Model Of QCD Vacuum Research Articles

Dipole polarizabilities of light pseudoscalar mesons within the domain model of the QCD vacuum

Dipole polarizabilities of light pseudoscalar mesons are calculated in the framework of the mean field approach to QCD vacuum and bosonization based on the statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields, the domain model of QCD vacuum. In this approach, a nonlocal effective action of meson fields is derived that describes all possible strong, weak, and electromagnetic interactions of meson fields including their excited states. The considered mean field implements confinement and chiral symmetry, which manifests itself both in the properties of quark and gluon fields as well as upon bosonization, in the mass spectrum, decays constants and form factors of nonlocal colorless hadrons, and leads to the qualitatively distinctive features of the effective meson action. Particularly relevant to the subject of the present paper are the nonlocality of meson-quark-antiquark vertices and the absence of poles at real momenta in the propagators of scalar meson fields composed of light quark-antiquark pairs. In view of this, studying the role of manifest nonlocality of mesons and contribution of intermediate scalar meson fields in formation of the polarizabilities is of special interest. It turns out that, for charged pions and kaons, this contribution is substantial but not the largest one. Nonlocal nature of mesons provides an additional contribution so that calculated polarizabilities are in reasonable agreement with COMPASS experimental data and chiral perturbation theory.

Instanton induced transverse single spin asymmetry for π0 production in pp scattering

We calculate the production cross-section and the transverse single-spin asymmetry for pion in $p^{\uparrow}+p\to \pi^0 + X$. Our computation is based on existence of the instanton induced effective quark-gluon and quark-gluon-pion interactions with a strong spin dependency. In this framework we calculate the cross section without using fragmentation functions. We compare predictions of the model with data from RHIC. Our numerical results, based on the instanton liquid model for QCD vacuum, are in agreement with unpolarized cross section data. The asymmetry grows with the transverse momentum of pion $k_t$ in accordance with experimental observations. It reach value $\sim 10\%$ but at higher $k_t$ than experiment shows.

Importance of confinement in instanton induced potential for bottomonium spectroscopy

Mass spectra of bottomonium states are computed using the Instanton Induced potential obtained from Instanton Liquid Model for QCD vacuum and incorporating a stronger confinement term. Spin dependent interactions through confined one gluon exchange potential are incorporated to remove the mass degeneracy. The mass spectra of the bbar{b} states up to 4S states are found to be in good agreement with the values reported by PDG(2020). Mixing of nearby isoparity states are also studied. We found the state varUpsilon (10{,}860) as an admixture of 5^3S_1 and 6^3D_1 Upsilon states with mixing angle theta = 39.98^{circ } and the mixed state di-leptonic decay width is found to be 0.25 keV as against the width of 0.31 pm 0.07 keV reported by PDG. Further the state varUpsilon (11{,}020) is also found to be the admixture of 6^3S_1 and 5^3D_1 Upsilon states with the mixing angle theta = 51.69^{circ } and the di-leptonic decay width of the mixed state is obtained as 0.14 keV which is very close to the width of 0.13 pm 0.03 keV reported by PDG. Present results indicates that addition of confinement to the instanton potential is crucial for the determination of the mass spectroscopy of heavy hadrons.

СЕТЬ ДОМЕННЫХ СТЕНОК КАК ВАКУУМ КХД: КОРРЕЛЯЦИОННЫЕ ФУНКЦИИ И КОНФАЙНМЕНТ СТАТИЧЕСКИХ КВАРКОВ

Within the domain model of QCD vacuum the properties of a statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields representing the physical vacuum of quantum chromodynamics are investigated. The two-point correlation function of the topological charge density is calculated and the topological susceptibility is found. It is shown that such vacuum fields ensure the implementation of the area law for the Wilson loop, i.e. the confinement of static quarks.

Gluonic Distribution in the Constituent Quark and Nucleon Induced by the Instantons

Instanton effects can give large contribution to strong interacting processes, especially at the energy scale where perturbative QCD is no longer valid. However instanton contribution to the gluon contribution in constituent quark and nucleon has never been calculated before. Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon for the first time. We find that the pion field plays an important role in producing both the unpolarized and the polarized gluon distributions.

