Nonperturbative Vacuum Research Articles

Coherent-state representation for the QCD ground state.

We make use of the temporal gauge to construct a coherent state which is meant to describe the gluon condensate in the QCD vacuum under the assumption that the condensate is in a zero-momentum mode. The state so constructed is a color singlet and will yield finite, nonperturbative vacuum expectation values such as . (This matrix element is found to have a value of about 0.012 GeV/sup 4/ in QCD sum-rule studies.)

Propagation properties and condensate formation of the confined Yang-Mills field.

The dynamical generation of a pole in the self-energy of a Yang-Mills field: an extension of the Schwinger mechanism: establishes a link between the tendency of the field to form nonperturbative vacuum condensates and its ''noninterpolating'' property in the confining phase: the fact that it has no particles associated with it. The nonvanishing residue of such a pole: a parameter b/sup 4/ of dimension (mass)/sup 4/: on the one hand provides for a nonvanishing value of , a contribution to the ''gluon condensate.'' On the other hand, it implies a dominant nonperturbative form of the propagator that has no particle singularity on the real k/sup 2/ axis; instead, it describes a quantized field whose elementary excitations are short lived. The dispersion law for these excitations is given and shows that they grow more particlelike (are asymptotically free) at large momenta, thus providing a qualitative description of the short-lived excitation at the origin of a gluon jet. At large k/sup 2/, the nonperturbative propagator reproduces nonperturbative corrections derived from the operator-product expansion.

Truncation of the operator-product expansion for the langleqq-bar>-condensate component of the quark mass.

Quark-condensate contributions to ${m}_{\mathrm{dyn}}$, the quark mass generated by the dynamical breakdown of chiral symmetry, are shown to arise from only the first two terms of the operator-product expansion (OPE) for the appropriate $O({g}^{2})$ nonperturbative vacuum expectation value. Since the $\frac{m}{|p|}$ expansion parameter of the OPE is unity on the gauge-invariant $p={m}_{\mathrm{dyn}}$ propagator pole, such truncation of OPE contributions is an essential support to the calculation of ${m}_{\mathrm{dyn}}$.

Variation on finite energy sum rules: Vacuum matrix elements

New finite energy sum rules for light quark systems are derived in QCD, which express nonperturbative vacuum matrix elements of a given dimension in terms of the spectral function and its derivatives. A phenomelogical definition of nonperturbative effects is proposed.

Calculating infrared contributions to vacuum expectation values of gluonic and quark fields

Based on the infrared asymptotics of the lower QCD Green's functions obtained before, we propose a definition and elaborate a technique for calculating non-perturbative vacuum expectations of gluon and quark fields. In our calculations, we use only the known QCD parameters: constitutent quark masses, the confining potential slope and the QCD parameter Γ. The values obtained for the vacuum expectations agree well with experiment.

Nonperturbative propagators in quantum chromodynamics.

Leading nonperturbative corrections to the quark and gluon propagators are derived following the assumption that the nonperturbative QCD vacuum can be described in terms of nonvanishing vac- uum expectation values for the composite operators [\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\psi}] and [${G}_{\ensuremath{\mu}\ensuremath{\nu}}$${\mathrm{}}^{2}$]. The nonperturbative quark propagator can be described in terms of a running gauge-dependent quark mass and a running normalization function. The nonperturbative gluon propagator can be described in terms of a running gauge parameter and a running normalization function.

Translation invariant calculation of nonperturbative quarkonium mass shifts

The mass shifts of q q bound states in the nonperturbative QCD vacuum are calculated by applying field theoretic perturbation theory as derived within the formalism of the Bethe-Salpeter equation. We obtain corrections to heavy quarkonium masses of the order of, but somewhat smaller than those of previous authors, who employed ordinary perturbation theory of nonrelativistic quantum mechanics.

Meson-gluonium mixing from QCD sum rules

We evaluate the off-diagonal two-point correlation function responsible for the gluonium-meson mixing, including the leading non-perturbative lowest dimension vacuum condensate contributions. Then, using spectral function sum rules approach, we deduce a small meson-gluonium mixing angle. We also derive upper bounds for the η′ and for the strange quark masses.

Non-perturbative QCD vacuum frome +e??I=1 hadron data

We estimate the gluon vacuum condensate α s 〈F 2〉 from thee +e−→I=1 hadron cross-section known below 2 GeV using moment sum rules ratios. We obtain α s 〈F 2〉= (3.9±1.0)10−2GeV4. We also re-evaluate the contribution of the dimension-six vacuum condensates to the above sum rule and test the factorization hypothesis of the four-quark operator. Useful rules for the evaluation of the dimension-six vacuum condensates contributions are given.

