Nambu–Jona-Lasinio model with the homogeneous background gluon field

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Abstract
Starting with the Euclidean generating functional of QCD we construct a generalization of the Nambu–Jona-Lasinio model, taking into account the homogeneous background gluon field, which ensures an analytical quark confinement. Colorless modes are determined by the confined gluons and are described by the nonlocal quark currents with appropriate radial and angular quantum numbers. The effective Lagrangian for the local meson fields corresponds to ultraviolet finite theory. The spectrum of the radial and orbital excitations is asymptotically equidistant; i.e., it has a qualitatively correct Regge behavior. It is found that in the heavy quark limit the mass of quarkonium tends to be equal to the sum of the masses of the constituent quarks.