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

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

2000-12-31

arxiv.org/abs/hep-ph/0101007v1

Phys.Lett.B499:135-140,2001

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/S0370-2693(01)00008-9

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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