One-loop proton decay from Peccei-Quinn symmetry

We promote the accidental $B+L$ symmetry of the Standard Model to a Peccei-Quinn (PQ) symmetry while realizing spontaneous proton decay radiatively. The PQ anomaly sector consists of vector-like quarks (VLQs), providing a Kim-Shifman-Vainshtein-Zakharov-type axion solution to the strong CP problem. After spontaneous PQ breaking, a residual $\mathcal{Z}_2$ symmetry remains, which forbids tree-level proton decay. The VLQs required to generate the QCD anomaly, together with scalar mediators, odd under the residual $\mathcal{Z}_2$, induce one-loop proton decay through the effective operator $u_R u_R d_R e_R$. We study its ultraviolet completions, featuring distinct vector-like fermion and scalar representations, and show that the resulting models lead to distinct predictions for the axion-to-photon coupling, testable in helioscope and haloscope experiments. In addition to the proton decay channel $p \rightarrow e^+ \pi^0$, this framework predicts proton decay with an axion in the final state, $p \rightarrow e^+ \pi^0 a$, suppressed by the PQ-breaking scale. We also discuss axion dark matter in pre- and post-inflationary cosmology.