Common Origin of 3.55 keV X-Ray Line and Galactic Center Gamma Ray Excess in a Radiative Neutrino Mass Model

We attempt to simultaneously explain the recently observed 3.55 keV X-ray line in the analysis of XMM-Newton telescope data and the galactic center gamma ray excess observed by the Fermi gamma ray space telescope within an abelian gauge extension of standard model. We consider a two component dark matter scenario with tree level mass difference 3.55 keV such that the heavier one can decay into the lighter one and a photon with energy 3.55 keV. The lighter dark matter candidate is protected from decaying into the standard model particles by a remnant $Z_2$ symmetry into which the abelian gauge symmetry gets spontaneously broken. If the mass of the dark matter particle is chosen to be within $31-40$ GeV, then this model can also explain the galactic center gamma ray excess if the dark matter annihilation into $b\bar{b}$ pairs has a cross section of $\langle \sigma v \rangle \simeq (1.4-2.0) \times 10^{-26} \; \text{cm}^3/\text{s}$. We constrain the model from the requirement of producing correct dark matter relic density, 3.55 keV X-ray line flux and galactic center gamma ray excess. We also impose the bounds coming from dark matter direct detection experiments as well as collider limits on additional gauge boson mass and gauge coupling. We also briefly discuss how this model can give rise to sub-eV neutrino masses at tree level as well as one-loop level while keeping the dark matter mass at few tens of GeV. We also constrain the model parameters from the requirement of keeping the one-loop mass difference between two dark matter particles below a keV. We find that the constraints from light neutrino mass and keV mass splitting between two dark matter components show more preference for opposite $CP$ eigenvalues of the two fermion singlet dark matter candidates in the model