Color confinement at the boundary of the conformally compactified AdS5

The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of AdS5 spacetime, topologically equivalent to the closed manifold S1× S3, by considering the coupling of two massless opposite charges on it. Taking the interaction potential as the analog of Coulomb interaction (derived from a fundamental solution of the S3 Laplace-Beltrami operator), a conformal S1× S3 metric deformation is proposed, such that free motion on the deformed metric is equivalent to motion on the round metric in the presence of the interaction potential. We give explicit expressions for the generators of the conformal algebra in the representation induced by the metric deformation.By identifying the charge as the color degree of freedom in QCD, and the two charges system as a quark-anti-quark system, we argue that the associated conformal wave operator equation could provide a realistic quantum mechanical description of the simplest QCD system, the mesons.Finally, we discuss the possibility of employing the compactification radius, R, as an- other scale along ΛQCD, by means of which, upon reparametrizing Q2c2 as (Q2c2+ħ2c2/R2), a perturbative treatment of processes in the infrared could be approached.

Bound state energy and wave function of tetraquark b̄b̄ud from lattice QCD potential

In this study, the bound state energy of a four-quark system was analytically calculated as a two heavy–heavy anti-quarks [Formula: see text] and two light–light quarks [Formula: see text]. Tetraquark was assumed to be a bound state of two-body system consisting of two mesons, each containing a light quark and a heavy antiquark. Due to the presence of heavy mesons in the tetraquark, Born–Oppenheimer approximation was used to study its bound states. To assess the bounding energy, Schrödinger equation was solved using lattice QCD [Formula: see text] potential, having expanded the tetraquark potential [Formula: see text] up to 11th term. Binding energy state and wave function, however, were obtained in the scalar [Formula: see text] channel. Graphical results for wave functions obtained versus antiquark–antiquark distance [Formula: see text] confirmed the existence of the tetraquark [Formula: see text]. Analytical bound state energy obtained here was in good agreement with several numerical ones published in the literature, confirming the accuracy of the approach taken here.

Radiative decays and the SU(6) Lie algebra

We present research on radiative decays of vector [Formula: see text] to pseudoscalar [Formula: see text] particles ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] quark system) using broken symmetry techniques in the infinite-momentum frame and equal-time commutation relations and the [Formula: see text] Lie algebra, and conducted without ascribing any specific form to meson quark structure or intra-quark interactions. We utilize the physical electromagnetic current [Formula: see text] including its singlet [Formula: see text] term and focus on the [Formula: see text] 35-plet. We derive new relations involving the electromagnetic current (including its singlet — proportional to the [Formula: see text] singlet). Remarkably, we find that the electromagnetic current singlet plays an intrinsic role in understanding the physics of radiative decays and that the charged and neutral [Formula: see text] meson radiative decays into [Formula: see text] are due entirely to the singlet term in [Formula: see text]. Although there is insufficient radiative decay experimental data available at this time, parametrization of possible predicted values of [Formula: see text] is made. For conciseness and self-containment, we compute all [Formula: see text] Lie algebra simple roots, positive roots, weights and fundamental weights which allow the construction of all [Formula: see text] representations. We also derive all nonzero [Formula: see text] generator commutators and anticommutators — useful for further research on grand unified theories.

Photo-absorption on deuteron contributed by d∗(2380) resonance

In order to understand the possible physical nature of the newly observed resonance [Formula: see text], we calculate the real photo-absorption cross-section on deuteron contributed by the resonance [Formula: see text] by considering the electromagnetic transition amplitude of [Formula: see text]. In our interpretation, the [Formula: see text] is regarded as a compact six-quark system with mainly two components of [Formula: see text] and hidden-color clusters [Formula: see text]. We find that only the next-to-leading terms contribute the [Formula: see text] and the obtained photo-absorption cross-section is quite small which is in the order of 10 nb. Compared with the data measured at ELPH and Mainz recently, it is almost about 20 times smaller.

Spectroscopy of light baryons in a semi-relativistic constituent three-quark model

We studied the non-strange baryon spectroscopy by presenting a simple semi-relativistic constituent three-quark model. Assuming a separation of the interaction potential in terms of a leading SU(6) symmetric component and a subleading SU(6) breaking term, we treated the baryons as a spin-independent three-quark system and presented the analytical solution for the problem. Using perturbative and approximative approaches in order to deal with problematic linear confining term in SU(6)-invariant interaction, we obtained analytical formulas for energy levels and the hyperradial wave functions and the average energy values of the nonstrange resonances are reproduced. To describe the hyperfine structure of the baryon, the splittings within the SU(6)-multiplets are produced by the perturbative spin- and isospin-dependent terms. The resulting description of the baryon spectrum for both approaches are given and compared with the experimental spectrum.

Source of the Kerr-Newman solution as a gravitating bag model: 50 years of the problem of the source of the Kerr solution

It is known that gravitational and electromagnetic fields of an electron are described by the ultra-extreme Kerr-Newman (KN) black hole solution with extremely high spin/mass ratio. This solution is singular and has a topological defect, the Kerr singular ring, which may be regularized by introducing the solitonic source based on the Higgs mechanism of symmetry breaking. The source represents a domain wall bubble interpolating between the flat region inside the bubble and external KN solution. It was shown recently that the source represents a supersymmetric bag model, and its structure is unambiguously determined by Bogomolnyi equations. The Dirac equation is embedded inside the bag consistently with twistor structure of the Kerr geometry, and acquires the mass from the Yukawa coupling with Higgs field. The KN bag turns out to be flexible, and for parameters of an electron, it takes the form of very thin disk with a circular string placed along sharp boundary of the disk. Excitation of this string by a traveling wave creates a circulating singular pole, indicating that the bag-like source of KN solution unifies the dressed and point-like electron in a single bag-string-quark system.

Vector interaction effect on thermodynamics and phase structure of QCD matter

The two-flavor Polyakov-loop extended model is generalized by taking into account the effective four-quark vector-type interaction with the coupling strengths, which are endowed with a dependence on the Polyakov field Φ. The effective vertex generates entanglement interaction between the Polyakov loop and the chiral condensate. We investigate the influence of an additional quark vector interaction and the entanglement interaction on thermodynamics of a quark system and in particular on the location of the critical end-point at the given chemical potential or quark density. It is shown that the finite value of the singlet vector interaction strength G v improves the model agreement with the lattice data. The influence of the nonzero G v and entanglement on the thermodynamic observables and the curvature of the crossover boundary in the T – μ plane is also examined.

Hadron formation from interaction among quarks

This paper deals with the hadronization process of quark system. A phenomenological potential is introduced to describe the interaction between a quark pair. The potential depends on the color charge of those quarks and their relative distances. Those quarks move according to classical equations of motion. Due to the color interaction, coloring quarks are separated to form color neutral clusters which are supposed to be the hadrons.