  According to the preceding studies, the lattice SU(2) gauge-scalar model with
a single scalar field in the fundamental representation of the gauge group has
a single confinement-Higgs phase where confinement and Higgs regions are
subregions of an analytically continued single phase and there are no
thermodynamic phase transitions, which is a well-known consequence of the
Osterwalder-Seiler-Fradkin-Shenker theorem. In this paper, we show that we can
define new types of gauge-invariant operators by combining the original
fundamental 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.
By performing the numerical simulations on the lattice without any gauge
fixing, we reproduce the conventional thermodynamic transition line in the weak
gauge coupling, and moreover we find a new transition line detected by the new
gauge-invariant operators which separates the confinement-Higgs phase into two
parts, confinement phase and the Higgs phase, 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 discuss a physical
interpretation for the new transition from the viewpoint of the realization of
a global symmetry.
