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

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 ωa (x). These transformations reduce to the usual SU3 gauge transformations in the special case ω μa (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. © 2014 Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg.