Late decaying axino as CDM and its lifetime bound

The axino with mass in the GeV region can be cold dark matter (CDM) in the galactic halo. However, if R-parity is broken, for example by the bilinear terms μα, then axino (ã) can decay to ν+γ. In this case, the most stringent bound on the axino lifetime comes from the diffuse photon background and we obtain that the axino lifetime should be greater than 3.9×1024 Ωãh [s] which amounts to a very small bilinear R-parity violation, i.e., μα<1 keV. This invalidates the atmospheric neutrino mass generation through bilinear R-violating terms within the context of axino CDM.