Higgs Mass from Casimir Energy Induced Cosmological Constant in the Standard Model

Abstract

Casimir vacuum energy is divergent. It needs to be regularized. The regularization introduces a renormalization scale which may lead to a scale dependent cosmological constant. We show that the requirement of physical cosmological constant is renormalization scale independent provides important constraints on possible particle contents and their masses in particle physics models. In the Standard Model of strong and electroweak interactions, besides the Casimir vacuum energy there is also vacuum energy induced from spontaneous symmetry breaking. The requirement that the total vacuum energy to be scale independent dictates the Higgs mass to be $m_H^4 = 8\sum_i N_i m^4_i - 12m^4_W - 6 m^4_Z$, where the summation is over fermions and $N_i$ equals to 3 and 1 for quarks and leptons, respectively. The Higgs mass is predicted to be approximately 382 GeV.