Abstract
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.
Highlights
JHEP04(2014)029 quadratic divergence for the Higgs mass disappear at the Planck scale under the Veltman condition (the vanishing anomalous dimension γmh(Mpl) = 0)
We will find that vanishing selfcoupling and Veltman condition at the Planck scale are realized with the 126 GeV Higgs mass and top pole mass, 172 GeV Mt 173.5 GeV, where a correct abundance of scalar dark matter is obtained with mass of 300 GeV mS 1 TeV
We will find that the vanishing selfcoupling and Veltman condition at the Planck scale are realized with the 126 GeV Higgs mass and top pole mass, 171.8 GeV Mt 173.5 GeV, where a correct abundance of scalar dark matter is obtained with mass of 300 GeV mS 1 TeV
Summary
We consider the SM with a gauge singlet real scalar S, and investigate the values of scalar quartic couplings at the Planck scale by solving renormalization group equations (RGEs) in the model. It is known as the vacuum instability that the value of λ becomes negative before the Planck scale in the SM with the experimental center values of the Higgs and top masses This is due to the negative contribution from the top Yukawa coupling to the β-function of λ as in eq (2.5). Once the gauge singlet scalar is added to the SM, the additional contribution of k2/2 with the plus sign appears in the β-function of λ This contribution can lift the running of λ, and λ can be around zero at the Planck scale. The position of the minimum in the running of λ comes to lower energy scale than O(1017) GeV by adding the gauge singlet scalar because the contribution of k2/2 in eq (2.5) becomes large at a high energy scale compared to the electroweak (EW) scale.
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