Narrow Results

We propose to resolve the controversy regarding the stability of the monopole condensation in QCD by calculating the imaginary part of the one-loop effective action perturbatively. We calculate the imaginary part perturbatively to the order g² with two different methods, with Feynman diagram and with Schwinger's method. Our result shows that with the magnetic background the effective action has no imaginary part, but with the electric background it acquires a negative imaginary part. This strongly indicates a stable monopole condensation in QCD.

We study the color confinement of QCD with the Coulomb gauge in lattice simulations. The color-Coulomb instantaneous interaction in color-singlet channel causes a linearly rising potential at large distances. We also estimate the other color-channel forces for two-quark states, i.e. color-octet, color-sextet and color-antitriplet channels. Moreover we investigate the volume dependence of color-nonsinglet potentials on finite lattices.

We investigate the Gribov-Zwanziger scenario in Coulomb gauge QCD using a SU(3) quenched lattice gauge simulation. The ghost propagator diverges in the infrared limit stronger than the free ghost propagator, and the ghost degree of freedom plays a central role in the confinement mechanism in the Coulomb gauge. The infrared divergent ghost dressing function results in the confining color-Coulomb instantaneous interaction. The equal-time transverse gluon propagator is suppressed in the infrared region. Therefore, in the Coulomb gauge, the instantaneous interaction mediated by time-like gluons is responsible for the confining force, and the would-be physical gluons are confined in hadrons.

We discuss how confinement property of QCD results in the rational unitarization scheme and how unitarity saturation leads to the appearance of a hadron liquid phase at very high temperatures.

The $X17$ particle, discovered by [A. J. Krasznahorkay et al., Phys. Rev. Lett.116, 042501 (2016), doi:10.1103/PhysRevLett.116.042501] at ATOMKI, was recently confirmed in the $\gamma \gamma$ invariant mass spectra by [K. U. Abraamyan, C. Austin, M. I. Baznat, K. K. Gudima, M. A. Kozhin, S. G. Reznikov and A. S. Sorin, arXiv:2311.18632] at JINR. We notice with surprise and interest that the $X17$ seems to have a double-peak structure. This is in a possible coincidence with our QCD sum rule study of [H.-X. Chen, arXiv:2006.01018], where we interpreted the $X17$ as a tetraquark state composed of four bare quarks ($uūd\bar{d}$), and claimed that “A unique feature of this tetraquark assignment is that we predict two almost degenerate states with significantly different widths”. These two different tetraquark states are described by two different chiral tetraquark currents ${ū}_L{\gamma }_{\mu }{d}_L{\bar{d}}_L{\gamma }^{\mu }{u}_L$ and ${ū}_L{\gamma }_{\mu }{d}_L{\bar{d}}_R{\gamma }^{\mu }{u}_R$. To verify whether the tetraquark assignment is correct or not, we replace the up and down quarks by the strange quarks, and apply the QCD sum rule method to study the other four chiral tetraquark currents ${ū}_L{\gamma }_{\mu }{s}_L{\bar{s}}_L{\gamma }^{\mu }{u}_L$, ${ū}_L{\gamma }_{\mu }{s}_L{\bar{s}}_R{\gamma }^{\mu }{u}_R$, ${\bar{d}}_L{\gamma }_{\mu }{s}_L{\bar{s}}_L{\gamma }^{\mu }{d}_L$ and ${\bar{d}}_L{\gamma }_{\mu }{s}_L{\bar{s}}_R{\gamma }^{\mu }{d}_R$. We calculate their correlation functions, and find that non-perturbative QCD effects do not contribute much to them. Our results suggest that there may exist four almost degenerate tetraquark states with masses about $236\sim 296$ MeV. Each of these states is composed of four bare quarks, either $uūs\bar{s}$ or $d\bar{d}s\bar{s}$.

