Low-energy restoration of parity and maximal symmetry

Abstract

The maximal symmetry of fermions of one generation, SU(16), which includes the left-right-symmetric Pati-Salam group, $\mathrm{SU}{(4)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}$, as a subgroup, allows the possibility of a low-energy (${M}_{R}\ensuremath{\sim}100$ GeV) breaking of the left-right symmetry. It is known that such a low-energy restoration of parity can be consistent with weak-interaction phenomenology. We examine different chains of descent of SU(16) that admit a low value of ${M}_{R}$ and determine the other intermediate symmetry-breaking mass scales associated with each of these chains. These additional mass scales provide an alternative to the "great desert" expected in some grand unifying models. The contributions of the Higgs fields in the renormalization-group equations are retained and are found to be important.