  In this note we propose an overview on the current theoretical and
experimental limits on a Higgs singlet extension of the Standard Model. We
assume that the Boson which has recently been measured by the LHC experiments
is the lightest Higgs boson of such model, while for the second Higgs Boson we
consider a mass range of 600 GeV to 1 TeV, i.e. outside the range of the direct
searches presented so far. In this light, we study the impact of perturbative
unitarity limits, Renormalisation Group Equations analysis and experimental
constraints (Electro-Weak Precision Tests, measurements of the light Higgs
coupling at the Large Hadron Collider). We show that, in the case of no
additional hidden sector contributions, the largest constraints for higher
Higgs masses stem from the assumption of perturbativity as well as vacuum
stability for scales on the order of the SM metastability scale, and that the
allowed mixing range is severely restricted. We discuss implications for
current LHC searches in the singlet extension, especially the expected
suppression factors for SM-like decays of the heavy Higgs. We present these
results in terms of a global scaling factor as well as the total width of the
new scalar.
