  The lattice gauge-scalar model with the scalar field in the fundamental
representation of the gauge group has a single confinement-Higgs phase which is
well-known as the Fradkin-Shenker-Osterwalder-Seiler analytic continuity
theorem: Confinement and Higgs regions are subregions of an analytically
continued single phase and there are no thermodynamics phase transitions
between them. In this talk, however, we show that we can define new type of
operators which enable to separate completely the confinement phase and the
Higgs phase. In fact, they are constructed in the gauge-invariant procedure by
combining the original scalar field and the so-called color-direction field
which is obtained by change of field variables based on the gauge-covariant
decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi.
We perform the numerical simulations for the model with SU(2) gauge group
without any gauge fixing and find a new transition line which agrees with the
conventional thermodynamic transition line in the weak gauge coupling and
divides the confinement-Higgs phase into two separate phases, confinement and
the Higgs, in the strong gauge coupling. All results are obtained in the
gauge-independent way, since no gauge fixing has been imposed in the numerical
simulations. Moreover, we give a physical interpretation for the new transition
from the viewpoint of the spontaneous breaking of a global symmetry. This talk
is based on the preprint [1].
