What is the discrete gauge symmetry of the minimal supersymmetric standard model

Abstract

We systematically study the extension of the supersymmetric standard model (SSM) by an anomaly-free discrete gauge symmetry ZN. We extend the work of Ibáñez and Ross with N=2, 3 to arbitrary values of N. As new fundamental symmetries, we find four Z6, nine Z9, and nine Z18. We then place three phenomenological demands upon the low-energy effective SSM: (i) the presence of the μ term in the superpotential, (ii) baryon-number conservation up to dimension-five operators, and (iii) the presence of the seesaw neutrino mass term LHuLHu. We are then left with only two anomaly-free discrete gauge symmetries: baryon triality, B3, and a new Z6, which we call proton hexality, P6. Unlike B3, P6 prohibits the dimension-four lepton-number violating operators. This we propose as the discrete gauge symmetry of the minimal SSM, instead of R parity. © 2006 The American Physical Society.