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.

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

Cited by in corpus (22)

• Dibaryons in a constituent quark model
• Do $c\bar{c}n\bar{n}$ bound states exist?
• Probabilities in nonorthogonal basis: Four--quark systems
• Tetraquark Spectroscopy: A Symmetry Analysis
• Production and detection of doubly charmed tetraquarks
• On a three-body confinement force in hadron spectroscopy
• Many-body forces with the envelope theory
• Partial conservation of the axial current and axial exchange currents in the nucleon
• Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
• On the smooth cross-over transition from the Delta-string to the Y-string three-quark potential
• On the Casimir operator dependences of QCD amplitudes
• Describing non-$q\bar{q}$ candidates
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Casimir operator dependences of non-perturbative fermionic QCD amplitudes
• Improvement of the Envelope Theory for Systems with Different Particles
• Three-body confinement force in a realistic constituent quark model
• Tests of the envelope theory for three-body forces
• Three-body Forces in Oscillator Bases Expansion
• Diquarkyonic matter: quarks, diquarks and baryons
• Molecular and compact four-quark states
• Stability of pentaquarks with a two- plus three-body chromoelectric interaction
• Introducing SU(3) color charge in undergraduate quantum mechanics