  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.
