occurring in QCD sum rules for light baryons and light vector mesons are discussed.
In treating the relativistic three-quark problem, a dressed-quark propagator parameterization is used which is compatible with recent lattice data and pion observables. Furthermore two-quark correlations are modeled as a series of quark loops in the scalar and axialvector channel. The resulting reduced Faddeev equations are solved for nucleon and delta. Nucleon electromagnetic form factors are calculated in a fully covariant and gauge--invariant scheme. Whereas the proton electric form factor $G_E$ and the nucleon magnetic moments are described correctly, the neutron electric form factor and t…
Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincare covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon's mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the r…
Nucleon and pion electromagnetic form factors are evaluated in the spacelike region within a light-front constituent quark model, where eigenfunctions of a mass operator, reproducing a large set of hadron energy levels, are adopted and quark form factors are considered in the one-body current. The hadron form factors are sharply affected by the high momentum tail generated in the wave function by the one-gluon-exchange interaction. Useful information on the electromagnetic structure of light constituent quarks can be obtained from the comparison with nucleon and pion experimental data.
Starting with a quark model of nucleon structure in which the valence quarks are strongly correlated within a nucleon, the light nuclei are constructed by assuming similar correlations of the quarks of neighboring nucleons. Applying the model to larger collections of nucleons reveals the emergence of the face-centered cubic (FCC) symmetry at the nuclear level. Nuclei with closed shells possess octahedral symmetry. Binding of nucleons are provided by quark loops formed by three and four nucleon correlations. Quark loops are responsible for formation of exotic (borromean) nuclei, as well. The mo…
The mean charge sum rule for the light sea quarks in the nucleon which holds under the same theoretical footing as the modified Gottfried sum rule shows that a usual parameterization of the strange sea quark distribution underestimate its contribution in the small $x$ region. We give a discussion of the soft pion contribution at high energy as a possible explanation of the saturation of the sum rule and show that it naturally explains why the strange sea quark is suppressed in the region above $x \sim 0.01$ while it becomes abundant below it.
We have evaluated nucleon and pion electromagnetic form factors using for the first time eigenfunctions of a light-front mass operator, reproducing a large set of energy levels, and constituent quark form factors in the one-body current. The comparison with the experimental data yields valuable information on the electromagnetic structure of light constituent quarks and on the different role played by their Dirac and Pauli form factors.
In this paper, we develop a general framework to study the meson-photoproductions of nucleons in the chiral quark model. The S and U channel resonance contributions are expressed in terms of the Chew-Goldberger-Low-Nambu (CGLN) amplitudes. The kaon-photoproduction processes, $γp\to K^+ Λ$, $γp\to K^+ Σ^0$, and $γp\to K^0Σ^+$, are calculated. The initial results show that the quark model provides a much improved description of the reaction mechanism for the kaon-photoproductions of the nucleon with less parameters than the traditional phenomenological approaches.
The electromagnetic form factors of the nucleon are calculated in an extended chiral constituent-quark model where the effective interaction is described by the exchange of pseudoscalar, vector, and scalar mesons. Two-body current-density operators, constructed consistently with the extended model Hamiltonian in order to preserve gauge invariance and current conservation, are found to give a significant contribution to the nucleon magnetic form factors and improve the estimates of the nucleon magnetic moments.
We present a general representation for the nucleon distribution amplitudes and for the nucleon to pion transition distribution amplitudes in terms of light-cone wave functions. We apply our formalism to a light-cone constituent quark model giving some numerical results for both the classes of observables.
Results for the proton and neutron electric and magnetic form factors as well asthe nucleon axial and induced pseudoscalar form factors are presented for the chiral constituent quark model based on Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure.
Using a quark model, we study the effect of charge symmetry breaking on the valence quark distributions of the nucleon. The effect due to quark mass differences and the Coulomb interaction of the electrically charged quarks is calculated and, in contrast to recent claims, found to be small. In addition, we investigate the effect of charge symmetry breaking in the confining interaction, and in the perturbative evolution equations used to relate the quark model distributions to experiment. We find that both these effects are small, and that the strong charge symmetry breaking effect included in …
We have investigated the effect of the finite size of the constituent quarks on singlet and triplet nucleon-nucleon potentials, obtained in the framework of the $SU(2)$ nonrelativistic quark model using the resonating group method in the Born-Oppenheimer approximation. The full Hamiltonian used in the investigation includes the kinetic energy, two-body confinement potential, one gluon exchange potential (OGEP), and instanton induced interaction (III). The effects of the smearing of the contact interactions and the variation of the constituent mass of the quarks are discussed.
