Long-Range Behavior of Dual-Restricted QCD Vacuum

We analyze the geometrical structure of the local non-Abelian gauge theory in terms of the magnetic symmetry, using the resemblance between the non-Abelian gauge formulations and Einstein's theory of gravitation in a higher dimensional unified space. The mathematical foundation of dual QCD in fiber bundle form is then discussed and used for the analysis of the important problem of color confinement in QCD. The associated Lagrangian formulation in magnetic gauge is shown to lead to dual dynamics due to the emergence of the topological charges of magnetic nature. The dynamical breaking of magnetic symmetry is shown to lead to the magnetic condensation of the QCD vacuum. A state of the dual superconductivity in the QCD vacuum is then shown to evolve which ultimately pushes the QCD vacuum to the confining phase. The flux tube structure of the magnetically condensed QCD vacuum is analyzed by computing the asymptotic string solutions of the field equations. The energy content of such confining structures is computed and analyzed in terms of its logarithmic and linear nature.     

Thermo-field dynamics and quark–hadron phase transition in QCD

Based on the topological structure of gauge theory, an effective dual version of QCD has been reviewed and analyzed for the phase structure and color confining properties of QCD by invoking the dynamical magnetic symmetry breaking. The multi-flux-tube configuration of condensed QCD vacuum has been explored and associated glueball masses and inter-quark potential have been derived. Thermal response of QCD vacuum has been analyzed using path-integral formalism alongwith the mean-field approach and associated thermodynamical potential is used to derive thermal form of glueball masses, monopole condensate, inter-quark potential and monopole density which then lead to an estimate of the critical temperature of QCD phase transition. During its thermal evolution, a smooth transition of hadronic system via a weakly bound QGP phase to the fully deconfined phase is established and the thermal evolution profiles of various parameters are shown to indicate a second-order deconfinement phase transition and the restoration of magnetic symmetry. Monopole density calculations have been shown to lead to gradual evaporation of magnetic condensate into thermal monopoles during QCD phase transition.     

Confinement and random fluxes

We discuss the concept of random fluxes in a confining QCD vacuum. It is shown that a necessary and sufficient condition for confinement is that a certain flux must be independently distributed [eq. (3.7)] over the minimal surface spanned by the Wilson loop.     

Effective potential between two gluons from the scalar glueball

Starting from the 0⁺⁺ glueball mass and wave function computed from lattice QCD, we compute the local potential between two constituent gluons. Since the properties of constituent gluons are still a matter of research, we allow for them to be either massless, or massive with a mass around 0.7GeV. Both pictures are actually used in the literature. When the gluons are massless, the corresponding local potential is shown to be compatible with a Cornell form, that is a linear confinement plus a short-range Coulomb part, with standard values for the flux tube energy density and for the strong coupling constant. When the gluons are massive, the confining potential is a saturating one, commonly used to simulate string-breaking effects. These results fill a gap between lattice QCD and phenomenological models: The picture of the scalar glueball as a bound state of two constituent gluons interacting via a phenomenological potential is shown to emerge from pure gauge lattice QCD computations. Moreover, we show that the allowed potential shape is constrained by the mass of the constituent gluons.     

Superconductivity in Restricted Chromo-Dynamics (RCD) in SU(2) and SU(3) Gauge Theories

Characterizing the dyonically condensed vacuum by the presence of two massive modes (one determining how fast the perturbative vacuum around a colour source reaches the condensation and the other giving the penetration length of colored flux) in SU(2) theory, it has been shown that due to the dynamical breaking of magnetic symmetry the vacuum of RCD acquires the properties similar to those of relativistic superconductor. Analysing the behaviour of dyons around RCD string, the solutions of classical field equations have been obtained and it has been shown that magnetic constituent of dyonic current is zero at centre of the string and also at the points far away from the string. Extending RCD in the realistic color gauge group SU(3), it has been shown that the resulting Lagrangian leads to dyonic condensation, color confinement and the superconductivity with the presence of two scalar modes and two vector modes.     

