$λϕ^4$ model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Abstract

Basing on new regularization-renormalization method, the $λϕ^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($μ_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($μ_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $μ_c\approx 0.547\times 10^{15}$GeV and $μ_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.