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 singlet, and the colour dissolution/anticonfinement problem of the F-i.F-j model is avoided. (C) 2001 Elsevier Science B,V. All rights reserved