Vector-Like Quarks and Leptons, SU(5) $\otimes$ SU(5) Grand Unification,   and Proton Decay
  SU(5) $\otimes$ SU(5) provides a minimal grand unification scheme for fermions and gauge forces if there are vector-like quarks and leptons in nature. We explore the gauge coupling unification in a non-supersymmetric model of this type, and study its implications for proton decay. The properties of vector-like quarks and intermediate scales that emerge from coupling unification play a central role in suppressing proton decay. We find that in this model, the familiar decay mode $p \to e^+ \pi^0$ may have a partial lifetime within the reach of currently planned experiments. 
Chang-Hun Lee and Rabindra N. Mohapatra
hep-ph