Confining Quark Model with General Yang-Mills Symmetry and Inadequate Faddeev-Popov Ghost

Abstract

A quark model with general Yang-Mills $SU_3$ symmetry leads to fourth-order field equations and linear confining potential. The confining gauge bosons (`confions') are treated as off-mass-shell particles and their indefinite energies are unobservable due to confinement. The ultraviolet divergence of the model appears to be no worse than that of QCD by power counting. Explicit calculations of the confion self-energy show that the usual Faddeev-Popov ghosts are inadequate to restore gauge symmetry for gauge invariant Lagrangians with higher order derivatives. `Computer experiments' with FeynCalc lead to a simple empirical method to restore the gauge invariance of the second-order confion self-energy with arbitrary gauge parameters. The approximate results of third-order vertex corrections suggest that the confining model could be asymptotically free.