最大解析性原理与Regge轨迹的若干性质

根据最大解析性原理,本文研究了Regge轨迹的某些性质。证明了与各粒子对应的Regge轨迹在阈能以下是能量的单调增加函数,当t→±∞时,每一轨迹的渐近极限是相同的。特别当-t₀p (0)应满足不等式1/t₀<α′_p(0)<1/4,其中t₀由α_p(t=-t₀)=0决定。     

Bare Reggeons in asymptotic free theories

Conformal symmetry is used to investigate the Regge asymptotics for the six dimensional scalar φ³ model and the QCD vacuum exchange amplitude. Resulting angular momentum cuts change into series of poles by scale breaking due to renormalization. The Regge pole trajectories are calculated for large momentum transfer.     

Dual Superconductivity in Abelian Higgs Model of QCD

The study of generalized field associated with Abelian dyons has been undertaken and it has been demonstrated that topologically, a non-Abelian gauge theory is equivalent to a set of Abelian gauge theories supplemented by dyons which undergo condensation leading to confinement and consequently to superconducting model of QCD vacuum, where the Higgs field plays the role of a regulator only. Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic) of dyon screens its own direct potential to which it minimally couples and anti-screens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. In this Abelian projection of QCD an Abelian Higgs model (AHM) has been successfully constructed and it has been shown to incorporate dual superconductivity and confinement as the consequence of dyonic condensation. It has been demonstrated that in AHM t’ Hooft loop creates the string (AHM-string) around which the monopole current under London limit leads to vanishing coherence length in the chromo-magnetic superconductor. It has also been shown that in London limit the squared density of monopole current around AHM-string has a maximum at the distance of the order of penetration length.     

WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS

The weak coupling approximate Schwinger-Dyson equation of the straton's pro-pagator in 4-dimensional QCD theory and the problem of the straton's confinement are discussed. It is proved that, when we choose Landaugauge, the obtained Sch-winger-Dyson integral equation of the straton's propagator can be transformed into a very simple form. Then we change it into a first order non-linear differential equation. It has two solutions: a confining solution and a solution that has no con-finement for the stratons. The effective potential in QCD is derived by functional method, and the ground-state energy difference between these two solutions is discussed. In our approximation, we calculate the vacuum graph to the 2-loop diagrams, We may conclude that stratons are not confined in our approximation.     

Proton-Proton Interaction in a Dual Model

The “background-pomeron” component of the amplitude is studied in the framework of a dual model with square-root trajectories. Double pomeron poles are used as vacuum exchanges in various channels, with exotic Regge poles dual to them. The expressions obtained are applied to describe total and differential cross sections of proton-proton interaction in wid eenergy regions.     

Theoretical evidence for a tachyonic ghost-state contribution to the gluon propagator in high-energy,forward quark-quark “scattering”

Implications stemming from the inclusion of nonperturbative confining effects, as contained in the stochastic vacuum model of H. Dosch and Yu.A. Simonov, are considered in the context of a (hypothetical) quark-quark “scattering process” in the Regge kinematical region. In a computation wherein the nonperturbative input enters as a correction to established perturbative results, a careful treatment of infrared divergences is shown to imply the presence of an effective propagator associated with the existence of a linear term in the static potential. An equivalent statement is to say that the modified gluonic propagator receives a contribution from a tachyonic ghost state, an occurrence which is fully consistent with earlier suggestions made in the context of low-energy QCD phenomenology.     

Spectrum and Regge trajectories in QCD

Starting in the 1960s, an active group of physicists under the guidance of Prof. K.A. Ter-Martirosyan began creating the theory of high-energy processes in QCD. From the beginning, the key element of this theory is the notion of Regge trajectories and, in particular, of the Pomeron trajectory, which have been introduced phenomenologically. In this talk, I review the problem of the spectrum and Regge trajectories as it can be derived from nonperturbative QCD dynamics.     

Monopole condensation and color confinement

Monopole condensation is responsible for confinement in U(1) lattice gauge theory. Using numerical simulations and the abelian projection, we demonstrate that this mechanism persists in SU(2) nonabelian gauge theories. Our results support the picture of the QCD vacuum as a dual superconductor.     

