Instanton Liquid Research Articles

Instantons and scalar multiquark states: From small to largeNc

We study scalar $(\overline{q}q)$ and $(\overline{q}{q)}^{2}$ correlation functions in the instanton liquid model. We show that the instanton liquid supports a light scalar-isoscalar (sigma) meson, and that this state is strongly coupled to both $(\overline{q}q)$ and $(\overline{q}{q)}^{2}.$ The scalar-isovector ${a}_{0}$ meson, on the other hand, is heavy. We also show that these properties are specific to QCD with three colors. In the large ${N}_{c}$ limit the scalar-isoscalar meson is not light, and it is mainly coupled to $(\overline{q}q).$

Instanton liquid at a finite density of quark matter

For the case of finite quark and baryon densities, the interaction of light quarks with an instanton liquid is considered in a phase that involves a nonvanishing chiral condensate. The generating functional is considered in the tadpole approximation, and the behavior of the dynamical quark mass and the behavior of the chiral condensate, as well as the behavior of the instanton-liquid (gluon-condensate) density, which grows slightly with the quark chemical potential, are explored. Arguments are presented in favor of the statement that the quark-density threshold for the emergence of a diquark condensate grows sizably owing to interaction with the instanton liquid.

ROLE OF QUARK INTERACTIONS WITH INSTANTON LIQUID IN COLOUR SUPERCONDUCTIVITY PHASE

The interaction of light quarks and instanton liquid is analyzed at finite density of quark/baryon matter and in the phase of nonzero values of diquark (colour) condensate. It is shown that instanton liquid perturbation produced by such an interaction results in an essential increase of the critical value of quark chemical potential μc which provokes the perceptible increase of quark matter density around the expected onset of the colour superconductivity phase.

Instantons in QCD with many colors

We study instantons in QCD with many colors. We first discuss a number of qualitative arguments concerning the large N_c scaling behavior of a random instanton ensemble. We show that most hadronic observables are compatible with standard large N_c counting rules provided the average instanton size is O(1) and the instanton density is O(N_c) in the large N_c limit. This is not the case for the topological susceptibility and the mass of the eta'. For these observables consistency with conventional large N_c counting requires that fluctuations in the instanton liquid are suppressed compared to Poissonian fluctuations. Using mean field estimates and numerical simulations we show that the required scaling behavior of the instanton density is natural in models in which the instanton density is regularized in terms of a classical repulsive core. We also show that in these models fluctuations of the topological charge are suppressed and that m^2_eta'=O(1/N_c). We conclude that the instanton liquid model is not necessarily in conflict with the 1/N_c expansion.

Local chirality of low-lying Dirac eigenmodes and the instanton liquid model

The reasons for using low-lying Dirac eigenmodes to probe the local structure of topological charge fluctuations in QCD are discussed, and the interpretation of the local chiral orientation probability distribution in these modes (as compared with the instanton picture) is clarified. The results with overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a{approx}0.04 fm to a{approx}0.12 fm are reported, and it is found that the size and density of local structures responsible for double-peaking of the distribution are in disagreement with the assumptions of the Instanton Liquid Model. We argue that our results suggest that vacuum fluctuations do not produce locally quantized (integer-valued) topological charge in QCD, contrary to the semiclassical picture.

Quark interaction with an instanton liquid

The effect of quarks on an instanton liquid through the excitation of adiabatic phonon-like modes in it is considered. An effective Lagrangian that includes a scalar color-singlet field interacting with quarks is derived, and the relevant generating functional is estimated in the tadpole approximation. The nature of this dynamical field as a mediator of interaction at soft momenta and its possible relationship with unusual properties of the sigma meson are discussed.

Proton electromagnetic form factors in the instanton liquid model

We report the first nonperturbative calculation of proton electromagnetic form factors in the random instanton liquid model and in the interacting instanton liquid model. By calculating the ratio of appropriate three-point to two-point functions, we divide out the coupling constants and compare our results directly to some integral of the form factors. Using various parametrizations of the electric form factor ${G}_{E}{(Q}^{2})$ at large ${Q}^{2}>3.5{\mathrm{GeV}}^{2},$ where it is not yet measured, we compare those with expected theoretical dependence. We find from this comparison that some distributions of charge are clearly excluded (e.g., the same as of the magnetic moment, $\ensuremath{\mu}{G}_{E}{/G}_{M}=1,$ as well as the opposite scenario in which $\ensuremath{\mu}{G}_{E}{/G}_{M}$ rapidly approach zero), restricting possible behavior of the form factor to a rather narrow band. Furthermore, we found that our calculation of the nucleon form factors is dominated by a configuration in which two out of three quarks interact with a single instanton, in spite of the fact that the evaluated three-point function has rather large distances $(\ensuremath{\sim}1.2\mathrm{fm})$ between points. We also estimate the size of the scalar diquark and found it to be very small, comparable to the typical instanton size.

Instanton vacuum at finite density of quark matter

We study light quark interactions in the instanton liquid at finite quark/baryon number density analyzing chiral and diquark condensates and investigate the behaviors of quark dynamical mass and both condensates together with instanton liquid density as a function of quark chemical potential. We conclude the quark impact (estimated in the tadpole approximation) on the instanton liquid could shift color superconducting phase transition to higher values of the chemical potential bringing critical quark matter density to the values essentially higher than conventional nuclear one.

