First study of the gluon-quark-antiquark static potential in SU(3) Lattice QCD

We study the long distance interaction for hybrid hadrons, with a static gluon, a quark and an antiquark with lattice QCD techniques. A Wilson loop adequate to the static hybrid three-body system is developed and, using a 24^3 x 48 periodic lattice with beta=6.2 and a ~ 0.075 fm, two different geometries for the gluon-quark segment and the gluon-antiquark segment are investigated. When these segments are perpendicular, the static potential is compatible with confinement realized with a pair of fundamental strings, one linking the gluon to the quark and another linking the same gluon to the antiquark. When the segments are parallel and superposed, the total string tension is larger and agrees with the Casimir Scaling measured by Bali. This can be interpreted with a type-II superconductor analogy for the confinement in QCD, with repulsion of the fundamental strings and with the string tension of the first topological excitation of the string (the adjoint string) larger than the double of the fundamental string tension.