  We discuss the vacuum energy density term resulting from the spontaneous
breakdown of the electroweak gauge symmetry, in the Higgs Mechanism. We
alternatively expand the scalar field at one of the degenerate states that lie
outside the circle of minimum, such that the Higgs Potential becomes free of
any constant field term, and describes a true vacuum. We show that this true
vacuum requires a slightly smaller quartic coupling, if the same $v$ and $m_H$
values of the electroweak model are imposed. We propose that this small
difference (exactly 20 percent) can be utilized as a test to distinguish and
identify the true vacuum, in future experiments at LHC. We shortly discuss the
resulting new Higgs Potential, and its cosmological implications.
