Gauged Baryon Parity and Nucleon Stability

Abstract

We show that the Standard Model Lagrangian, including small neutrino masses, has an anomaly-free discrete Z_6 symmetry. This symmetry can emerge naturally from I^{3}_{R}+L_i+L_j-2L_k gauge symmetry (L_i is the i-th lepton number) and ensure the stability of the nucleon even when the threshold of new physics \Lambda is low. All \Delta B=1 and \Delta B=2 (B is the baryon number) effective operators are forbidden by the Z_6 symmetry. \Delta B=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 \Lambda can be as low as 10^2 GeV. We suggest a simple mechanism for realizing reasonable neutrino masses and mixings even with such a low scale for \Lambda.