Models with Peccei-Quinn symmetry and vector-like quarks realize one-loop proton decay through the operator u_R u_R d_R e_R while preserving a residual Z2 that forbids tree-level decay, yielding testable axion-photon couplings and an axion-accompanied decay mode.
Axion Paradigm with Color-Mediated Neutrino Masses,
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One-loop proton decay from Peccei-Quinn symmetry
Models with Peccei-Quinn symmetry and vector-like quarks realize one-loop proton decay through the operator u_R u_R d_R e_R while preserving a residual Z2 that forbids tree-level decay, yielding testable axion-photon couplings and an axion-accompanied decay mode.