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A confining quark model and new gauge symmetry

We discuss a confining model for quark-antiquark system with a new color $SU_3$ gauge symmetry. New gauge transformations involve non-integrable phase factors and lead to the fourth-order gauge field equations and a linear potential. The massless gauge bosons have non-definite energies, which are not observable because they are permanently confined in quark systems by the linear potential. We use the empirical potentials of charmonium to determine the coupling strength of the color charge $g_s$ and find $g_s^2/(4π) \approx 0.2.$ We discuss Feynman-Dyson rules for the confining quark model, which involve propagators with poles of order 2 associated with new gauge fields. The confining quark model may be renormalizable by power counting and compatible with perturbation theory.