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 2 to 3 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% for the variational states used in this study, at the largest value of beta=4/g(2)=2.4 considered.