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

Abstract 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 singlet, and the “colour dissolution/anticonfinement” problem of the F i ·F j model is avoided.