Left-right symmetry and supersymmetric unification.

The existence of an SU(3)×SU(2)L×SU(2)R×U(1) gauge symmetry with gL = gR at the TeV energy scale is shown to be consistent with supersymmetric SO(10) grand unification at around 10 GeV if certain new particles are assumed. The additional imposition of a discrete Z2 symmetry leads to a generalized definition of R parity as well as highly suppressed Majorana neutrino masses. Another model based on SO(10)× SO(10) is also discussed. Possible unification of the three gauge couplings of the standard SU(3)C×SU(2)L×U(1)Y model of quark and lepton interactions in its minimal supersymmetric extension has revived widespread interest in this topic.[1] The success of such a scenario seems to imply that no new physics beyond the minimal supersymmetric standard model (MSSM) would be observed below an energy scale of a few TeV. In particular, the left-right gauge extension appears to be excluded, except for one very special case,[2] but even then, the condition gL = gR cannot be maintained.[3] If gL = gR is desired, the scale MR of SU(2)R symmetry breaking obtained in previous studies[4] is typically of the order 10 GeV. The purpose of this paper is to show in an explicit first example that it is actually possible to have supersymmetric SO(10) grand unification at around 10 GeV as well as an SU(3)× SU(2)L × SU(2)R ×U(1) gauge symmetry with gL = gR at the TeV energy scale. New particles will be assumed together with a discrete Z2 symmetry, resulting in a generalized definition of R parity together with highly suppressed Majorana neutrino masses. Another model based on SO(10) × SO(10) will also be discussed. Consider a supersymmetric SO(10) model which breaks down at the unification scale MU to a supersymmetric SU(3) × SU(2)L × SU(2)R × U(1) model with left-right exchange symmetry, which then breaks down at MR to the standard (nonsupersymmetric) SU(3) × SU(2)L × U(1)Y model. The scale of supersymmetry breaking is assumed to coincide with MR. Before going into the details of the evolution of the various gauge couplings, note that with a left-right model, there should be two scalar bidoublets in order that realistic quark and lepton mass matrices be obtained. Hence there are four SU(2)L doublets which will change the evolution of the SU(2)L coupling gL but not that of the SU(3) coupling gS, leading to the loss of unification of the gauge couplings. In the MSSM, this corresponds to the well-known fact that unification occurs with two, but not four, Higgs doublets. Note also that this problem exists whether or not gL = gR unless MR = MU. Consequently, new