We study the nucleon-nucleon interaction in a chiral constituent quark model by using the resonating group method, convenient for treating the interaction between composite particles. The calculated phase shifts for the 3S1 and 1S0 channels show the presence of a strong repulsive core due to the combined effect of the quark interchange and the spin-flavour structure of the effective quark-quark interaction. Such a symmetry structure stems from the pseudoscalar meson exchange between the quarks and is a consequence of the spontaneous breaking of the chiral symmetry. We perform single and couple…
In a world with two quark flavors and a large number of colors (N_c), the polarized and unpolarized quark distributions in the delta are completely determined by those in the nucleon up to {\cal O}(1/N_c). In particular, we find q_Δ(x) =[(1\pm 2T_z)u_N(x)+ (1\mp 2T_z)d_N(x)]/2 and Δq_Δ(x) =[(5\pm 2T_z)Δu_N(x) + (5\mp 2T_z)Δd_N(x)]/10, where q = u, d and $T_z$ the charge state of a delta. The result can be used to estimate the leading chiral-logarithmic corrections to the quark distributions in the nucleon.
The quark helicity measured in polarized deep inelastic scattering is different from the quark spin in the rest frame of the nucleon. We point out that the quark spin distributions $Δq_{RF}(x)$ are connected with the quark helicity distributions $Δq(x)$ and the quark transversity distributions $δq(x)$ by an approximate relation: $Δq_{RF}(x) + Δq(x)=2 δq(x)$. This relation will be useful in order to measure the rest frame (or quark model) spin distributions of the nucleon once the quark helicity distributions and quark transversity distributions are themselves measured. We also calculate the $x…
We investigate the nucleon to Delta(1232) vector and axial vector amplitudes in the non-relativistic quark model of the Isgur-Karl variety. A particular interest is to investigate the SU(6) symmetry breaking, due to color hyperfine interaction. We compare the theoretical estimates to recent experimental investigation of the Adler amplitudes by neutrino scattering.
On the basis of the Friedberg-Lee model we formulate a semiclassical transport theory to describe the phase-space evolution of nucleon-nucleon collisions on the quark level. The time evolution is given by a Vlasov-equation for the quark phase-space distribution and a Klein-Gordon equation for the mean-field describing the nucleon as a soliton bag. The Vlasov equation is solved numerically using an extended testparticle method. We test the confinement mechanism and mean-field effects in 1+1 dimensional simulations.
We point out that charge symmetry violation in both the valence and sea quark distributions of the nucleon has a non-perturbative source. We calculate this non-perturbative charge symmetry violation using the meson cloud model, which has earlier been successfully applied to both the study of SU(2) flavour asymmetry in the nucleon sea and quark-antiquark asymmetry in the nucleon. We find that the charge symmetry violation in the valence quark distribution is well below 1%, which is consistent with most low energy tests but significantly smaller than the quark model prediction about 5%-10%. Our …
Properties of the three-nucleon bound state are examined in the Faddeev formalism, in which the quark-model nucleon-nucleon interaction is explicitly incorporated to calculate the off-shell T-matrix. The most recent version, fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy ^3H=-8.514 MeV in the 34 channel calculation, when the np interaction is used for the nucleon-nucleon interaction. The charge root mean square radii of the ^3H and ^3He are 1.72 fm and 1.90 fm, respectively, including the finite size correction of the nucleons. These values are the closest to t…
Treating the quark and diquark as elementary particles, the Bethe-Salpeter equation for the nucleon is solved numerically. The dependence of the mass on the diquark mass and on the coupling constants is investigated. The resulting relativistic quark-diquark-nucleon vertex is presented and discussed.
Through a quantitative comparative study of the properties of deuteron and nucleon-nucleon interaction with chiral quark model and quark delocalization color screening model. We show that the $σ$-meson exchange used in the chiral quark model can be replaced by quark delocalization and color screening mechanism.
We report on our calculation of the nucleon axial and tensor charges in 2+1-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated at a single lattice spacing 0.12 fm and at a strange quark mass close to its physical value. We employ the all-mode-averaging technique to calculate the relevant nucleon correlation functions, and the disconnected quark loop is efficiently calculated by using the all-to-all quark propagator. We present our preliminary results for the isoscalar and isovector charges obtained at pion masses $m_π$ = 450 and 540 MeV.
We study the effects of free space nucleon radius on nuclear matter and neutron stars within the framework of quark mean field model. The nucleon radius is treated self-consistently with this model, where quark confinement is adjusted to fit different values of nucleon radius. Corrections due to center-of-mass motion, quark-pion coupling, and one gluon exchange are included to obtain the nucleon mass in vacuum. The meson coupling constants that describe the behavior of many-body nucleonic system are newly-constructed by reproducing the empirical saturation properties of nuclear matter, includi…
