On the Breaking of the U(1) Peccei-Quinn Symmetry and Its Implications for Neutrino and Dark Matter Physics

The Standard Model of electroweak interactions is based on the fundamental SU(2)(weak) x U(1)(elect) representation. It assumes massless neutrinos and purely left-handed massive W-+/- and Z(0) bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)(strong) group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)(strong) x SU(2)(weak) x U(1)(elect) to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)(PQ) symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics.