  The lattice SU(2) gauge-scalar model with the scalar field in the adjoint
representation of the gauge group has two completely separated confinement and
Higgs phases according to the preceding studies based on numerical simulations
which have been performed in the specific gauge fixing based on the
conventional understanding of the Brout-Englert-Higgs mechanism.
  In this paper, we re-examine this phase structure in the gauge-independent
way based on the numerical simulations performed without any gauge fixing. This
is motivated to confirm the recently proposed gauge-independent
Brout-Englert-Higgs mechanism for generating the mass of the gauge field
without relying on any spontaneous symmetry breaking. For this purpose we
investigate correlation functions between gauge-invariant operators obtained by
combining the original adjoint scalar field and the new field called the
color-direction field which is constructed from the gauge field based on the
gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov
and Faddeev-Niemi.
  Consequently, we reproduce gauge-independently the transition line separating
confinement phase and Higgs phase, and show surprisingly the existence of a new
transition line that divides completely the confinement phase into two parts.
Finally, we discuss the physical meaning of the new transition and implications
to confinement mechanism.
