Leptoquarks, axions and the unification of B, L, and Peccei-Quinn symmetries

In this paper, axion models supplemented by leptoquarks and diquarks are systematically analyzed. Turning on some couplings to and among these latter states permits to unify the Peccei-Quinn symmetry with baryon (B) and lepton (L) numbers, such that the axion becomes associated to the spontaneous breaking of the three $U(1)$ symmetries. All possible four- and six-fermion patterns of B and L violation are discussed, including those inducing proton decay, with $\mathrm{\Delta }B=1$ and $\mathrm{\Delta }L=\pm 1,\pm 3$, neutron-antineutron oscillations with $\mathrm{\Delta }B=2$, and Majorana neutrino masses with $\mathrm{\Delta }L=2$. Scenarios in which one or two axion fields necessarily appear in any B and/or L violating operators are also constructed. Nucleon decays would then necessarily involve an axion in the final state, while neutron-antineutron oscillations would only happen in an axionic background. This could have implications for the neutron lifetime puzzle, and more generally, opens the door to new phenomenological and cosmological applications.