Pion transition form factor in the domain model of QCD vacuum

Domain model of QCD allows for description of wide range of meson observables, dynamical chiral symmetry breaking, and resolution of $U_A(1)$ and strong $CP$ problems. The purpose of the present study is transition form-factor of neutral pseudoscalar mesons, and how they are influenced by the typical vacuum configurations of the model -- almost everywhere homogeneous Abelian (anti-)self-dual fields. Asymptotic behavior of the calculated pion form-factor supports Belle trend, but the asymptotic value of $Q^2F_{\pi\gamma^*\gamma}$ differs from the prediction of factorization theorems.

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.

Gluonic structure of the constituent quark

Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon. Our approach consists of the two main steps. At the first step, we calculate the gluon distributions inside the constituent quark generated by the perturbative quark-gluon interaction, the non-perturbative quark-gluon interaction, and the non-perturbative quark-gluon-pion anomalous chromomagnetic interaction. The non-perturbative interactions are related to the existence of the instantons, strong topological fluctuations of gluon fields, in the QCD vacuum. At the second step, the convolution model is applied to derive the gluon distributions in the nucleon. A very important role of the pion field in producing the unpolarized and the polarized gluon distributions in the hadrons is discovered. We discuss a possible solution of the proton spin problem.

Anomalous quark chromomagnetic moment and single-spin asymmetries

We discuss a nonperturbative mechanism for the single-spin asymmetries in the strong interaction. This mechanism is based on the existence of a large anomalous quark chromomagnetic moment induced by the nontrivial topological structure of QCD vacuum. Our estimations within the instanton liquid model for QCD vacuum show that AQCM generates very large SSA on the quark level. Therefore, this mechanism can be responsible for the anomalously large SSA observed in different high energy reactions with hadrons.

Role of Anomalous Quark-Gluon Chromomagnetic Interaction in Hadron Physics

We calculate the contribution arising from nonperturbative quark-gluon chro- momagnetic interaction to the high energy total quark-quark cross section. The estimation obtained within the instanton model of QCD vacuum leads to the conclusion that this type of interaction gives the dominating contribution to the Pomeron coupling with the light quarks and to gluon distribution in light hadrons at small virtualities of quarks and gluons.

Role of anomalous chromomagnetic interaction in Pomeron and Odderon structures and in gluon distribution

We calculate the contribution arising from nonperturbative quark-gluon chromomagnetic interaction to the high-energy total quark-quark cross section and to gluon distributions in nucleon. The estimation obtained within the instanton model of QCD vacuum leads to the conclusion that this type of interaction gives the dominating contribution to the Pomeron coupling with the light quarks and to gluon distribution in light hadrons at small virtualities of quarks and gluons. We argue that the Odderon, which is the P = C = −1 partner of the Pomeron, is governed by the spin-flip component related to nonperturbative three-gluon exchange induced by anomalous quark-gluon chromomagnetic interaction.

OFF-SHELL TWIST-FOUR PHOTON LIGHT-CONE WAVEFUNCTION FOR THE CHIRALITY-CONSERVING QUARK–ANTIQUARK VECTOR CURRENT IN THE LOW-ENERGY EFFECTIVE THEORY OF QCD

Within the framework of the low-energy effective theory arising from the instanton vacuum model of QCD, the twist-four virtual photon wavefunction, gγ3(u, P2), corresponding to the nonlocal quark–antiquark vector current is calculated at the low-energy scale. The coupling constant, fγ(P2), of the quark–antiquark vector current to the virtual photon state is also obtained. The behavior of the coupling as well as the obtained photon wave function especially at the end points is discussed.

Instanton contribution to the Sivers function

We study the Sivers function for valence u and d quarks in the proton within the instanton model for QCD vacuum, adopting the MIT bag model wave functions for quarks. Within approaches based on perturbative one-gluon final state interactions a non-zero value of the Sivers function is related to the presence of both S and P wave components in quark wave functions. We show that the instanton-induced chromomagnetic, nonperturbative interaction leads to very specific spin-spin correlations between the struck and spectator quarks, resulting in a non-trivial flavour dependence of the Sivers function. Comparison of the obtained Sivers functions with phenomenological parameterizations is discussed.