Nonperturbative vacuum energy density in two-dimensional scalar models

Nonperturbative vacuum energy density in two-dimensional scalar models

On leading non-perturbative effects for heavy-quark systems

Non-perturbative effects for heavy-quark systems in the physical region are considered. The summation of the leading infinite subsequence of non-perturbative corrections is carried out in the non-relativistic approximation. From the analysis follows that there must exist at least two types of vacuum fluctuations — relatively hard and soft ones — in the non-perturbative QCD vacuum.

CP Violation and supersymmetry

We re-examine the phenomenology of CP violation in the context of broken supersymmetric theories. We argue that since it is related to the mass counter-terms for fermion fields which vanish in a supersymmetric theory, the non-perturbative vacuum parameter θ is not renormalized and is hence “naturally” small in a theory with spontaneously broken supersymmetry. We argue that the usual estimates of CP violating phenomena in the Kobayashi-Maskawa model are likely to remain valid in such a theory, with the possible exception of the neutron electric dipole moment which may be large if supersymmetry is broken on a scale ⪢ O(100)GeV.

The MIT bag model lagrangian and QCD vacuum

It is shown that the existance of the quark condensate in the nonperturbative QCD vacuum leads to the MIT bag model lagrangian with broken chiral symmetry.

Quark-Gluon correlations and vacuum fluctuations

We study the effect of non-perturbative vacuum fluctuations on the angular correlation of a quark and gluon produced in e +e − annihilation at high energies. Long-wavelength background fields induce and exponential falloff in the invariant mass q 2 of the quark-gluon system for moderate q 2.

Perturbative QCD in a non-perturbative vacuum

We propose a procedure for interpreting the presence of a background gluon field in the context of perturbative QCD. We expect our method to be useful when non-perturbative effects are significant but not completely dominant.

The effect of the non-perturbative vacuum in e +e − annihilation

The vacuum polarization due to quarks is investigated in trial QCD vacuum with non-vanishing squared chromomagnetic field strength. Its asymptotic behaviour can be understood by means of the operator product expansion provided an operator matrix element is evaluated non-perturbatively. Power-like corrections are obtained for the total cross section of the e +e − annihilation into hadrons.

Instantons in non-perturbative QCD vacuum

The effects of large-scale vacuum fluctuations on instantons of a small size ϱ are considered. We find the instanton density with account of the gluon vacuum condensate. It is shown that the instanton gas approximation fails at unexpectedly small ϱ. The instanton interaction with the gluon condensate already becomes strong at ϱ ≈ (1.1 GeV) −, while the absolute bound for the use of quasiclassical methods lies at ϱ ≈ (0.5 GeV) −1.

Non-perturbative effects in e +e − annihilation in quantum chromodynamics

We study the change of one two-point function of hadronic electromagnetic currents in the presence of background gauge fields. It is found that it has the asymptotic behavior of 1/ q 4 as compared to ln(- q 2) behavior from the bare fermion loop contribution. The effects of the non-perturbative vacuum in QCD on the two-point function is studied in an explicit calculation. We obtain the same qualitative behavior as in our general discussion. The effects on the total hadronic e +e − annihilation is also discussed. We find that the effect ΔR I / R is of the order of o(1/ q 4) or O(1/ q 6). This may explain the precocious scaling in the e +e − annihilation.

On dynamics of heavy quarks in a non-perturbative QCD vacuum

Non-perturbative large scale fluctuations of gluonic fields, which are present in the exact vacuum of QCD, result in a modification of the interaction between quarks in quarkonium. Such effects are considered for heavy quarks in cases when the size of the quarkonium system is much smaller than that of the dominating gluonic fluctuations. The Green function of relative motion in heavy quarkonium is calculated for energies below threshold taking account of leading non-perturbative effects. It is shown that once non-perturbative gluonic degrees of freedom are taken into consideration they can never be absorbed into a sort of interaction potential between quarks.

General approach to the computation of instanton effects

A systematic approach is developed for the computation of physical effects associated with nonperturbative vacuum structure generated by instantons. The new feature of this approach is that the size of instantons which naturally contribute to the effect in question is governed by the momentum q of the experimental probe. In that sense, nonperturbative vacuum structure can be controlled in the same way as perturbative short-distance corrections. The contribution of an instanton of size rho to certain measurable quantities falls as e/sup -rhoq/. Consequently, since the instanton density function decreases with decreasing rho, by making q large enough the effects due to a single instanton can be isolated. No ad hoc cutoff or assumption about the behavior of large, overlapping instantons need be introduced. The exponential falloff (essential to cutoff-independent calculations) emerges only in momentum space and is seen to depend on a set of smoothness and integrability properties of the instanton contribution to the effect in coordinate space. An analysis of these properties provides a characterization of the quantities which may be reliably computed in momentum space. The general approach is illustrated by two specific computations: instanton contributions to the static interaction of a heavy QQ-bar pair and to themore » correlation function of two electromagnetic currents, which is related to sigma/sub tot/ (e/sup +/e/sup -/ ..-->.. hadrons).« less