Misleading Coupling Unification and Lifshitz Type Gauge Theory

Grand unification is an attractive idea and enables the unification of forces and the (partial) unification of quarks and leptons in each family.1) The introduction of supersymmetry (SUSY) increases the reality of grand unification. In the minimal supersymmetric standard model (MSSM), the gauge couplings meet at MX = 2.1× 1016GeV if the superpartners and Higgs particles exist below or around O(1)TeV.2) It is natural to guess that the grand unification occurs at MX and physics above MX can be described as a supersymmetric grand unified theory (SUSY GUT). This scenario is very attractive, but, in general, it suffers from problems related to Higgs multiplets. The typical one is the proton decay problem3) in the minimal SUSY GUT.4) The proton decay problem comes from a significant contribution from the dimension 5 operators. Stronger constraints on the colored Higgs mass MHC and the sfermion mass m f̃ have been obtained (e.g. MHC > 6.5 × 10 16GeV for m f̃ < 1TeV) from analysis including a Higgsino dressing diagram with right-handed matter fields in the minimal SUSY SU(5) GUT.5) Extra particles such as X, Y gauge bosons, the colored Higgs bosons and their superpartners are expected to acquire heavy masses of O(MU ) after the breakdown of grand unified symmetry. Here MU is the grand unification scale or the grand unified symmetry breaking scale. The constraints contradict with the relation MHC = O(MU ) if MU is identified with the gauge coupling unification scale MX . From this observation, we come across the conjecture that the proton stability can be realized to be compatible with the grand unification, if MX is not directly related to MU and the order of MU is bigger than that of MX . It might lead to the idea that gauge couplings agree with accidentally at MX . In this paper, we propose a new grand unification scenario for ensuring proton stability on the basis of the above conjecture and the standpoint that the scale MX has a physical meaning beyond the fact that the agreement of gauge couplings occurs accidentally there. We discuss a Lifshitz type gauge theory as a candidate to realize our scenario.