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Non-abelian Dark Matter Solutions for Galactic Gamma-ray Excess and Perseus 3.5 keV X-ray Line

We attempt to explain simultaneously the Galactic center gamma-ray excess and the 3.5 keV X-ray line from the Perseus cluster based on a class of non-abelian $SU(2)$ DM models, in which the dark matter and an excited state comprise a "dark" $SU(2)$ doublet. The non-abelian group kinetically mixes with the standard model gauge group via dimensions-5 operators. The dark matter particles annihilate into standard model fermions, followed by fragmentation and bremsstrahlung, and thus producing a continuous spectrum of gamma-rays. On the other hand, the dark matter particles can annihilate into a pair of excited states, each of which decays back into the dark matter particle and an X-ray photon, which has an energy equal to the mass difference between the dark matter and the excited state, which is set to be 3.5 keV. The large hierarchy between the required X-ray and $γ$-ray annihilation cross-sections can be achieved by a very small kinetic mixing between the SM and dark sector, which effectively suppresses the annihilation into the standard model fermions but not into the excited state.