arXiv subjects
Publications and source records attributed to Yu. A. Simonov.
Nonperturbative contribution to the one-gluon exchange produces a universal linear term in the static potential at small distances $ΔV=\frac{6N_c α_s σr}{2π}$. Its role in the resolution of long--standing discrepancies in the fine splitting of heavy quarkonia and improved agreement with lattice data for static potentials is discussed, as well as implications for OPE violating terms in other processes.
This paper is an extended version of hep-th/9802134. Dual QCD Lagrangian is derived by making use of the generalized coordinate gauge, where 1-form (vector potential) is expressed as an integral of the 2-form (field strength) along an (arbitrary) contour. As another application a simple proof of the nonabelian Stokes theorem is given.
Field strength correlators are semi-classically evaluated in the dilute gas model of non-Abelian sources (instantons) and compared with lattice data for QCD at zero temperature. We show that one of the Euclidean invariant, tensorial structures vanishes for configurations being purely selfdual or anti-selfdual. We compute the invariant functions contributing to the correlators within the two lowest orders in an instanton density expansion. Fitting instanton size and density for quenched and full QCD, we obtain a reasonable description.
The cancellation of perturbative contributions to the string tension in gluodynamics in the framework of vacuum field correlators method is shown at the order $O(g^4)$ by explicit calculation. The general pattern of these cancellations at all orders and relation with the renormalization properties of the Wilson loop is discussed.
A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour $C$. For a special class of contours the gauge condition reduces to $k_μ(x) A_μ(x) = 0 $ where $k_μ(x)$ is a tangent vector to the contour $C$. A simple proof of the nonabelian Stokes theorem is given demonstrating the advantage of the gauge.
New nonlinear equations for field correlators in the large $N_c$ gluodynamics are derived. Nonperturbative confining correlators are shown to satisfy a system of nonlinear scale-invariant equations. Keeping only the simplest, bilocal correlators one can find the exponential large distance behaviour for both independent correlators $D$ and $D_1$ and express coefficients in the exponentials -- the gluonic correlation length $T_g$ -- through the string tension. Numerically these results are in agreement with lattice data.
The effective quark Lagrangian is derived from the QCD action by means of averaging over the vacuum fields. In the limit of large N_c and keeping for simplicity the lowest order gluonic correlator one obtains nonlinear equations for the quark propagator, exhibiting scalar confinement. Connection to the quark zero mode density is discussed.
Numerous aspects and mechanisms of color confinement in QCD are surveyed. After a gauge-invariant definition of order parameters, the phenomenon is formulated in the language of field correlators, to select a particular correlator responsible for confinement. In terms of effective Lagrangians confinement is viewed upon as a dual Meissner effect and a quantitative correspondence is established via the popular abelian projection method, which is explained in detail. To determine the field configurations possibly responsible for confinement, the search is made among the classical solutions, and selection criterium is introduced.
The light quark propagation in the confining vacuum, described by an (infinite) set of gauge-invariant vacuum correlators, is studied in detail. To keep gauge invariance at each step the system of light quark and heavy antiquark is considered, and the nonlinear equations are written explicitly for the quark propagator in the limit of large $N_c$. For the lowest (Gaussian) correlator the system is studied in various approximations, and the relativistic WKB method is used to demonstrate the scalar confining interaction of light quarks, which implies chiral symmetry breaking. The chiral condensate is estimated by the relativistic WKB method, and connection to the density of global zero modes is clarified. The higher even order correlators are shown to yield the same properties of scalar confining interaction for light quarks. No attempt was made to solve the obtained nonlinear equations numerically, but the qualitative conclusion on connection between confinement and chiral symmetry breaking is drawn, and an estimate of the chiral condensate is performed.
The light-cone Hamiltonian, incorporating the nonperturbative dynamics of the $q\bar q$ system connected by the string is solved numerically. The spectrum is shown to coincide with that of the center-of-mass Hamiltonian within the accuracy of computation, displaying the expected degeneracies of the string states, but an overall shift due to different treatment of Z-graphs is obtained. The nonperturbative wave functions are calculated directly from the light-cone Hamiltonian for the first time, thus allowing the explicit estimation of nonperturbative effects in the parton model language. In this way one obtains the string contribution to the parton distributions and in the formfactors and structure functions.
A straightforward derivation of the effective quark Lagrangian is presented for the topologically neutral chiral broken phase of the dilute instanton gas. The resulting quark Lagrangian is a nonlocal NJL-type and contains 4q, 6q,... vertices for any number of flavours. Correspondence of this result with previously known in literature is discussed in detail.
A new approach to 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.
Exact relations between gauge-invariant vacuum correlators in QCD are derived. Derivatives of the correlators are expressed in terms of higher orders correlators. The behaviour of the correlators at large and small distances due to these relations is discussed.
A new approach to 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 resembles that of the Nambu--Jona--Lasinio model. The commonly used zero--mode approximation is shown to be invalid in the chiral limit.
Using cumulant expansion for an averaged Wilson loop we derive an action of the gluodynamics string in the form of a series in powers of the correlation length of the vacuum. In the lowest orders it contains the Nambu-Goto term and the rigidity term with the coupling constants computed from the bilocal correlator of gluonic fields. Some higher derivative corrections are calculated.
Dyonic classical solutions of $SU(2)$ gluodynamics are discussed. Exact form of dyonic solutions in different gauges is presented and the nontrivial problem of composition of the dilute gas of dyons is settled. Classical interaction between (anti)dyons is considered both analytically and numerically. Confinement in the dyonic gas is discussed in connection with the topological properties of individual dyon solution. Fermionic zero modes of dyonic are displayed and the chiral symmetry breaking in the dyonic gas is demonstrated.
Dyonic classical solutions of $SU(2)$ gluodynamics are discussed. Exact form of dyonic solutions in different gauges is presented and the nontrivial problem of composition of the dilute gas of dyons is settled. Classical interaction between (anti)dyons is considered both analytically and numerically. Confinement in the dyonic gas is discussed in connection with the topological properties of individual dyon solution. Fermionic zero modes of dyonic are displayed and the chiral symmetry breaking in the dyonic gas is demonstrated.
Confined and deconfined phases are defined through nonperturbative correlators and nonperturbative background perturbation theory is used to compute the critical temperature $T_c$ and spatial string tension. Taking evolution along one of the spatial axes the set of Hamiltonians $H(n_1,n_2)$ with different Matsubara frequencies is obtained. Meson and glueball screening masses and wave functions are computed for $H(0,0)$ and compared with available lattice data.