Eur. Phys. J. Plus (2014) 129: 108
https://doi.org/10.1140/epjp/i2014-14108-1

Regular Article

A confining model for charmonium and new gauge-invariant field equations

Department of Physics, University of Massachusetts Dartmouth, 02747-2300, North Dartmouth, MA, USA

^* e-mail: jhsu@umassd.edu

Received: 20 March 2014
Revised: 6 April 2014
Accepted: 23 April 2014
Published online: 3 June 2014

Abstract

We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized SU₃ gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions ω _ω ^a (x). These transformations reduce to the usual SU₃ gauge transformations in the special case ω _μ ^a (x) = ∂ _μ ξ ^a (x). Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless gauge boson has non-definite energy. However, the new gauge boson is permanently confined in a quark system by the linear potential. We use the empirical potentials of the Cornell group for charmonium to obtain the coupling strength f ²/(4π) ≈ 0.19 for the strong interaction. Such a confining model of quark dynamics could be compatible with perturbation. The model can be applied to other quark-antiquark systems.