What is the Discrete Gauge Symmetry of the MSSM?

TL;DR

The work systematically identifies which discrete gauge symmetries Z_N can remain as low-energy remnants of a broken U(1)_X in the MSSM, guided by anomaly-cancellation constraints. Extending Ibáñez–Ross to arbitrary N and accounting for charge rescalings reduces the landscape to a finite set of 27 fundamental DGSs, among which two stand out phenomenologically: baryon-triality B_3 and proton-hexality P_6. Requiring the μ-term and neutrino masses via a see-saw mechanism eliminates most options, leaving P_6 as a highly attractive MSSM DGS because it forbids dangerous dimension-four L-violating operators and dimension-five proton-decay operators while preserving necessary Yukawas. A concrete gauged U(1)_X model is constructed that flows to P_6, illustrating a viable UV completion and highlighting the UV–IR interplay in DGS realizations and the role of heavy fermions in anomaly cancellation.

Abstract

We systematically study the extension of the Supersymmetric Standard Model (SSM) by an anomaly-free discrete gauge symmetry Z_N. We extend the work of Ibanez and Ross with N=2,3 to arbitrary values of N. As new fundamental symmetries, we find four Z_6, nine Z_9 and nine Z_18. We then place three phenomenological demands upon the low-energy effective SSM: (i) the presence of the mu-term in the superpotential, (ii) baryon-number conservation upto dimension-five operators, and (iii) the presence of the see-saw neutrino mass term LHLH. We are then left with only two anomaly-free discrete gauge symmetries: baryon-triality, B_3, and a new Z_6, which we call proton-hexality, P_6. Unlike B_3, P_6 prohibits the dimension-four lepton-number violating operators. This we propose as the discrete gauge symmetry of the Minimal SSM, instead of R-parity.