Mass of the Higgs boson in the trinification subgroup ofE6

Abstract

The extension of the standard model to $SU(3{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(3{)}_{R}\ifmmode\times\else\texttimes\fi{}SU(3{)}_{C}$ is considered. Spontaneous symmetry breaking requires two Higgs field multiplets with a strong hierarchical structure of vacuum expectation values. These vacuum expectation values, some of them known from experiment, are used to construct invariant potentials in the form of a sum of individual potentials relevant at the weak scale. As in a previous suggestion one may normalize the most important individual potentials such that their mass eigenvalues agree with their very large vacuum expectation values. In this case (for a wide class of parameters) the scalar field corresponding to the standard model Higgs turns out to have the precise mass value ${m}_{\mathrm{Higgs}}=\frac{v}{\sqrt{2}}=123\text{ }\text{ }\mathrm{GeV}$ at the weak scale. The physical mass (pole mass) is larger and found to be $125\ifmmode\pm\else\textpm\fi{}1.4\text{ }\text{ }\mathrm{GeV}$.