Axions without Peccei-Quinn Symmetry

Understand

We argue that the axion arising in the solution of the strong CP problem can be identified with the Majoron, the (pseudo-)Goldstone boson of spontaneously broken lepton number symmetry.

• At low energies, the associated $U(1)_L$ becomes, via electroweak parity violation and neutrino mediation, indistinguishable from an axial Peccei-Quinn symmetry in relation to the strong interactions.
• The axionic couplings are then fully computable in terms of known SM parameters and the Majorana mass scale, as we illustrate by computing the effective couplings to photons and quarks at two loops.