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.     

Fixed order matrix elements of the parafermi operators

Explicit representation formulae are found for the parafermi operators of arbitrary order p.     

Yang-Mills vacuum and the gluon mass

The vacuum sector of the pureSU(3) Yang-Mills theory in temporal gauge has been investigated. A variational calculation based on a BCS trial wave functions is performed. It is shown that this is equivalent to solving the Dyson-Schwinger equation in the Hartree approximation. By extending the Dyson-Schwinger approach, we shown using simple examples that it is possible to obtain an effective mass for the transverse gluons which is generated dynamically by the exchange of longitudinal gluons in a non perturbative vacuum.     

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.     

Hadronic vacuum polarization correction in muonic atoms

The contribution of hadronic vacuum polarization to the energy levels of muonic atoms is reevaluated using an improved parametrization of the total cross section for e⁺ e^?→hadrons. The numerical results can be simply related to the correction due to muonic vacuum polarization.     

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.     

Sigma meson and phonon-like excitations of the instanton vacuum

The possible nature of two experimentally observed scalar mesons that are widely spaced in mass and whose special features may be caused by the excitations of the instanton liquid considered as a model of the QCD vacuum. It is shown that mass changes in the scalar sector may prove to be unexpectably large, even though the scale of such corrections to the dynamical quark mass is relatively small.     

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.     

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.     

Chiral properties of low-energy matrix elements of local four-quark operators

The chiral properties of low-energy matrix elements of four-quark operators describing the weak vertices in the effective Lagrangian of weak interactions are investigated. A constituent quark diagram technique for the derivation of soft pion low-energy theorems is proposed. The technique is applied to the calculation of the-term operator correlator in the low-energy theorem of the penguin-operator matrix elements.     

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.