Gauged baryon parity and nucleon stability

We show that the Standard Model Lagrangian, including small neutrino masses, has an anomaly-free discrete Z6 symmetry. This symmetry can emerge naturally from (I3R+Li+Lj−2Lk) gauge symmetry (Li is the ith lepton number) and ensure the stability of the nucleon even when the threshold of new physics Λ is low. All ΔB=1 and ΔB=2 (B is the baryon number) effective operators are forbidden by the Z6 symmetry. ΔB=3 operators are allowed, but they arise only at dimension 15. We estimate the lifetime for “triple nucleon decay” resulting from these operators and find that Λ can be as low as 102 GeV. We suggest a simple mechanism for realizing reasonable neutrino masses and mixings even with such a low scale for Λ.