Galactic Center Gamma Ray Excess in a Radiative Neutrino Mass Model

The Fermi gamma ray space telescope data have pointed towards an excess of gamma rays with a peak around $1-3$ GeV in the region surrounding the galactic center. This anomalous excess can be described well by a dark matter candidate having mass in the range $31-40$ GeV annihilating into $b\bar{b}$ pairs with a cross section of $< \sigma v > \simeq (1.4-2.0) \times 10^{-26} \; \text{cm}^3/\text{s}$. In this work we explore the possibility of having such a dark matter candidate within the framework of a radiative neutrino mass model. The model is a simple extension of the standard model by an additional $U(1)_X$ gauge symmetry where the standard model neutrino masses arise both at tree level as well as radiatively by the anomaly free addition of one singlet fermion $N_R$ and two triplet fermions $\Sigma_{1R}, \Sigma_{2R}$ with suitable Higgs scalars. The spontaneous gauge symmetry breaking is achieved in such a way which results in a residual $Z_2$ symmetry and hence providing a stable cold dark matter candidate. We show that the singlet fermionic dark matter candidate in our model can give rise to the galactic center gamma ray excess. The parameter space which simultaneously satisfy the constraints on relic density, direct detection scattering as well as collider bounds essentially corresponds to an s-wave resonance where the gauge boson mass $m_X$ is approximately twice that of dark matter mass $m_{\chi}$. We also discuss the compatibility of such a light fermion singlet dark matter with light neutrino mass.