The Nucleon-Nucleon interaction in the singlet ($^1 S_0$) and triplet ($^3 S_1$) channels have been studied in the framework of Relativistic Harmonic Model using the Resonating Group Method in Born-Oppenheimer approximation. The full Hamiltonian consists of the kinetic energy, two body confinement potential, confined one gluon exchange potential and one pion exchange potential. Contribution of Confined One Gluon Exchange Potential and One Pion Exchange Potential to the adiabatic nucleon-nucleon interaction potential is discussed.
Three current models of QCD in (1+1) dimensions are examined and extended in light-front coordinates. A pion of high momentum is found to have an infinite extent along its direction of motion.
We examine the two solutions (massive and scaling) for the covariant Yang-Mills Dyson-Schwinger equations within stochastic quantization, and find that the scaling solution does not survive outside Landau gauge. We also see that the (rainbow) massive solution has less Faddeev-Popov effective action. Finally, we argue that gluon confinement has only been marginally established in experiment and suggest further empirical work.
We study the particle production in the early stage of the ultrarelativistic heavy-ion collisions. To this end the Boltzmann kinetic equations for gluons and pions with elastic rescattering are considered together with a simple model for the parton-hadron conversion process (hadronisation). It is shown that the overpopulation of the gluon phase space in the initial state leads to an intermediate stage of Bose enhancement in the low-momentum gluon sector which due to the gluon-pion conversion process is then reflected in the final distribution function of pions. This pattern is very similar to …
We investigate two-pion Bose-Einstein correlations of quark-gluon plasma droplet sources in single-event measurements. We find that the distribution of the fluctuation between correlation functions of the single- and mixed-events provide useful signals to detect the granular structure of the source.
In this work, we investigate the gluon distribution functions for the pion and kaon, in addition to the improved result of the valence-quark ones, in the gauge-invariant nonlocal chiral-quark model (NL$χ$QM), in which the momentum dependence of the quark interactions is properly taken into account. We then analyze the gluon distribution functions, generated dynamically through the splitting functions in the DGLAP QCD evolution. By comparing with the recent lattice QCD results and JAM global analyses, it is found that the present numerical results for the gluon parton distribution functions for…
In this paper we study the gluon and valence quark distributions in the pion and kaon in nuclear medium for various nuclear densities as well as in vacuum within the Nambu--Jona-Lasinio (NJL) model with the help of the proper-time regularization scheme which simulates a confinement of QCD. The nuclear medium effect is also determined in the same model for the symmetric nuclear matter. We then analyze the gluon and valence quark distributions for the bound pion and kaon in symmetric nuclear matter as well as those in vacuum. We find that the valence quark and gluon distributions in vacuum have …
Experimental verifications of Confinement in hadron physics have established the absence of charges with a fraction of the electron's charge by studying the energy deposited in ionization tracks at high energies, and performing Millikan experiments with charged droplets at rest. These experiments test only the absence of particles with fractional charge in the asymptotic spectrum, and thus "Quark" Confinement. However what theory suggests is that Color is confined, that is, all asymptotic particles are color singlets. Since QCD is a non-Abelian theory, the gluon force carriers (indirectly reve…
A one parameter, model confined-gluon propagator is employed in a phenomenological application of the Dyson-Schwinger and Bethe-Salpeter equations to the calculation of a range of $π$- and $ρ$-meson observables. Good agreement is obtained with the data. The calculated quark propagator does not have a singularity on the real-$p^2$ axis. A mass formula for the pion, involving only the vacuum, dressed quark propagator, is presented and shown to provide an accurate estimate of the mass obtained via a direct solution of the Bethe-Salpeter equation.
