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 MP 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)L×{}SU(2)R×{}G [G is SU(4)C or SU(3)C×{}U(1)_B-L] can appear as an intermediate symmetry with gL{≠}gR. 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)L×{}U(1)Y×{}SU(3)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×{}10³² yr, sin²{{{θ}}}W$(${M}W) =0.22±0.02, and{{α}}ₛ$(${M}W)=0.10--0.12. This chain is SO(10)→SU(2{)}L×SU(2{)}R×SU(4{)}C×P →SU(2{)}L×SU(2{)}R×SU(4{)}C→SU(2{)}L×U(1{)}R×U(1{)}_{B{{-}}1}×SU(3{)}C→SU(2{)}L×U(1{)}Y×SU(3{)}C$ and allows for the following detectable consequences: (a) neutron oscillations with ${{τ}}_{nn{}}~{10}⁸$--${10}⁹$ sec; (b) a branching ratio for ${K}L→μ ē \=e of 7×{(10}^{{{-}}8}$--${10}^{{{-}}12}$); (c) a second neutral ${Z}R$ boson in the (1/2)-to-10-TeV range; (d) a proton lifetime ${{τ}}ₚ=6.5×{10}^{35.0±{}0.9}(Λ MS/160 MeV{)}⁴$ 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 MP{}10^14.3±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.