Gluon chains and the quark-antiquark potential

TL;DR

This paper investigates the quark-antiquark potential using a gluon-chain model in Coulomb gauge, showing that including gluonic states reduces the discrepancy between the Coulomb potential and the true string tension.

Contribution

It introduces a lattice gauge theory approach diagonalizing the transfer matrix with gluonic states, improving the understanding of the quark-antiquark potential.

Findings

Coulomb potential overshoots true string tension by a factor of three.

Including gluonic states reduces the discrepancy to about 1.4 times.

The minimal energy state exhibits a linearly rising potential.

Abstract

The flux tube between a quark and an antiquark in Coulomb gauge is imagined in the gluon-chain model as a sequence of constituent gluons bound together by Coulombic nearest-neighbor interactions. We diagonalize the transfer matrix in SU(2) lattice gauge theory in a finite basis of states containing a static quark-antiquark pair together with zero, one, and two gluons in Coulomb gauge. We show that while the string tension of the color-Coulomb potential (obtained from the zero-gluon to zero-gluon element of the transfer matrix) overshoots the true asymptotic string tension by a factor of about three, the inclusion of a few states with constituent gluons reduces the discrepancy considerably. The minimal energy eigenstate of the transfer matrix in the zero-, one-, and two-gluon basis exhibits a linearly rising potential with the string tension only about 1.4 times larger than the asymptotic one.