The leading-twist parton distribution functions of the pion and kaon are calculated for the first time using a rainbow-ladder truncation of QCD's Dyson-Schwinger equations (DSEs) that self-consistently sums all planar diagrams. The non-perturbative gluon dressing of the quarks is thereby correctly accounted for, which in practice means solving the inhomogeneous Bethe-Salpeter equation (BSE) for the quark operator that defines the spin-independent quark distribution functions. An immediate consequence of using this dressed vertex is that gluons carry 35% of the pion's and 30% of the kaon's ligh…
We study a model Dyson-Schwinger equation for the quark propagator closed using an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \sim q^2/[(q^2)^2 + b^4]$} and two {\it Ansätze} for the quark-gluon vertex: the minimal Ball-Chiu and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of $b=b_c$ such that the model does not support dynamical chiral symmetry breaking for $b>b_c$. We discuss and apply a confinement test which suggests that, for all values of $b$, the quark propagator in the m…
The Gluon and Ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find t…
We calculate the Gaussian radius parameters of the pion-emitting source in high energy heavy ion collisions, assuming a first order phase transition from a thermalized Quark-Gluon-Plasma (QGP) to a gas of hadrons. Such a model leads to a very long-lived dissipative hadronic rescattering phase which dominates the properties of the two-pion correlation functions. The radii are found to depend only weakly on the thermalization time tau_i, the critical temperature T_c (and thus the latent heat), and the specific entropy of the QGP. The dissipative hadronic stage enforces large variations of the pi…
We present the first determination of the $x$-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, at two lattice spacings $a\approx 0.12$ and 0.15~fm and three pion masses $M_π\approx 220$, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our resu…
We examine the two-pion interferometry for a granular source of quark-gluon plasma droplets. The evolution of the droplets is described by relativistic hydrodynamics with an equation of state suggested by lattice gauge results. Pions are assumed to be emitted thermally from the droplets at the freeze-out configuration characterized by a freeze-out temperature $T_f$. We find that the HBT radius $R_{out}$ decreases if the initial size of the droplets decreases. On the other hand, $R_{side}$ depends on the droplet spatial distribution and is relatively independent of the droplet size. It increase…
We obtain the energy-momentum tensor (EMT) in the 't Hooft model of two-dimensional quantum chromodynamics. The EMT is decomposed into contributions from quark and gluon fields, with all of the (plus component of) the light front momentum being carried by the quark field. The energy is split between quark and gluon fields, with the gluon field carrying the self-energy of the dressed quarks. We consider the pion in the limit of small but non-zero quark masses -- which has previously withstood numerical treatment -- as as a concrete example. We solve for the pion wave function using a variationa…
We present the $x$-dependent nucleon and pion gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.56~GeV on three lattice spacings $a\approx 0.9, 0.12$ and 0.15~fm and three pion masses $M_π\approx 220$, 310 and 690~MeV. We compare our pion and preliminary nucleon gluon results with the determination by global fits.
We study gluon condensate in a pion superfluid, through calculating the equation of state of the system in the Nambu-Jona-Lasinio model. While in mean field approximation the growing pion condensate leads to an increasing gluon condensate, meson fluctuations reduce the gluon condensate and the broken scalar symmetry can be smoothly restored at finite isospin density.
We obtain the light meson mass spectroscopy from the light-front quantum chromodynamics (QCD) Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock components, together with a three-dimensional confinement. The eigenvectors of the light-front effective Hamiltonian provide a good quality description of the pion electromagnetic form factor, decay constant, and the valence quark distribution functions following QCD scale evolution. We also show that the pion's gluon densities can be probed through the pion-nucleus induced $J/ψ$ production data. Our pion part…
The gluon distributions of the pion obtained from various global fits exhibit large variations among them. Within the framework of the color evaporation model, we show that the existing pion-induced $J/ψ$ production data, usually not included in the global fits, can impose useful additional constraints on the pion parton distribution functions (PDFs). In particular, these data can probe the pion's gluon densities at large $x$. Existing pion-induced $J/ψ$ data covering a broad range of beam momenta are compared with next-to-leading-order QCD calculations using various sets of pion PDFs. It is f…
Photocouplings for the nucleon resonances most relevant to total photoabsorption are calculated in a constituent quark model including gluon and pion exchange. The sensitivity of the results to the different ingredients of the model is discussed.
We calculate the variation of the chiral condensate in medium with respect to the quark chemical potential and evaluate the pion-nucleon sigma term via the Hellmann-Feynman theorem. The variation of chiral condensate in medium are obtained by solving the truncated Dyson-Schwinger equation for quark propagator at finite chemical potential, with different models for the quark-gluon vertex and gluon propagator. We obtain the value of the sigma term $σ_{πN}$ = 62(1)(2) MeV, where the first represents the systematic error due to our different model for the quark-gluon vertex and gluon propagator an…
We point out that the existence of Glauber gluons in the $k_T$ factorization theorem can account for the violation of the Lam-Tung relation, namely, the anomalous lepton angular distribution, observed in pion-induced Drell-Yan processes. Radiations, that balance the lepton-pair transverse momentum, cause the responsible spin-transverse-momentum correlation in the Glauber-gluon background. It is argued that the Glauber effect is significant in the pion due to its unique role of being a Nambu-Goldstone boson and a $q\bar q$ bound state simultaneously. This mechanism is compared to other resoluti…
Pionic contributions to static nucleon properties are calculated in a chiral extension of the colour-dielectric model. The pion field and residual gluon field are treated perturbatively. It is shown that with a simple choice for the energy of the scalar confining field and in the chiral limit, the system of equations describing the bare soliton and the perturbative pion and gluon fields may be cast in a dimensionless, parameter free form for large glueball mass. This enables a formula for the masses of the nucleon and delta including leading order pionic and gluonic contributions and correctio…
The holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model{\color{blue},} without additional free parameters. The gluonic and quark distributions are shown to have significantly different effecti…
Hanburry-Brown-Twiss (HBT) correlation functions and radii of negatively charged pions from C+C, Si+Si, Cu+Cu, and In+In at lower RHIC/SPS energies are calculated with the UrQMD transport model and the CRAB analyzing program. We find a minimum in the excitation function of the pion freeze-out volume at low transverse momenta and around $E_{lab}\sim 20-30A$GeV which can be related to the transition from hadronic to string matter (which might be interpreted as a pre-cursor of the QGP). The existence of the minimum is explained by the competition of two mechanisms of the particle production, reso…
The infrared behavior of Yang-Mills theory at finite temperature provides access to the role of confinement. In this review recent results on this topic from lattice calculations and especially Dyson-Schwinger studies are discussed. These indicate persistence of a residual confinement even in the high-temperature phase. The confinement mechanism is very similar to the one in the vacuum for the chromomagnetic sector. In the chromoelectric sector screening occurs at the soft scale g^2T, although not leading to a perturbative behavior.
