  The Complex singlet extension of the Standard Model (CxSM) is the simplest
extension that provides scenarios for Higgs pair production with different
masses. The model has two interesting phases: the dark matter phase, with a
Standard Model-like Higgs boson, a new scalar and a dark matter candidate; and
the broken phase, with all three neutral scalars mixing. In the latter phase
Higgs decays into a pair of two different Higgs bosons are possible. In this
study we analyse Higgs-to-Higgs decays in the framework of singlet extensions
of the Standard Model (SM), with focus on the CxSM. After demonstrating that
scenarios with large rates for such chain decays are possible we perform a
comparison between the NMSSM and the CxSM. We find that, based on
Higgs-to-Higgs decays, the only possibility to distinguish the two models at
the LHC run 2 is through final states with two different scalars. This
conclusion builds a strong case for searches for final states with two
different scalars at the LHC run 2. Finally, we propose a set of benchmark
points for the real and complex singlet extensions to be tested at the LHC run
2. They have been chosen such that the discovery prospects of the involved
scalars are maximised and they fulfil the dark matter constraints. Furthermore,
for some of the points the theory is stable up to high energy scales. For the
computation of the decay widths and branching ratios we developed the Fortran
code, sHDECAY, which is based on the implementation of the real and complex
singlet extensions of the SM in HDECAY.
