Perturbative Vacuum Research Articles

Color-singlet condensation in quantum chromodynamics and flux squeezing

The nonperturbative condensation of the operator G/sub munu/ /sup 2/ in quantum chromodynamics is discussed using the renormalization-group technique. It is shown that magnetic condensation, >0, leads to a new vacuum which has lower energy than the perturbative vacuum. From this fact it is concluded that Green's functions calculated in the normal vacuum have tachyonic singularities. By assuming the gauge-invariant local expansion of the effective action it is shown that the condensed vacuum has the property of a vanishing dielectric constant. If the color electric field is applied by introducing heavy quarks at infinity, the condensation is partly broken and there is a consistent solution in which an infinite tube of the color electric flux is formed. Arguments used rely heavily on the instability of the normal vacuum and on the negative character of the ..beta.. function. An attempt at the mean-field-type approximation is made. Comparison with the previous phenomenological approach is also given.

QCD Vacuum in the Strong External Fields

In the very strong external gauge field the QCD true vacuum is shown to have lower energy than the perturbative vacuum. By using the same calculation a possibility of restoration of the spontaneously broken chiral symmetry of the vacuum is pointed out.

Non-abelian gauge theories in a background field

Green functions of on-mass-shell transverse gauge fields in a background gauge are proved to be obtained from Green functions in the perturbative vacuum by a mere translation.

Instanton Effects on the Exotic Meson (Q2Formula2) Spectroscopy

The effects of the effective determinantial interaction on the exotic meson (Q'Q') mass spectra are studied. The effective interaction is related to the Fermion zero mode of the background instanton field and is introduced by 't Hooft. The mass shift due to the effective interaction is obtained by the first order perturbation calculation. Our results are expressed by the ground state quark wave function, inside the hadron. The numerical calcula­ tion is carried out by borrowing the quark wave function of the MIT bag model. From our analysis it is found that the study of the pattern of mass shift of Q'Q' states will offer information on the distributions of instantons inside the hadron. is studied in the framework of dilute gas approximation by group. 3' Horn and Yankielowicz 4' studied the effect of the determinantial interaction on ordinary meson and baryon spectra by combined use of QCD and MIT bag model, and succeeded in explaining the n: and r; mass difference. In this article we study its effect on the exotic meson (Q2Q2) spectra. The level shifts due to the determinantial interaction are obtained in the lowest order perturbation calculation. Recently, group has studied the confinement mechanism in QCD, and proposed the Princeton 5' In this model, the instantons and merons conden­ sate in the vacuum, and inside the hadron the perturbative vacuum is realized. And the instantons are distributed in the fringe of the hadron. It is a very in­ teresting problem to study the mass spectra of hadrons in the bag model but it has not been carried out yet. Our results for the level shifts due to the determinantial interaction are ex­ pressed by the quark wave function inside the hadron and are applicable to wider models of hadron. It is more interesting to study the mass shifts of the exotic mesons in the framework of QCD; namely, by using the bag model. But unfortunately we have not obtained the quark wave function inside the Prince­ ton bag. Then in carrying out the numerical calculation of the mass shifts, we have borrowed the quark wave function of the MIT bag model,6''n on the assump-

Approximate QCD lower bound for the bag constant B

Using an article by Savvidy from 1977 in which a state in QCD with lower energy than the perturbative vacuum was found, we calculate an approximate lower bound for the MIT bag constant B relative to the QCD coupling parameter Λ. With an MIT bag constant B 1/4 = 145 MeV we find Λp ⩽ 0.89 GeV when the propagator of the gluon is used to renormalize the coupling constant.

A further pathology of the Coulomb gauge in non-abelian Yang-Mills theories

In the first part the vacuum structure of SU(2) Yang-Mills theories in the Coulomb gauge is discussed. It is proved that the only transverse pure gauge field A μ( x) = U −1 ϖ μ U with U( x) r→∞ → const. is the trivial one A μ ( x) ≡ 0; the features of other possible vacua with U(x) r→∞ → U(θ, ¢p) are studied. In the second part, regular Euclidean configurations that connect a vacuum state at x 4 = −∞ to another at x 4 = +∞ are discussed. It is proved, always working in the Coulomb gauge, that the perturbative vacuum A μ ( x) ≡ 0 cannot tunnel into any other one and that regular configurations with non-vanishing Pontryagin number q cannot affect such a vacuum. Moreover, strong arguments are given to show that many-instanton configurations (| q|⩾2) cannot be expressed at all in the Coulomb gauge, that is by a regular field A μ satisfying the transversality condition ϖ i A i ( x, x 4) = 0.

Instantons and Restoration of Symmetries

Effects of instantons in gauge theories of the Higgs type are investigated. In the two-dimensional Abelian Higgs model and the three-dimensional Georgi-Glashow model, it is shown that the vacuum expectation values of the Higgs scalars vanish, and the global gauge invariance, which is spontaneously broken in the perturbative vacuum, is restored due to the effects of instantons. Four-dimensional models are briefly discussed.

Inclusive distributions for Reggeon theory on a transverse lattice

We compute high-energy inclusive distributions for a pomeron intercept α larger than one. The framework is cut reggeon field theory (CRFT) where the inclusive amplitudes are expressed in terms of certain mass insertion Green functions. We generalize to CRFT the spin model on a transverse lattice recently proposed for Gribov's theory. We show that, for α > 1 there are four states degenerate with the “perturbative vacuum” φ 0. Local operators, such as creation of pomerons and mass insertions, acting on the φ 0 vacuum, generate a disturbance that expands in transverse space toward one of the other vacua with definite velocity. The study of this dynamical vacuum instability, similar to the one of Gribov's theory, allows to evaluate the inclusive distributions, which in one transverse dimension and for α very large, are computed exactly. The resulting distributions violate logarithmically Feynman scaling and have long range correlations. Inelastic unitary is satisfied in the form of energy-momentum conservation and positivity of cross sections. We discuss also the generalization to higher transverse dimensions and smaller α.

One-component formulation of Reggeon field theory

We present a nonperturbative formulation of the anti-Hermitian cubic Reggeon field theory (RFT) in terms of a single field $\ensuremath{\chi}$. We analyze the structure of RFT as ${\ensuremath{\alpha}}_{0}$ is increased above 1 and clarify the relation between the perturbative vacuum and the classical stationary points. A canonical transformation is performed so that the new Hamiltonian depends on the sign of ${\ensuremath{\Delta}}_{0}\ensuremath{\equiv}1\ensuremath{-}{\ensuremath{\alpha}}_{0}$ only through a potential of the Landau-Ginzburg type. Our one-component theory is normal-ordered with respect to the original Pomeron field without tadpoles, and it allows a path-integral formalism with undistorted contours. For $\frac{|{\ensuremath{\Delta}}_{0}|}{{g}_{0}}$ large and ${\ensuremath{\Delta}}_{0}<0$, we formulate two different and yet equivalent analog models. We unambiguously derive an analog model in terms of a single classical spin at each rapidity-impact-parameter site. Through the use of an asymmetrical transfer matrix, we obtain a kinklike ground-state configuration for the $D = 0$ model. Alternatively, by going on a lattice for the impact-parameter space only, we arrive at a quantum lattice-spin model. We explicitly demonstrate that the quantum spin model at $D = 0$ is equivalent to the classical lattice spin model.