In this study it is demonstrated that a simple picture of the QCD gluon liquid emerges in the dynamical quasiparticle model that specifies the active degrees of freedom in the time-like sector and yields a potential energy density in the space-like sector. By using the time-like gluon density (or scalar gluon density) as an independent degree of freedom - instead of the temperature $T$ as a Lagrange parameter - variations of the potential energy density lead to effective mean-fields for time-like gluons and an effective gluon-gluon interaction strength at low density. The latter yields a simpl…
We study three subjects on quark confinement in hadrons in SU(3)$_{\rm c}$ lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. We also study the multi-quark (4Q, 5Q) potentials in lattice QCD, and find that they are well described by the one-gluon-exchange (OGE) Coulomb plus string-theoretical linear potential, which supports the {\it infrared string picture} even for the multi-quarks. The second subject is a lattic…
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft …
We present a relativistic calculation of the saturation properties of nuclear matter which contains the correlation energy. Pion loops are incorporated on top of a relativistic Hartree-Fock (RHF) approach based on a chiral theory. It includes the effect of nucleon structure through its response to the background chiral invariant scalar field. All the parameters which enter the RHF calculation are fixed or strongly constrained by hadron phenomenology or lattice data. The new input for the correlation energy is the Landau-Migdal parameter g? governing the short-range part of the spin-isospin int…
QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms of fluctuating topology in the QCD vacuum. We then describe the recent work with E. Levin that links the confinement of gluons and color screening to the fluctuating topology, and discuss implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.
Experimental data of the pion charge form factor are well represented by Poincaré invariant constituent-quark phenomenology depending on two parameters, a confinement scale and an effective constituent--quark mass. Pion states are represented by eigenfunctions of mass and spin operators and of the light-front momenta. An effective current density is generated by the dynamics from a null-plane impulse current density. A simple shape of the wave function depending only on the confinement scale is sufficient.
QCD perturbation theory ignores the compact nature of $SU(3)$ gauge group that gives rise to the periodic $θ$-vacuum of the theory. We propose to modify the gluon propagator to reconcile perturbation theory with the anomalous Ward identities for the topological current in the $θ$-vacuum. As a result, the gluon couples to the Veneziano ghost describing the tunneling transitions between different Chern-Simons sectors of the vacuum; we call the emerging gluon dressed by ghost loops a "glost". We evaluate the glost propagator and find that it has the form $G(p) = (p^2 + χ_{top}/p^2)^{-1}$ where $χ…
We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian Monte Carlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-$x$ asymptotics of the valence quark distribution $\sim (1-x)^{β_v}$ can differ significantly, with $β_v$ ranging from $\approx 1$ to $> 2.5$ at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts t…
Applying the Hellmann-Feynman theorem to a charged pion gas, the quark and gluon condensates at low isospin density are determined by precise pion properties. At intermediate density around $ f_π^2m_π$, from both the estimation for the dilute pion gas and the calculation with Nambu--Jona-Lasinio model, the quark condensate is strongly and monotonously suppressed, while the gluon condensate is enhanced and can be larger than its vacuum value. This unusual behavior of the gluon condensate is universal for Bose condensed matter of mesons. Our results can be tested by lattice calculations at finit…
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determ…
Aspects of the dressed-quark-gluon vertex and their role in the gap and Bethe-Salpeter equations are briefly surveyed using an intuitive model. The model allows one to elucidate why a linear extrapolation to the chiral limit of extant lattice data on the dressed-quark mass-function overestimates this function and hence the value of the vacuum quark condensate. The diagrammatic content of the vertex described is explicitly enumerable. This property is essential to the symmetry preserving study of bound state properties. It facilitates a realistic analysis of vector and pseudoscalar meson masses…
In Landau gauge QCD the Kugo-Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson--Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantit…