OFF-SHELL PHOTON LONGITUDINAL LIGHT-CONE WAVE FUNCTION AT LEADING TWIST

The leading twist longitudinal virtual photon light-cone wave function, ϕγ‖(u, P2), is calculated within the framework of the low-energy effective theory arising from the instanton model of QCD vacuum. Corresponding to the non-perturbative effects at low-energy scale, a suitable regularization scale T is fixed by analysing the differential behavior of the photon wave function on the internal transverse momentum cut-off in the light-cone frame. The coupling constant, Fγ(P2), of the quark-antiquark vector current to the virtual photon state is also obtained by imposing the normalization condition. The feature of the obtained photon wave function has been discussed at the end as well as the coupling constant.

Off-Shell Longitudinal Photon Light-Cone Wavefunction in theLow-Energy Effective Theory of QCD

Within the framework of the low-energy effective theory arisingfrom the instanton vacuum model of QCD, the longitudinal virtualphoton light-cone wavefunction, ϕγ∥(u,P2),corresponding to the nonlocal quark–antiquark vector current iscalculated at the low-energy scale. The coupling constant,Fγ(P2) or equivalently fγ(P2), of thequark–antiquark vector current to the virtual photon state is alsoobtained by imposing the normalization condition to the photon wavefunction. The behaviour of the coupling constant as well as the obtainedphoton wavefunction is discussed.

$VA\widetilde{V}$ correlator within the instanton vacuum model

The correlator of vector and nonsinglet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of QCD vacuum. In general the correlator has two Lorentz structures: longitudinal w_L and transversal w_T with respect to axial-vector index. Within the instanton model the saturation of the anomalous w_L structure is demonstrated. It is known that in the chiral limit the transversal structure w_T is free from perturbative corrections. In this limit within the instanton model we calculate the transversal invariant function w_T at arbitrary momentum transfer, q, and show the absence of power corrections to this structure at large q^2. Instead there arise the exponential corrections to w_T at large q^2 reflecting nonlocal properties of QCD vacuum. The slope of w_T at zero virtuality, the QCD vacuum magnetic susceptibility of the quark condensate and its momentum dependence are estimated.

Singlet $$\tilde V$$ correlator within the instanton vacuum model

The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of QCD vacuum. In the chiral limit we calculate the longitudinal w_L^0 and transversal w_T^0 with respect to axial-vector index invariant amplitudes at arbitrary momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U_A(1) anomaly.

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

In terms of the Nambu–Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple local gauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalar fields is derived by solving the Euler equation for the gauge fields. Based on this relation the gauge potential is given which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinement behavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can be melted away under high temperatures.

Dynamical Model of QCD Vacuum and Quark Confinement**The project supported by Science Foundation of the Ministry of Science and Technology of China under Grant No. 2100CCA00700

The phase transition of a simple local gauge model is investigated in terms of the Nambu–Jona-Lasinio mechanism and it is pointed out that the physical vacuum of QCD is bound state of quark-antiquark pairs which can be viewed, generally, as a nearly perfect color dia-electric medium. An important relation between the vacuum expectation value of gauge fields and scalar fields is also derived by solving the Euler equation for the gauge fields. Based on this relation the gauge potential is given which can be used to explain the asymptotic behavior and confinement of quarks in a hadron, and at the same time the Yukawa potential of strong interaction can be given too.

Pion distribution amplitudes within the instanton model of QCD vacuum

Pion transition form factor for the process $\gamma*\gamma*\to \pi^0$ at space-like values of photon momenta is calculated within the effective quark-meson model with the interaction induced by instanton exchange. The leading and next-to-leading order power asymptotics of the form factor and the relation between the light-cone pion distribution amplitudes of twists 2 and 4 and the dynamically generated quark mass are found.