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

TL;DR

This paper proposes a quark confinement model based on a generalized Yang-Mills symmetry that results in higher-order equations, explores the limitations of Faddeev-Popov ghosts, and suggests a new empirical approach to restore gauge invariance, indicating potential asymptotic freedom.

Contribution

It introduces a novel confining quark model with higher-order derivatives and develops an empirical method to restore gauge invariance where traditional ghosts are inadequate.

Findings

Confions are off-mass-shell with unobservable indefinite energies.

Faddeev-Popov ghosts are insufficient for gauge invariance in higher-derivative models.

The model shows signs of being asymptotically free.

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.