Experimental tests of new SO(10) grand unification

A new approach to SO(10) grand unification was recently proposed by three of the authors (D.C., R.N.M., and M.K.P.), where the mass scale ${M}_{P}$ at which the D-parity symmetry present in the SO(10) group breaks was of the right-handed currents. In contrast with the conventional treatment of the SO(10) model, SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}G [G is SU(4${)}_{\mathrm{C}}$ or SU(3${)}_{\mathrm{C}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{B}\mathrm{\ensuremath{-}}\mathrm{L}}$] can appear as an intermediate symmetry with ${g}_{L}$\ensuremath{\ne}${g}_{R}$. Calculations in the one-loop approximation lead to a substantially different picture of intermediate mass scales for SO(10)-symmetry breaking than before. In this paper, this analysis is extended to include two-loop contributions which are significant for several symmetry-breaking chains. All possible chains descending to the standard group SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{Y}}$\ifmmode\times\else\texttimes\fi{}SU(3${)}_{\mathrm{C}}$ are examined. A unique chain emerges if one imposes a minimality condition (using the lowest-dimensional Higgs multiplet at each symmetry-breaking stage) and the phenomenological requirements of \ensuremath{\ge}2\ifmmode\times\else\texttimes\fi{}${10}^{32}$ yr, ${\mathrm{sin}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\mathrm{W}}$(${\mathrm{M}}_{\mathrm{W}}$) =0.22\ifmmode\pm\else\textpm\fi{}0.02, and ${\ensuremath{\alpha}}_{s}$(${M}_{W}$)=0.10--0.12. This chain is SO(10)\ensuremath{\rightarrow}SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}SU(4${)}_{\mathrm{C}}$ \ifmmode\times\else\texttimes\fi{}P \ensuremath{\rightarrow}SU(2${)}_{\mathrm{L}}$ \ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}SU(4${)}_{\mathrm{C}}$\ensuremath{\rightarrow}SU(2${)}_{\mathrm{L}}$ \ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{R}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{B}\mathrm{\ensuremath{-}}1}$\ifmmode\times\else\texttimes\fi{}SU(3${)}_{\mathrm{C}}$ \ensuremath{\rightarrow}SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{Y}}$ \ifmmode\times\else\texttimes\fi{}SU(3${)}_{\mathrm{C}}$ and allows for the following detectable consequences: (a) neutron oscillations with ${\ensuremath{\tau}}_{\mathrm{nn}\ifmmode\bar\else\textasciimacron\fi{}}$ \ensuremath{\sim}${10}^{8}$--${10}^{9}$ sec; (b) a branching ratio for ${K}_{L}$\ensuremath{\rightarrow}\ensuremath{\mu}\ifmmode \bar{e}\else \={e}\fi{} of 7\ifmmode\times\else\texttimes\fi{}${(10}^{\mathrm{\ensuremath{-}}8}$--${10}^{\mathrm{\ensuremath{-}}12}$); (c) a second neutral ${Z}_{R}$ boson in the (1/2)-to-10-TeV range; (d) a proton lifetime ${\ensuremath{\tau}}_{p}$=6.5\ifmmode\times\else\texttimes\fi{}${10}^{35.0\ifmmode\pm\else\textpm\fi{}0.9}$(\ensuremath{\Lambda} MS\ifmmode\bar\else\textasciimacron\fi{}/160 MeV${)}^{4}$ yr (MS\ifmmode\bar\else\textasciimacron\fi{} denotes the modified minimal subtraction scheme), which, given the theoretical uncertainties, may barely be within experimental reach; (e) a Majorana mass for the electron neutrino in the range of electron volts. This experimentally interesting chain also predicts ${M}_{P}$\ensuremath{\simeq}${10}^{14.3\ifmmode\pm\else\textpm\fi{}1.0}$ GeV, which satisfies all cosmological constraints. All other symmetry-breaking chains that satisfy the phenomenological requirements do not have experimentally testable consequences at low energies.