Massive and Massless Scalar Field and Confinement

Generalization of QCD motivated classical SU(2) Yang--Mills theory coupled to the scalar field is discussed. The massive scalar field, corresponding the scalar glueball, provides a confining potential for static, point-like, external sources. In case of massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions are compared with phenomenological potentials. The case of non-dynamical permittivity is also discussed.