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

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.