  We study the coupled system consisting of a complex matter scalar field, a
U(1) gauge field, and a complex Higgs scalar field that causes spontaneously
symmetry breaking. We show by numerical calculations that there are spherically
symmetric nontopological soliton solutions. Homogeneous balls solutions, all
fields take constant values inside the ball and in the vacuum state outside,
appear in this system. It is shown that the homogeneous balls have the
following properties: charge density of the matter scalar field is screened by
counter charge cloud of the Higgs and gauge field everywhere; an arbitrary
large size is allowed; energy density and pressure of the ball behave
homogeneous nonrelativistic gas; a large ball is stable against dispersion into
free particles and against decay into two smaller balls.
