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 Λ_QCD, are discussed.     

The scalar glueball in the instanton vacuum

We study the contribution of instantons to the binding and the mass of the lightest scalar glueball, in gluon dynamics. We show that the short-range correlations introduced by such non-perturbative vacuum fluctuations are sufficient to give rise to a scalar glueball bound state, with a mass in good agreement with the results of recent lattice calculations.     

A comparative study of optic phonon-like excitations in liquid mixtures and molten salts

We report a study of collective excitations in an equimolar Lennard–Jones liquid mixture KrAr and a molten salt NaCl within the parameter-free generalized collective modes (GCM) approach. It is shown that the high-frequency propagating modes in liquid KrAr and molten NaCl correspond to optic phonon-like excitations, caused by fast mass-concentration (charge in NaCl) fluctuations. Dispersion curves for optic collective excitations are discussed.     

Spin structure of the pion from the instanton vacuum

We investigate the spin structure of the pion within the framework of the nonlocal chiral quark model from the instanton vacuum. We first evaluate the tensor form factors of the pion for the first and second moment (n=1,2)$(n=1,2)$ and compare it with the lattice data. Combining the tensor form factor of the pion with the electromagnetic one, we determine the impact-parameter dependent probability density of transversely polarized quarks inside the pion. It turns out that the present numerical results for the tensor form factor as well as those for the probability density are in good agreement with the lattice data. We also discuss the distortion of the spatial distribution of the quarks in the transverse plane inside the pion.     

Modified action for light quarks in the instanton vacuum

The procedure of averaging in an instanton medium in quarks with any number of flavors is discussed. It is shown that the effect of the instanton medium is equivalent to an interaction of light quarks with dynamically generated mass (four-quark interaction N _f = 2) and massless bosonic spinor fields (ghosts). The fact that the instanton liquid is dilute makes it possible to use perturbation theory. The article is published in the original.     

Secondary vacuum trajectories and scalar meson exchange

A new second vacuum trajectory passing throughf*(1515) and σ(548), α(t)=? 0.3+t, is proposed, which, together with α_p″(t=0)=? 0.5, overcomes the failure of Igi's original superconvergent πN sum rule and avoids the ghost-state of the conventionalP′-trajectory. The negative residue att=0 confirms the repulsive contribution of a vacuum pole component withJ=0 to the generalizeds-reaction potential, as postulated by Chew (1965). TheP- andP′-poles can build the non resonating background. The Gell-Mann nonsense mechanism at the negative integers with wrong signature explains the dips in the elastic π^± p-scattering att=?0.7, ?2.7 and ?4.5 (GeV/c)². σ(∞) for πN reactions turns out to be 24.3 mb, if α _p (t=0)=1, but the best fits to the total πN cross sections for pion momenta between 2 and 29 GeV/c yield α _p (t=0)=0.93.     

Pion distribution amplitudes within the instanton model of QCD vacuum

The pion transition form factor for the process γ*γ* → π⁰ at spacelike 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.     

The Dyson-Schwinger equations in the instanton vacuum of the Schwinger model

Using the exact path integral solution of the Schwinger model — a model where instantons are present — the Dyson-Schwinger equations are shown to hold by explicit computation. It turns out that the Dyson-Schwinger equations separately hold for every instanton sector. This is due to the invariance of the Schwinger model.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr.P8444-TEC.     

The instanton vacuum of generalized CP models

It has recently been pointed out that the existence of massless chiral edge excitations has important strong coupling consequences for the topological concept of an instanton vacuum. In the first part of this paper we elaborate on the effective action for “edge excitations” in the Grassmannian U (m + n)/U (m) × U (n) non-linear sigma model in the presence of the θ term. This effective action contains complete information on the low energy dynamics of the system and defines the renormalization of the theory in an unambiguous manner. In the second part of this paper we revisit the instanton methodology and embark on the non-perturbative aspects of the renormalization group including the anomalous dimension of mass terms. The non-perturbative corrections to both the β and γ functions are obtained while avoiding the technical difficulties associated with the idea of constrained instantons. In the final part of this paper we present the detailed consequences of our computations for the quantum critical behavior at θ = π. In the range 0 ? m, n ? 1 we find quantum critical behavior with exponents that vary continuously with varying values of m and n. Our results display a smooth interpolation between the physically very different theories with m = n = 0 (disordered electron gas, quantum Hall effect) and m = n = 1 (O (3) non-linear sigma model, quantum spin chains) respectively, in which cases the critical indices are known from other sources. We conclude that instantons provide not only a qualitative assessment of the singularity structure of the theory as a whole, but also remarkably accurate numerical estimates of the quantum critical details (critical indices) at θ = π for varying values of m and n.     

Effective quark Lagrangian in the instanton vacuum with nonzero modes included

A new approach to the effective theory of quarks in the instanton vacuum is presented. Exact equations for the quark propagator and Lagrangian are derived which contain contributions of all quark modes with known coefficients. The resulting effective Lagrangian differs from the standard one and resembles that of the Nambu-Jona-Lasinio model. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 128–132 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

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 the QCD vacuum. In the chiral limit, we calculate the longitudinal w _L ⁽⁰⁾ and transversal w _T ⁽⁰⁾ , with respect to the axial-vector index, invariant amplitudes at an arbitrary spacelike 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.     

Axial anomaly and low energy tests for instanton vacuum models in QCD

We propose to test instanton models of QCD – in particular the single instanton approximation and the Diakonov and Petrov model – against some exact relations inferred from QCD + QED axial anomaly. One of these relations, in chiral limit, is satisfied by the latter model, but not by the former one. More refined tests, obtained beyond the chiral limit, are not fulfilled by the Diakonov and Petrov model. Received: 24 November 1997 / Published online: 10 March 1998     

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

The correlator of vector and non-singlet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of the QCD vacuum. In general the correlator has two Lorentz structures: longitudinal, w_L, and transversal, w_T, with respect to the 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 space-like momentum transfer q and show the absence of power corrections to this structure at large q². Instead there arise exponential corrections to w_T at large q² reflecting non-local properties of the 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.Received: 7 May 2005, Published online: 6 July 2005