Stability of spontaneous symmetry breaking in a class of SO(10) models

Abstract

Absolute minima with specific symmetries are constructed in SO(10) models with the 210 representation. The relation between the appearance of the zeroth-mass order and the stability of symmetry breaking is discussed and a generalization of the Georgi-Glashow theorem is presented. The stability of the SO(10) breaking into ${H}_{224}$=SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}SU(4), ${H}_{2231D}$=SU(2${)}_{\mathrm{L}}$ \ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}U(3)\ifmmode\times\else\texttimes\fi{}D, and ${H}_{2231}$=SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}U(3) is studied in a range of scales between ${10}^{16}$ GeV and ${10}^{19}$ GeV. Starting with a special sum-of-square form of the potential, we find regions of parameters for which the ${H}_{224}$ and ${H}_{2231D}$ patterns are stable; for the ${H}_{2231}$ pattern, no such region is found.