Cubic Casimir operator of SUc(3) and confinement in the nonrelativistic quark model

Only two-body [F-i.F-j] confining potentials have been considered, thus far , in the quark model without gluons, which by construction can only depend on the quadratic Casimir operator of the colour SU(3) group. A three-quark potential that depends on the cubic Casimir operator is added to the quark model. This results in improved properties of q(3) colour nonsinglet states , which can now be arranged to have (arbitrarily) higher energy than the si nglet, and the "colour dissolution/anticonfinement" problem of the F-i.F-j model is avoided. (C) 2001 Elsevier Science B,V. All rights reserved.