Motivated by the dark matter and the baryon asymmetry problems, we analyze a complex singlet extension of the Standard Model with a ${\mathbb{Z}}_2$ symmetry (which provides a dark matter candidate). After a detailed two-loop calculation of the renormalization group equations for the new scalar sector, we study the radiative stability of the model up to a high energy scale (with the constraint that the 126 GeV Higgs boson found at the LHC is in the spectrum) and find it requires the existence of a new scalar state mixing with the Higgs with a mass larger than 140 GeV. This bound is not very sensitive to the cutoff scale as long as the latter is larger than ${10}^{10}\mathrm{GeV}$. We then include all experimental and observational constraints/measurements from collider data, from dark matter direct detection experiments, and from the Planck satellite and in addition force stability at least up to the grand unified theory scale, to find that the lower bound is raised to about 170 GeV, while the dark matter particle must be heavier than about 50 GeV.

• Received 7 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.025024