Instanton Model Research Articles

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlator of topological charge densities and related to it longitudinal part of the correlator of singlet axial currents is considered in the framework of instanton model. The coupling constant of eta'-meson with the singlet axial current is determined. Its value appears to be in a good coincidence with the value determined recently from the connection of the part of proton spin, carried by u,d,s quarks, with the derivative of QCD topological susceptibility. From the same sum rule eta-eta' mixing angle is found in the framework of two mixing angles model. Its value is close to that found in the chiral effective theory. The correlator of topological charge densities at large momenta is calculated.

Pion structure function within the instanton model

The leading-twist valence-quark distribution function in the pion is obtained at a low normalization scale of an order of the inverse average size of an instanton ${\ensuremath{\rho}}_{c}.$ The momentum dependent quark mass and the quark-pion vertex are constructed in the framework of the instanton liquid model, using a gauge invariant approach. The parameters of instanton vacuum, the effective instanton radius and quark mass, are related to the vacuum expectation values of the lowest dimension quark-gluon operators and to the pion low energy observables. An analytic expression for the quark distribution function in the pion for a general vertex function is derived. The results are QCD evolved to higher momentum-transfer values, and reasonable agreement with phenomenological analyses of the data on parton distributions for the pion is found.

Twist-3 contribution tohLin the instanton vacuum

We show that the instanton model of the QCD vacuum indicates the parametric smallness of the twist-3 contributions to the polarized structure function ${h}_{L}.$ This smallness is related to the diluteness of the QCD instanton vacuum.

High-Density QCD and Instantons

Instantons generate strong nonperturbative interactions between quarks. In vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300–400MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as ∼100MeV. We provide a systematic treatment of color superconductivity in the instanton model. We show that the structure of the superconductor depends on the number of flavors. In the case of two flavors, we verify the standard scenario, and provide an improved calculation of the mass gap. For three flavors, we show that the ground state is color–flavor locked and calculate the chiral condensate in the high-density phase. We show that as a function of the strange quark mass, there is a sharp transition between the two phases. Finally, we go beyond the mean-field approximation and investigate the role of instanton/anti-instanton molecules, which—in addition to superconducting gap formation—provide a competitive mechanism for chiral restoration at finite density.

Instantons and η meson production near threshold in NN collisions

An enhancement for the η production in proton–neutron collisions as compared with that in proton–proton scattering has been recently observed. We present a calculation for the production cross section, in proton–neutron collisions near threshold, within instanton model for the QCD vacuum and show that a specific flavor dependent nonperturbative quark–gluon interaction related to instantons is able to explain the observed enhancement.

Gluon field strength correlation functions within a constrained instanton model

Gluon field strength correlation functions within a constrained instanton model

Quark propagator, instantons, and gluon propagator

The Schwinger-Dyson formalism is used to check the consistency of instanton model solutions for the quark propagator with recent models of confining gluon propagators. We find that the models are not consistent. A major discrepancy is the absence of a vector condensate in the instanton model that is present in the solutions with nonperturbative confining gluons.

Symmetry and broken symmetries in molecular orbital descriptions of unstable molecules II. Alignment, flustration and tunneling of spins in mesoscopic molecular magnets

As an extention of previous work [Yamaguchi K (1983) J Mol Structure (Theochem) 103:101], our theoretical efforts toward molecular materials are briefly reviewed. Axial, helical and general (cone, tetrahedron, etc) spin structures of carbon clusters, manganese oxide clusters and iron-sulfur clusters were investigated using the classical Heisenberg model and generalized Hartree-Fock theory. The spin flustrations in the clusters were also studied in relation to theoretical descriptions of the magnetism and the chemical bonds in active sites of several enzymes. The macroscopic quantum tunneling and coherence of spins in the manganese oxide clusters were analyzed using the instanton model, and the tunneling rate of spins was calculated by the coherent state path integral method. The spin transitions induced by an external magnetic field were studied by the path integral Monte Carlo method. The theoretical results were explained in terms of the symmetry and broken symmetry of the wavefunctions in the mesoscopic molecular systems, which are intermediate in the scale factor. The results were also applied to molecular design of mesoscopic clusters of clusters in the intermediate and strong correlation regime. The active control of spins is finally discussed from the viewpoint of functionalities in molecular and biological materials, and technological applications of mesoscopic molecular magnets are discussed with regard to quantum computing.

Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton (SI) case, in particular, the form factor $D_{1}$ is small, which is in agreement with the lattice calculations.

Vector mesons from tensor couplings in the NJL model

We propose to describe vector mesons in a pure quark model such as the one of Nambu and Jona-Lasinio by means of four point tensor interactions, but with vanishing vector and axial couplings. This becomes possible due to tensor-vector mixing at the one quark loop level. As a consequence a bound particle with ρ quantum numbers is generated. This has the advantage of avoiding the A− π mixing which is known to generate a wrong off-shell pion wave function renormalization. In addition, there is no A 1 meson. We make our arguments quantitative by computing Euclidean correlators via dispersion relations and comparing with lattice QCD and random instanton model results.

A comparison of two methods for direct tunneling dynamics: Hydrogen exchange in the glycolate anion as a test case

Two methods for studying tunneling dynamics are compared, namely the instanton model and the approach of Truhlar and co-workers, which are based on the direct output of electronic structure calculations and thus are parameter free. They are employed to evaluate the zero-level tunneling splitting due to intramolecular hydrogen exchange in the glycolate anion. The first method was developed in a series of recent studies and presents a combination of the instanton theory with quantum-chemically computed potentials and force fields. For the compound at hand, which has 21 internal degrees of freedom, a complete potential-energy surface is generated in terms of the normal modes of the transition-state configuration. It is made up of the potential-energy curve along the tunneling coordinate and harmonic force fields at the stationary points. The level of theory used is HF/6–31++G**. All modes that are displaced between the equilibrium configuration and the transition state are linearly coupled to the tunneling mode, the couplings being proportional to the displacements in dimensionless units. These couplings affect the instanton trajectory profoundly and, depending on the symmetry of the skeletal modes, can enhance or suppress the tunneling. In the glycolate anion all modes have such displacements and thus are included in the calculation. Based on the similarity with malonaldehyde, it is argued that tunneling prevails in the studied process, and the zero-level tunneling splitting is predicted. The latter is found within the computational scheme developed earlier, which avoids explicit evaluation of the instanton path and thus greatly simpli-fies the tunneling dynamics. These results are tested by the method of large-curvature tunneling of Truhlar and co-workers implemented in a dual-level scheme. The potential energy surface needed for the dynamics calculations is generated at the semiempirical PM3 level of theory and then corrected by interpolation with high-level HF/6–31++G** results for the stationary points. The code corresponding to this approximation is in the package MORATE 6.5. The tunneling splittings found by the two approaches are in quantitative agreement. We have found that the computational scheme based on the instanton model is much less time consuming both in the static and dynamics part. This computational efficiency, also demonstrated in a number of earlier studies, merits future application of the method to fairly large systems of practical interest, such as clusters and organic compounds with excited-state proton transfer.

A multidimensional semiclassical method for treating tunneling in molecular collisions

A semiclassical method for treating tunneling in molecular collisions is presented. The procedure incorporates tunneling into standard classical trajectory simulations. The tunneling rate is computed by calculating the JWKB tunneling probabilities along predefined tunneling paths at the classical turning points which are determined by classical trajectory calculations. The method is illustrated for the collinear H+H2 atom-exchange reaction on the Porter–Karplus surface. The calculated reaction probabilities are in good agreement with the quantum-mechanical values, and are in fact as good as the results obtained from more sophisticated semiclassical treatments such as the S-matrix theory and the instanton model. The method can readily be extended to higher dimensions.

