PQ-symmetry for a small Dirac neutrino mass, dark radiation and cosmic neutrinos

We propose a supersymmetric scenario in which the small Yukawa couplings for the Dirac neutrino mass term are generated by the spontaneous-breaking of Pecci-Quinn symmetry. In this scenario, a right amount of dark matter relic density can be obtained by either right-handed sneutrino or axino LSP, and a sizable amount of axion dark radiation can be obtained. Interestingly, the decay of right-handed sneutrino NLSP to axino LSP is delayed to around the present epoch, and can leave an observable cosmological background of neutrinos at the energy scale of (10-100) GeV.