F. Zachariasen

Dual QCD: A review

Abstract We review the attempts to use dual (electric) vector potentials rather than the standard magnetic vector potentials to describe QCD, particularly in the infrared regime. The use of dual potentials is motivated by the fact that in classical electrodynamics, in a medium with a dielectric constant vanishing at small momenta (as is believed to be the case in QCD), electric potentials provide a far more convenient language than do magnetic potentials. To begin with, we outline attempts to construct the QCD Lagrangian in terms of dual potentials and describe the various possibilities, their shortcomings and advantages, which so far exist. We then proceed to use the most attractive (albeit consistent as a field theory only at the tree leve l) of these Lagrangians in a number of applications. We show that it describes a non-Abelian dual superconductor (so that it automatically confines color), derive the static quark-antiquark potential, and various temperature dependent effects, such as deconfinement and chiral symmetry breaking.

The quark propagator in axial gauge

Abstract We study the Dyson equation for the quark propagator S ( p ) in QCD, making use of both the Ward identity and an infrared singular gluon propagator naively corresponding to a linear confining potential. We find that, assuming massless free quarks, the singularity at p 2 = 0 in S ( p ) is greatly softened by the gluon infrared singularity, perhaps hinting at confinement. We also find that chiral symmetry may be, but does not have to be, broken.

Self-consistent diffraction in the multiperipheral model☆

Abstract An exact self-consistent solution, for small t and very large s, of the multiperipheral bootstrap equations is presented. The solution predicts that total cross sections grow like log s, that elastic total cross sections are constant, that elastic diffraction peaks shrink like (log s)2, and that multiplicities grow like log s, all in the limit of infinite s.

Comparison of lattice and dual QCD results for heavy quark potentials

Lattice results and dual QCD results for all heavy quark potentials through order (quark mass)-2 are exhibited and compared. The agreement on the whole is quite good, confirming the validity of dual QCD.

Infrared properties of the gauge theory coupling constant III

Abstract In previous papers we have outlined a program for deriving the infrared behavior of the axial gauge gluon propagator in a pure Yang-Mills theory. The program is based on an integral equation for the gluon propagator derived from the Dyson equation and the Ward identities. Here we present a solution to this equation, obtained numerically. The solution exhibits a Singularity in the infrared, and therefore presumably predicts confinement of color. The method is supposed to be exact in the infrared. Away from the infrared, therefore, our solution is only approximate. Nevertheless, even in the ultraviolet, our solution for the propagator is not very different from the known asymptotic freedom result, so it may be that it is a reasonable approximation over the entire range of momentum.

Unitary non-shrinking diffraction peaks

Abstract A simplified model of n-particle production amplitudes is constructed, which, combined with unitary, yields a non-shrinking elastic scattering amplitude, and an integral equation which can be used to determine the shape of the diffraction peak.

The radius of the pomeron and absorptive cuts

Abstract It is pointed out that absorption in quantum number exchange two-body reactions with a Pomeron whose radius in impact parameter is proportional to log s, and whose opacity is not totally black, yields singularities which, asymptotically, are dominated for all t by the original Regge pole. Thus for such Pomerons, in the limit of infinite energy, the simple phenomenology associated with pure Regge pole exchange should be valid.

Experimental consequences of a multiperipheral bootstrap model

Abstract Lower energy corrections to a recently proposed model of high energy elastic scattering are estimated and the predictions of the model compared with experiment. The agreement with the t-dependence of pp elastic differential cross sections at small t is excellent, but the agreement with the s-dependence is less compelling.

A CONSTITUENT QUARK-ANTIQUARK EFFECTIVE LAGRANGIAN BASED ON THE DUAL SUPERCONDUCTING MODEL OF LONG DISTANCE QCD

We review the assumptions leading to the description of long distance QCD by a Lagrangian density expressed in terms of dual potentials. We find the color field distribution surrounding a quark-antiquark pair to first order in their velocities. Using this distribution we eliminate the dual potentials from the Lagrangian density and obtain an effective interaction Lagrangian LI(x1, x2; v1, v2) depending only upon the quark and antiquark coordinates and velocities, valid to second order in their velocities. We propose LI as the Lagrangian describing the long distance interaction between constituent quarks. In this paper, for simplicity of presentation, we treat the quarks as classical particles.

QCD based spin-orbit potential between heavy quarks

Abstract We calculate the spin-orbit potential between a heavy quark-antiquark pair using dual potentials to describe long distance Yang-Mills theory.