Finite temperature QCD: Progress and outstanding problems

I review recent progress in numerical simulations of finite temperature quantum chromodynamics and discuss the status of some outstanding problems. Included is (1) a discussion of recent results determining the temperature of the ``phase transition'' in full QCD, (2) a scaling analysis of the Polyakov loop variable, leading to the determination of a constituent quark free energy, (3) studies of critical behavior near the phase transition in two-flavor QCD, (4) a discussion of problems and new results in thermodynamic simulations with Wilson fermions, (5) recent results in pure gauge theory with a mixed fundamental/adjoint action, and (6) the nonperturbative determination of the equation of state with dynamical fermions included. Finally I mention briefly new developments in efforts to construct a phenomenology of deconfinement and chiral symmetry restoration, namely (7) the dual superconducting model and (8) the instanton model.

The QCD sum rule for the delta (1232) in the instanton medium

The QCD sum rule for the Δ (1232) is considered in the instanton medium. It is found that the instanton effect improves the chirally odd sum rule significantly. This indicates that the operator product expansion does not converge rapidly in the delta state. The chirally even sum rule of Δ suggests that the “standard” value of the higher dimensional condensate m 0 is much smaller than that derived from the instanton model.

Hadronic wave functions in the instanton model.

In this paper we wish to study hadronic wave functions using an instanton model for the QCD vacuum. The wave functions are defined in terms of gauge-invariant Bethe-Salpeter amplitudes which we have determined numerically using a Monte Carlo simulation of the instanton ensemble. We find that the pion and the proton, as well as the \ensuremath{\rho} meson and the \ensuremath{\Delta}, have very similar wave functions but observe a sizable splitting between mesons or baryons with different spin. We compare our results with data obtained in lattice gauge simulations.

Baryonic correlators in the random instanton vacuum

This is the third paper of a series devoted to a systematic study of QCD correlation functions in the framework of an instanton model for the QCD vacuum. In this paper we concentrate on the quark-quark (diquark) and three quark (baryon) channels. We have found that the quark-quark interaction resembles the one between quarks and antiquarks. Similar to the pion and rho channels, the interaction in the scalar isospin I = 0 and vector I = 1 diquark channels is completely different: the former has a much stronger attractive interaction. As a consequence, the SU(3) octet (nucleon) and decuplet (delta) correlators are also found to be qualitatively different. Using a complete set of all available correlation functions, we determine masses and coupling constants for the nucleon and delta. Our results agree surprisingly well with the first lattice data on point to point correlators.

Chiral dynamics and hadronic structure

General aspects of chiral symmetry breaking are discussed in the context of the instanton model of the QCD vacuum. In the long wavelength limit, a Landau-Ginzburg effective Lagrangian is derived after proper coarse graining of the liquid phase. This approach leads naturally to the concept of chiral solitons much like vortex excitation in liquids. Some pertinent issues related to Skyrmions are discussed. The issue of the relevance of confinement versus chiral symmetry in low energy processes is raised in the context of the Cheshire can principle, using the flavor singlet axial current as a specific example.

Instantons and the hyperfine splitting ofB andB Smesons

In this short note we wish to point out that the instanton model, which was theoretically fascinating, has recently found application in explaining the hyperfine splitting of mesons and baryons. In particular, the flavour independence ofM v 2 -M P 2 (i.e. the squared mass difference of the vector and the pseudoscalar mesons), known to be constant for the strange and non-strange mesons in theu,d and the charm quark sectors, have recently been shown to be the same for the beauty sector through experiments. This flavour independence and the magnitude of the splitting agrees remarkably well with the instanton model.

Chiral symmetry restoration at finite temperature in the instanton liquid

We extend the instanton model of the QCD vacuum with quark-induced interactions to nonzero temperature. Using the mean field approximation, we compare the free energies of the two phases, the “polymer” and “molecular” ones. We have found that the phase transition should occur in a narrow temperature interval around 200 MeV.

Pseudoscalar mesons and instantons

We discuss the QCD sum rules for the correlators of pseudoscalar currents with quantum numbers of π, K, η, η′ mesons. In the framework of the instanton model of the QCD vacuum suggested earlier by the author, we calculate SU(3) breaking effects such as K, η masses and ηη′ mixing, as well as the U(1) breaking effect, the η′ mass. We conclude that all these phenomena are very well reproduced by this model.