Gauge-invariant formalism and quark confinement in QCD2

New gauge-invariant vector and spinor fields are introduced. Gauge-invariant quark propagator is defined in terms of these new fields. The equation for such a propagator, taken in 1/N approximation, does not require the introduction of an infrared regularization. As the regularization parameter in our approach there stands such a parameter which limit value corresponds to the gauge-invariant fields and translationally invariant quark propagator. It is shown that in this limit the pole of the gauge-invariant quark propagator shifts towards infinity what is usually treated as the confinement of a single quark.     

A new energy-dependent quark interaction from a Tamm-Dancoff reduction of an effective field theory quark model

A new quark interaction is derived, by means of a Tamm-Dancoff reduction, from an effective field theory constituent quark model. In contrast to the standard Coulombic potential, the obtained interaction is nonlocal and energy dependent. Furthermore, it becomes positive and rises up to a maximum value when the interquark distance increases, partially resembling some aspects of the phenomenological Cornell potential.     

Dynamical mass function of quark and effective potential in QCD

Direct variational method is applied to the problem of the dynamical breaking of chiral symmetry in QCD. The minimum of the effective potential corresponding to the phase with spontaneous chiral symmetry breaking is found.     

Test of the Skyrme effective field theory using quenched lattice QCD

The Skyrme effective field theory is tested by evaluating nucleon ground-state matrix elements of the correlation functions for two flavor density operators and two pseudoscalar density operators in the Skyrme model and comparing them with results in quenched lattice QCD. The possibility of using quenched lattice QCD to study higher-order terms in effective field theory is also discussed.     

Gauge-invariant bilocal formalism in quantum field theory

A gauge-invariant continuation of the S-matrix generating functional outside the mass shell is proposed. A generating functional of gauge-invariant Green functions is obtained. Using the path integral formalism, collective gauge-invariant bilocal field variables are introduced. With the aid of the bilocal formalism, an integral equation is obtained for the gauge-invariant spinor propagator. It is shown that the propagator of the bilocal field corresponds to the gauge-invariant wave function of a two-particle system in ladder approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 105–111, April, 1990.The authors thank A. N. Sisakyan, N. B. Skachkov, and O. Yu. Shevchenko for their interest to this work and useful discussions of the obtained results.     

Structure of the exact effective action and quark confinement in MSSM QCD

An expression for the exact (beyond perturbation theory) effective action in N=1 supersymmetric gauge theories where all particles, with the exception of gauge bosons, are massive is proposed. By analyzing the form of this expression, it is shown that, in supersymmetric theories, instanton effects can lead to quark confinement. On the basis of first principles, the characteristic scale of confinement is calculated within MSSM QCD, and the result is found to be consistent with experimental data. The proposed explanation differs drastically with the dual Higgs mechanism.     

High-energy QCD as a topological field theory

We propose an identification of the conformal field theory underlying Lipatov's spin-chain model of high-energy scattering in perturbative QCD. It is a twisted N = 2 supersymmetric topological field theory, which arises as the limiting case of the SL(2,R)/U(1) non-linear model that also plays a role in describing the Quantum Hall effect and black holes in string theory. The doubly-infinite set of non-trivial integrals of motion of the high-energy spin-chain model displayed by Faddeev and Korchemsky are identified as the Cartan subalgebra of a bosonic sub-symmetry possessed by this topological theory. The renormalization group and an analysis of instanton perturbations yield some understanding why this particular topological spin-chain model emerges in the high-energy limit, and provide a new estimate of the asymptotic behaviour of multi-Reggeized-gluon exchange. Received: 31 August 1998 / Published online: 11 March 1999     

The Skyrme model,the strong coupling theory and the static quark model

We show that to leading order in the quark number N, the Skyrme model, the strong coupling theory and the static quark model share a common underlying symmetry group.     

The β-function for effective quark masses to two loops in QCD

We calculate the evolution equation for effective masses in QCD to two loops in the minimal subtraction scheme of 't Hooft. We compare our result with two other recent calculations and make some comments on the gauge independence and regularization dependence of the β-functions.     

Electroweak Higgs boson production in the standard model effective field theory beyond leading order in QCD

We study the impact of dimension-six operators of the standard model effective field theory relevant for vector-boson fusion and associated Higgs boson production at the LHC. We present predictions at the next-to-leading order accuracy in QCD that include matching to parton showers and that rely on fully automated simulations. We show the importance of the subsequent reduction of the theoretical uncertainties in improving the possible discrimination between effective field theory and standard model results, and we demonstrate that the range of the Wilson coefficient values allowed by a global fit to LEP and LHC Run I data can be further constrained by LHC Run II future results.