Constraints on proton lifetime andsin2θWin SO(10) grand unified theory

Abstract

Simple constraints on the proton-decay lifetime are derived in SO(10) grand unified theory for major descents to the standard group $\mathrm{SU}{(3)}_{C}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$. It is shown that the only unambiguous pattern of symmetry breaking that predicts a longer proton lifetime [than SU(5)] goes through the Pati-Salam group $\mathrm{SU}(4)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}$ and distinguishes quarks from leptons [i.e., SU(4) breaks down to $\mathrm{SU}{(3)}_{C}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{B\ensuremath{-}L}$] before parity is broken [i.e., $\mathrm{SU}{(2)}_{R}$ is broken]. The lifetime depends on ${M}_{R}$ [the mass scale associated with $\mathrm{SU}{(2)}_{R}$ breaking] but neither on the other intermediate mass scales nor on ${{sin}^{2}\ensuremath{\theta}}_{W}$ in the limit where Higgs-boson contributions are neglected.