Planck scale boundary conditions in the standard model with singlet scalar dark matter

We investigate Planck scale boundary conditions on the Higgs sector of the standard model with a gauge singlet scalar dark matter. We will find that vanishing self-coupling and Veltman condition at the Planck scale are realized with the 126 GeV Higgs mass and top pole mass, 172 GeV $\lesssim M_t\lesssim$ 173.5 GeV, where a correct abundance of scalar dark matter is obtained with mass of 300 GeV $\lesssim m_S \lesssim$ 1 TeV. It means that the Higgs potential is flat at the Planck scale, and this situation can not be realized in the standard model with the top pole mass.

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