Cubic Casimir operator of SU${}_C$(3) and confinement in the nonrelativistic quark model

Abstract

Only two-body [${\mathrm{F}}_i\cdot {\mathrm{F}}_j$] 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 non-singlet states, which can now be arranged to have (arbitrarily) higher energy than the singlet, and the "colour dissolution/anticonfinement" problem of the ${\mathrm{F}}_i\cdot {\mathrm{F}}_j$ model is avoided.

Comments: 10 pages, 2 tables, RevTex, to appear in Phys. Lett. B