Reggeon, Pomeron and Glueball, Odderon-Hadron-Hadron Interaction at High Energies - From Regge Theory to Quantum Chromodynamics

Based on analysis of scattering matrix S, and its properties such as analyticity, unitarity, Lorentz invariance, and crossing symmetry relation, the Regge theory was proposed to describe hadron-hadron scattering at high energies before the advent of QCD, and correspondingly a Reggeon concept was born as a mediator of strongly interaction. This theory serves as a successful approach and has explained a great number of experimental data successfully, which proves that the Regge theory can be regarded as a basic theory of hadron interaction at high energies and its validity in many applications. However, as new experimental data come out, we have some difficulties in explaining the data. The new experimental total cross section violates the predictions of Regge theory, which shows that Regge formalism is limited in its applications to high energy data. To understand new experimental measurements, a new exchange theory was consequently born and its mediator is called Pomeron, which has vacuum quantum numbers. The new theory named as Pomeron exchange theory which reproduces the new experimental data of diffractive processes successfully. There are two exchange mediators： Reggeon and Pomeron. Reggeon exchange theory can only produce data at the relatively lower energy region, while Pomeron exchange theory fits the data only at higher-energy region, separately. In order to explain the data in the whole energy region, we propose a Reggeon-Pomeron model to describe high-energy hadron- hadron scattering and other diffractive processes. Although the Reggeon-Pomeron model is successful in describing high-energy hadron-hadron interaction in the whole energy region, it is a phenomenological model. After the advent of QCD, people try to reveal the mystery of the phenomenological theory from QCD since hadron-hadron processes is a strong interaction, which is believed to be described by QCD. According to this point of view, we study the QCD nature of Reggeon and Pomeron. We claim that the Reggeon exchange is an exchange of mult     

Asymptotic properties of regge trajectories and elastic pseudoscalar-meson scattering on nucleons at high energies

A phenomenological Regge-eikonal model featuring nonlinear monotonic parametrizations of vacuum Regge trajectories, where their asymptotic behavior in the perturbative sector is taken explicitly into account, is proposed for describing the elastic diffractive scattering of light pseudoscalar mesons on nucleons. In analyzing available experimental data on angular distributions, it is shown that, at collision energies in the region √s > 13 GeV, the diffraction pattern of the processes π ^± p → π ^± p and K ^± p → K ^± p at low momentum transfers can be described qualitatively by using the same phenomenological approximations to vacuum Regge trajectories as in the case of nucleon-nucleon scattering. This fact is indicative of the possibility of explicitly relating Regge phenomenology of various hadron-hadron processes to fundamental results obtained within QCD.     

Regge asymptotics and conformal symmetry in impact space

Conformal symmetry in impact space has been used to calculate the scattering amplitude in the Regge region and in the region of large energy and large momentum transfer in the six-dimensional ³ model. The new method overcomes difficulties with the conformal approach in cases where the asymptotics is determined by double-logarithmic contributions. This is a methodical study preparing the analysis of the Regge asymptotics of QCD amplitudes with flavour exchange and of the asymptotics of large energy and large momentum transfer for the vacuum exchange amplitude.     

The dynamical holographic QCD method for hadron physics and QCD matter

In this paper we present a short overview on the dynamical holographic QCD (DhQCD) method for hadron physics and QCD matter. The five-dimensional DhQCD model is constructed in the graviton-dilaton-scalar framework with the dilaton background field Φ and the scalar field X dual to the gluon condensate and the chiral condensate operator thus can represent the gluodynamics (linear confinement) and chiral dynamics (chiral symmetry breaking), respectively. The dilaton background field and the scalar field are a function of the 5th dimension, which plays the role of the energy scale, in this way, the DhQCD model can resemble the renormalization group from ultraviolet (UV) to infrared (IR). By solving the Einstein equation, the metric structure at IR is automatically deformed by the nonperturbative gluon condensation and chiral condensation in the vacuum. We review the results on the hadron spectra including the glueball spectra, the light/heavy meson spectra, as well as on QCD phase transitions, and thermodynamical as well as transport properties in the framework of the DhQCD model.     

Spontaneous colour confinement

The long-range order of the confinement phase of QCD is characterized by a macroscopic field (order parameter) transforming as a general Lorentz symmetric tensor, and as a (8, 8) representation of the SU(3)×SU(3) group. The resulting Ginzburg-Landau chromodynamics has the condensate vacuum behaving like a Lorentz-invariant dual colour superconductor capable of describing the spontaneous formation of the colourless domains (hadrons) immersed in the confining medium.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.It gives me much pleasure to express my gratitude to Professor Votruba for introducing me into his beloved field of elementary-particle physics, and for a great number of pleasant and informative discussions.