We study the flux tube structure of the nonperturbative QCD vacuum in terms of its dyonic excitations by using an infrared effective Lagrangian and show that the dyonic condensation of QCD vacuum has a close connection with the process of color confinement. Using the fiber bundle formulation of QCD, the magnetic symmetry condition is presented in a gauge covariant form and the gauge potential has been constructed in terms of the magnetic vectors on global sections. The dynamical breaking of the magnetic symmetry has been shown to lead the dyonic condensation of QCD vacuum in the infrared energy sector. Deriving the asymptotic solutions of the field equations in the dynamically broken phase, the dyonic flux tube structure of QCD vacuum is explored which has been shown to lead the confinement parameters in terms of the vector and scalar mass modes of the condensed vacuum. Evaluating the charge quantum numbers and energy associated with the dyonic flux tube solutions, the effect of electric excitation of monopole is analyzed using the Regge slope parameter (as an input parameter) and an enhancement in the dyonic pair correlations and the confining properties of QCD vacuum in its dyonically condensed mode has been demonstrated.

Color confinement is studied in dual version of SU(2) color gauge theory using its topological structure and the dynamical breaking of the magnetic symmetry which has been shown to effectively trigger the QCD monopole condensation in a dynamical way. The resulting flux tube structure of the QCD vacuum is explored which has been shown to lead to the perfect dual superconducting nature to the QCD vacuum in its dynamically broken phase. The analysis of the flux tube energy at different hadronic length scales has been shown to lead to the appearance of the strong confinement forces in QCD vacuum at large hadronic distances and an indication for the deconfinement phase at small scales. The analysis of the flux tube energy is then used to compute numerically the critical radius and the critical flux tube density of the phase transition from the flux tube phase to deconfined one inside hadrons. The numerical estimates are shown to be in fairly good agreement with the analytical values. The possible implications of these critical parameters on the formation of QGP as a result of the flux tubes fusion in intermediate energy regime are also discussed.

The key ingredients of the Gribov program of attacking quark confinement are reviewed.

Unlike some models whose relevance to Nature is still a big question mark, Quantum Chromodynamics (QCD) will stay with us forever. QCD, born in 1973, is a very rich theory supposed to describe the widest range of strong interaction phenomena: from nuclear physics to Regge behavior at large E, from color confinement to quark–gluon matter at high densities/temperatures (neutron stars); the vast horizons of the hadronic world: chiral dynamics, glueballs, exotics, light and heavy quarkonia and mixtures thereof, exclusive and inclusive phenomena, interplay between strong forces and weak interactions, etc. Efforts aimed at solving the underlying theory, QCD, continue. In a remarkable entanglement, theoretical constructions of the 1970's and 1990's combine with today's ideas based on holographic description and strong–weak coupling duality, to provide new insights and a deeper understanding.

We discuss various aspects of the multiparticle production processes at the LHC energy range with emphasis on the collective effects associated with appearance of the new scattering mode, which corresponds to the reflective scattering and its impact on multiparticle production processes.

We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.

We show that the monopole condensation is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence, and show that the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation.

We discuss how the existence of the Gribov horizon affects the deep infrared behavior of ghost and gluon propagators of the D-dimensional SU(N) Yang-Mills theory in the Landau gauge. If we use a horizon function in the Gribov-Zwanziger framework to restrict the functional integral to the first Gribov region for avoiding Gribov copies, we can show that the ghost propagator behaves like free, while the gluon propagator is non-vanishing in deep infrared region (the decoupling solution) in harmony with recent results obtained from numerical simulations on lattice, the Schwinger-Dyson equation and the functional renormalization group. This result should be compared with the Gribov prediction that such a restriction leads to the vanishing gluon propagator and enhanced ghost propagator (the scaling solution). We raise some questions on current understanding on the ghost propagator and its implications for quark confinement à la Wilson and color confinement à la Kugo-Ojima.

We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance (“the C-projection”) we show that the effective potential generates the stable monopole condensation which generates the mass gap.