Shadow Higgs from a scale-invariant hidden $U(1)_s$ model

We study a scale invariant $SU(2)\times U(1)_Y \times U(1)_s$ model which has only dimensionless couplings. The shadow $U(1)_s$ is hidden, and it interacts with the Standard Model (SM) solely through mixing in the scalar sector and kinetic mixing of the U(1) gauge bosons. The gauge symmetries are broken radiatively by the Coleman-Weinberg mechanism. Lifting of the flat direction results in a light shadow Higgs or "scalon", and a heavier scalar which we identify as the SM Higgs boson. The phenomenology of this model is discussed. It is possible that shadow Higgs boson can be discovered in precision $t$-quark studies at the LHC. The conditions that it be a dark matter candidate is also discussed.