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

V. Dmitrasinovic
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Abstract

Only two-body [${\rm F}_{i} \cdot {\rm F}_{j}$] 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 ${\rm F}_{i} \cdot {\rm F}_{j}$ model is avoided.

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V. Dmitrasinovic. 2000-12-31. Cubic Casimir operator of SU$_C$(3) and confinement in the nonrelativistic quark model. https://doi.org/10.1016/s0370-2693(01)00008-9

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