ALPino to ALP: Solution to Small-Scale Problems

We show that an axino-like particle (ALPino) decaying into an axion-like particle (ALP) and gravitino with a lifetime around the age of the Universe could solve small-scale problems in the cold dark matter paradigm. The ALPino mass is sub-PeV and just slightly ($Δm/m\sim 10^{-4}$) larger than the gravitino mass and thus the dark matter abundance does not alter virtually before and after the ALPino decays. On the other hand, the resultant gravitino obtains a kick velocity of $\sim 30 \,{\rm km / s}$, which is sufficiently large to impact the dark matter distribution in small-size halos. Constraints from probes of the high-redshift matter distribution, such as Lyman-$α$ forest measurements, are relieved when compared to warm dark matter since only a tiny fraction ($\sim10$%) of dark matter experience the decay at that time. The decaying ALPino dark matter is thus promoted to a viable solution to small-scale problems. The ALPino relic abundance is determined predominantly by the decay of the lightest ordinary supersymmetric particle. The monochromatic ALP emission from the ALPino decay is converted to $\sim 50 \,{\rm GeV}$ photon under the Galactic magnetic field. The morphology of the gamma-ray flux shows a distinctive feature of the model when compared to decaying dark matter that directly decays into photons.