Toward a Strongly Interacting Scalar Higgs Particle

摘要

We calculate the vacuum energy of the non-Hermitian and PT symmetric (g4)2+1 scalar field theory. Rather than the corresponding Hermitian theory and due to the asymptotic freedom property of the theory, the vacuum energy does not blow up for large energy scales which is a good sign to solve the hierarchy problem when using this model to break the U(1)×SU(2) symmetry in the standard model. The theory is strongly interacting and in fact, all the dimensionful parameters in the theory like mass and energy are finite even for very high energy scales. Moreover, relative to the vacuum energy for the Hermitian 4 theory, the vacuum energy of the non-Hermitian and PT symmetric (g4)2+1 theory is tiny, which is a good sign toward the solution of the cosmological constant problem. Remarkably, these features of the non-Hermitian and PT symmetric (g4)2+1 scalar field theory make it very plausible to be employed as a Higgs mechanism in the standard model instead of the problematic Hermitian Higgs mechanism.