Quark induced excitations of the instanton liquid

The selfconsistent approach to the quark interactions in the instanton liquid is developed within the tadpole approximation calculating the basic functional integral. The effective Lagrangian obtained includes colorless scalar field interacting with quarks. The origin of this dynamical field as an interaction carrier in soft momentum region is discussed.

Topological charge fluctuations and low-lying Dirac eigenmodes

We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a ≈ 0.04 fm to a ≈ 0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in disagreement with the assumptions of the Instanton Liquid Model. We conclude that the fluctuations of topological charge in the QCD vacuum are not locally quantized.

Diquark condensate and quark interaction with an instanton liquid

The interaction of light quarks and instanton liquid is analyzed at finite density of quark/baryon matter and in the phase of nonzero values of diquark (colour) condensate. It is shown that instanton liquid perturbation produced by such an interaction results in an essential increase of the critical value of quark chemical potential $\mu_c$ which provokes the perceptible increase of quark matter density around the expected onset of the colour superconductivity phase.

Systematic study of the single instanton approximation in QCD

The single-instanton approximation (SIA) is often used to evaluate analytically instanton contributions to the Euclidean correlation function in QCD at small distances. We discuss how this approximation can be consistently derived from the theory of instanton ensemble and give precise definitions to a number of different ``quark effective masses,'' generalizing the parameter ${m}^{*},$ which was introduced long ago to account for the collective contribution of the whole ensemble. We test numerically the range of applicability of the SIA for different quantities. Furthermore, we determine all the effective masses (for random and interacting instanton liquid models) as well as from phenomenology, and discuss to what extent those are universal.

Non-perturbative non-locality: V±A correlators in euclidean position space

Using an OPE modification, which takes non-perturbative non-locality into account, the difference and sum of vector and axial-vector correlators are evaluated in euclidean position space. For distances up to 0.8 fm the calculated behavior is close to the instanton liquid result and the ALEPH data, in contrast to the implications of the conventional OPE.

Short distance current correlators: Comparing lattice simulations to the instanton liquid

Point to point correlators of currents are computed in quenched QCD using a chiral lattice fermion action, the overlap action. I compare correlators made of exact quark propagators with correlators restricted to low (less than 500 MeV) eigenvalue eigenmodes of the Dirac operator. In many cases they show a qualitative resemblance (typically at small values of the quark mass and distances larger than 0.4 fm) and they differ qualitatively at larger quark masses or at very short distance. Lattice results are in qualitative agreement (and in the difference of vector and axial vector channels, quantitative agreement) with the expectations of instanton liquid models. The scalar channel shows the effects of a quenched finite volume zero mode artifact, a negative correlator.

Low-lying fermion modes, topology, and light hadrons in quenched QCD

We explore the properties of low lying eigenmodes of fermions in the quenched approximation of lattice QCD. The fermion action is a recently proposed overlap action and has exact chiral symmetry. We find that chiral zero-eigenvalue modes are localized in space and their positions correlate strongly with the locations (as defined through the density of pure gauge observables) of instantons of the appropriate charge. Nonchiral modes are also localized with peaks which are strongly correlated with the positions of both charges of instantons. These correlations slowly die away as the fermion eigenvalue rises. Correlators made of quark propagators restricted to these modes closely reproduce ordinary hadron correlators at small quark mass in many channels. Our results are in qualitative agreement with the expectations of instanton liquid models.

Chiral random matrix model for critical statistics

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a non-interacting Fermi-gas we show that for energy differences less than a critical energy $E_c$ the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than $E_c$ the number variance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provides a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge field configurations given by a liquid of instantons is obtained.

Phonon-like excitations of instanton liquid

Phonon-like excitations of an anti-instanton-instanton liquid that are due to adiabatic variations in the instanton dimension are considered on the basis of an approximate calculation of the relevant path integral, which is saturated by quasizero modes. The kinetic term and the effective Lagrangian are found for such excitations. The properties of their spectrum, which has a mass gap determined by ΛQCD, are discussed.

Proton strangeness induced by instantons

We report on a calculation of the dilute instanton liquid contribution to the strangeness in the proton. Specifically, we express the proton matrix elements of strange-quark operators in terms of a model valence nucleon state and the strangeness producing interactions. This enables us to evaluate the strangeness in different Lorentz channels in the same way. We find that in the context of the MIT bag model only the scalar strangeness is induced by the random instanton liquid. We discuss these results in the light of the recent experiments.

Instanton size distribution

By studying the non-linear effects of overlapping instanton pairs we address difficulties in the identification of instanton distributions when the average instanton size is comparable to the average distance. For the exact charge two solution, we study how its parametrisation relates to a description in terms of individual instantons. There exist two dual sets of parameters describing the same charge two instanton solution. This duality implies the existence of a minimal separation between two instantons. Conventionally used lattice instanton finder algorithms based on the assumption of diluteness tend to underestimate instanton sizes. Finally we numerically confirm this for realistic parameters of the instanton liquid. The effect is enhanced by parallel orientation in group space.

Phononlike excitations of the instanton liquid

The phonon-like excitations of (anti)-instanton ($\bar II$) liquid due to adiabatic variations of vacuum wave functions are studied in this paper. The kinetic energy term is found and the proper effective Lagrangian for such excitations is evaluated. The properties of their spectrum, while corresponding masses are defined by $\Lambda_{QCD}$, are investigated.