Massive or 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. 1 The model Recently, Dick and Fulcher [1] have proposed an interesting model where the lowest glueball, represented by a massive scalar field φ, has been in a non-minimal way coupled to the SU(2) gauge fields. They have chosen, in analogy with the chiral quark models [2], one–glueball coupling: φF F a μν . Their model provides confinement of quarks and gives a quite reasonable [email protected] [email protected]