From screening to confinement in a Higgs-like model

We investigate a recently proposed Higgs-like model [G. Gabadadze, R.A. Rosen, arXiv:0811.4423 [hep-th]], in the framework of a gauge-invariant but path-dependent variables formalism. We compute the static potential between test charges in a condensate of scalars and fermions. In the case of charged massive scalar we recover the screening potential. On the other hand, in the Higgs case, with a “tachyonic” mass term and a quartic potential in the Lagrangian, unexpected features are found. It is observed that the interaction energy is the sum of an effective-Yukawa and a linear potential, leading to the confinement of static charges.