Two neutralZbosons in an SO(10) supergravity model

Abstract

We consider here the supergravity model of the grand unification gauge group SO(10), which breaks to $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{B\ensuremath{-}L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(3)}_{C}(\ensuremath{\equiv}{G}_{2113})$ at a mass scale of ${10}^{15}$ GeV. The low-energy breaking of the gauge group ${G}_{2113}$ to $\mathrm{U}{(1)}_{Q}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(3)}_{C}$ is induced by supergravity. The model has the following distinctive features: (i) There should be another neutral gauge boson, whose mass could be less than 1 TeV. (ii) The proton lifetime for the decay mode $p\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\pi}}^{0}$ is very much enhanced, but, under some circumstances, it could be barely observable. (iii) Weak-interaction phenomenology in the charged-current sector remains unaltered.