Several groups have analyzed the publicly-available Fermi-LAT data and reported a spatially extended $\gamma-$ray excess of around $1-3$ GeV from the region surrounding the Galactic Center that might originate from annihilation of dark matter particles with a rest mass $m_\chi \sim 30-40$ GeV. In this work we examine the role of the diffuse Galactic gamma ray emission (DGE) templates played in suppressing the GeV excess. For such a purpose, we adopt in total 128 background templates that have been generated by Ackermann et al. \cite{FermiLAT:2012aa} in the study of the {Fermi-LAT} observations of the diffuse gamma ray emission considering the effects of cosmic rays and the interstellar medium. The possible GeV excess, assumed to follow the spatial distribution of the prompt gamma-rays produced in the annihilation of dark matter particles taking a generalized NFW profile with an inner slope $\alpha=1.2$, has been analyzed in some regions of interest. The introduction of such an additional component centered at the Galactic center is found to have improved the goodness of fit to the data significantly in all background template models regardless of whether the excess spectrum is fixed or not. Our results thus suggest that the presence of a statistically significant GeV excess in the inner Galaxy is robust thought its spectrum depends on the DGE model adopted in the analysis. The possible physical origin of the GeV excess component is discussed and in the dark matter model the annihilation cross section of such particles is evaluated.
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