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${)}_{\mathrm{L}}$×SU(2${)}_{\mathrm{R}}$×G [G is SU(4${)}_{\mathrm{C}}$ or SU(3${)}_{\mathrm{C}}$×U(1${)}_{\mathrm{B}\mathrm{-}\mathrm{L}}$] can appear as an intermediate symmetry with $g_L$≠$g_R$. 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${)}_{\mathrm{L}}$×U(1${)}_{\mathrm{Y}}$×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 &≥2×${10}^{32}$ yr, ${\sin }^2$ ${\mathrm{\theta }}_{\mathrm{W}}$(${\mathrm{M}}_{\mathrm{W}}$) =0.22±0.02, and ${\alpha }_s$($M_W$)=0.10–0.12. This chain is SO(10)→SU(2${)}_{\mathrm{L}}$×SU(2${)}_{\mathrm{R}}$×SU(4${)}_{\mathrm{C}}$ ×P →SU(2${)}_{\mathrm{L}}$ ×SU(2${)}_{\mathrm{R}}$×SU(4${)}_{\mathrm{C}}$→SU(2${)}_{\mathrm{L}}$ ×U(1${)}_{\mathrm{R}}$×U(1${)}_{\mathrm{B}\mathrm{-}1}$×SU(3${)}_{\mathrm{C}}$ →SU(2${)}_{\mathrm{L}}$×U(1${)}_{\mathrm{Y}}$ ×SU(3${)}_{\mathrm{C}}$ and allows for the following detectable consequences: (a) neutron oscillations with ${\tau }_{\mathrm{nn}¯}$ ∼${10}^8$–${10}^9$ sec; (b) a branching ratio for $K_L$→μē of 7×${(10\mathrm{}}^{\mathrm{-}8}$–${10}^{\mathrm{-}12}$); (c) a second neutral $Z_R$ boson in the (1/2)-to-10-TeV range; (d) a proton lifetime ${\tau }_p$=6.5×${10}^{35.0\pm 0.9}$(Λ MS¯/160 MeV${)}^4$ yr (MS¯ 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 $M_P$≃${10}^{14.3\pm 1.0}$ 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.