Properties of $Λ,~Ξ^0$ hypernuclei and neutron stars are investigated in quark mean field model with pion and gluon corrections. Firstly, $u, ~d$, and $s$ quarks are confined by relativistic harmonic oscillator potentials to generate the baryons, like nucleon, $Λ, ~Σ$, and $Ξ$ hyperons. The effects of pion-quark coupling and one-gluon exchange are considered perturbatively. Then, the baryons interact with each other through exchanging $σ, ~ω,$ and $ρ$ mesons between quarks in hypernuclei and nuclear matter. The strengths of confinement potentials for $u, ~d,$ and $s$ quarks are determined by t…
Gluon dressing of the light quarks within hadrons is very strong and extremely important in that it dynamically generates most of the observable mass through the breaking of chiral symmetry. The quark and gluon parton densities, $q(x)$ and $g(x)$, are necessarily interrelated since any gluon emission and absorption process, especially dressing of a quark, contributes to $g(x)$ and modifies $q(x)$. Guided by long-established results for the parton-in-parton distributions from a strict 1-loop perturbative analysis of a quark target, we extend the non-perturbative QCD approach based on the Rainbo…
Pion dissociation in a medium of hot quark matter is studied. The decay width of pion is found to be large but finite at temperatures much higher than the so called critical temperature of chiral or deconfinement transition. Consequently, pions should coexist with quarks and gluons at such high temperatures. The result is in agreement with the lattice calculations. The implication of the above result in the study of Quark-Gluon plasma is discussed.
We investigate the nucleon and pion gluon distribution functions in the framework of holographic QCD, focusing on the small Bjorken x region. Based on an approximate relation, the gluon distributions are extracted from structure functions of the unpolarized deep inelastic scattering which can be calculated with a holographic QCD model, assuming the Pomeron exchange. All the adjustable parameters of the model are determined with the HERA data of the proton structure functions. We explicitly show that the extracted proton gluon distribution is consistent with results of the recent global QCD ana…
We suggest a new mechanism for the energy loss of fast heavy quarks in quark-gluon plasma. This mechanism is based on pion production caused by the anomalous chromomagnetic quark-gluon-pion interaction induced by strong topological fluctuations of the gluon fields represented by instantons. We found that this mechanism gives a considerable contribution to the collisional energy loss of a heavy quark in quark-gluon plasma, which shows a nontrivial role of nonperturbative phenomena in strongly interacting quark-gluon plasma.
We investigate how charmonium hadroproduction at fixed-target energies can be used to constrain the gluon distribution in pions. Using nonrelativistic QCD (NRQCD) formulation, the $J/ψ$ and $ψ(2S)$ cross sections as a function of longitudinal momentum fraction $x_F$ from pions and protons colliding with light targets, as well as the $ψ(2S)$ to $J/ψ$ cross section ratios, are included in the analysis. The color-octet long-distance matrix elements are found to have a pronounced dependence on the pion parton distribution functions (PDFs). This study shows that the $x_F$ differential cross section…
Pion and kaon dissociation in a medium of hot quark matter is studied in the Nambu Jona-Lasinio model. The decay width of pion and kaon are found to be large but finite at temperatures much higher than the so called critical temperature of chiral or deconfinement transition, kaon decay width being larger. Consequently, pions and even kaons (with a lower density compared to pions) should coexist with quarks and gluons at such high temperatures. The implication of the above result in the study of Quark-Gluon plasma is discussed.
Based on a recent manifestly covariant time-ordered approach to the relativistic many-body problem, the quark propagator is defined by a nonlinear Dyson--Schwinger-type integral equation, with a one-gluon loop. The resulting energy-dependent quark mass is such that the propagator is singularity-free for real energies, thus ensuring confinement. The self-energy integral converges without regularization, due to the chiral limit of the quark mass itself. Moreover, the integral determines the low-energy limit of the quark-gluon coupling constant, for which a value of $g^2/4π=4.712$ is found.
Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mil…
We perform a direct calculation of the gluon momentum fraction of the nucleon using maximally twisted mass fermion ensembles with $N_f=2+1+1$ flavors at a pion mass of about $370\,\mathrm{MeV}$ and a lattice spacing of $a\approx 0.082\,\mathrm{fm}$ and with $N_f=2$ flavors at the physical pion mass and a lattice spacing of $a\approx 0.093\,\mathrm{fm}$. In the definition of the gluon operator we employ stout smearing to obtain a statistically significant result for the bare matrix elements. In addition, we perform a lattice perturbative calculation including 2 levels of stout smearing to carry…
