Vanishing Higgs potential at the Planck scale in a singlet extension of the standard model

Understand

We discuss the realization of a vanishing effective Higgs potential at the Planck scale, which is required by the multiple-point criticality principle (MPCP), in the standard model with singlet scalar dark matter and a right-handed neutrino.

• We find the scalar dark matter and the right-handed neutrino play crucial roles for realization of the MPCP, where a neutrino Yukawa becomes effective above the Majorana mass of the right-handed neutrino.
• Once the top mass is fixed, the MPCP at the (reduced) Planck scale and the suitable dark matter relic abundance determine the dark matter mass, $m_S$, and the Majorana mass of the right-handed neutrino, $M_R$, as $8.5~(8.0)\times10^2~{\rm GeV}\leq m_S\leq1.4~(1.2)\times10^3~{\rm GeV}$ and $6.3~(5.5)\times10^{13}~{\rm GeV}\leq M_R\leq1.6~(1.2)\times10^{14}~{\rm GeV}$ within current experimental values of the Higgs and top masses.
• This scenario is consistent with current dark matter direct search experiments, and will be checked by future experiments such as LUX with further exposure and/or the XENON1T.