Constituent Gluon Content of the Static Quark-Antiquark State in Coulomb Gauge

TL;DR

This study investigates the gluon content in static quark-antiquark states using lattice SU(2) gauge theory, revealing that including gluon states reduces the discrepancy in the string tension compared to the standard potential.

Contribution

It introduces a variational Monte Carlo approach to compute the transfer matrix with gluon states, providing insights into flux tube formation and the gluon-chain model.

Findings

Adding gluon states reduces the discrepancy in string tension to 38%.

The potential remains linear with gluon states, aligning more closely with the standard string tension.

The Coulomb potential's slope is significantly larger than the asymptotic string tension.

Abstract

Motivated by the gluon-chain model of flux tube formation, we compute and diagonalize the transfer matrix in lattice SU(2) gauge theory for states containing heavy static quark-antiquark sources, with separations up to one fermi. The elements of the transfer matrix are calculated by variational Monte Carlo methods, in a basis of states obtained by acting on the vacuum state with zero, one, and two-gluon operators in Coulomb gauge. The color Coulomb potential is obtained from the zero gluon to zero gluon element of the transfer matrix, and it is well-known that while this potential is asymptotically linear, it has a slope which is two to three times larger than the standard asymptotic string tension. We show that the addition of one and two gluon states results in a potential which is still linear, but the disagreement with the standard asymptotic string tension is reduced to 38% at the largest lattice coupling we have studied.