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The recent LHC Run-2 data have shown a possible excess in diphoton events,suggesting the existence of a new resonance $\phi$ with mass $M\sim 750$~GeV.If $\phi$ plays the role of a portal particle connecting the Standard Model andthe invisible dark sector, the diphoton excess should be correlated withanother photon excess, namely, the excess in the diffuse gamma rays towards theGalactic center, which can be interpreted by the annihilation of darkmatter(DM). We investigate the necessary conditions for a consistentexplanation for the two photon excesses, especially the requirement on thewidth-to-mass ratio $\Gamma/M$ and $\phi$ decay channels, in a collection of DMmodels where the DM particle can be scalar, fermionionic and vector, and $\phi$can be generated through $s$-channel $gg$ fusion or $q\bar q$ annihilation. Weshow that the minimally required $\Gamma/M$ is determined by a single parameterproportional to $(m_{\chi}/M)^{n}$, where the integer $n$ depends on the natureof the DM particle. We find that for the scalar DM model with $\phi$ generatedfrom $q\bar q$ annihilation, the minimally required $\Gamma/M$ can be as low as$\mathcal{O}(10^{-3})$. For the scalar DM model with $\phi$ generated from $gg$fusion and fermionic DM model with $\phi$ from $q\bar q$ annihilation, therequired $\Gamma/M$ are typically of $\mathcal{O}(10^{-2})$. The vector DMmodels, however, require very large $\Gamma/M$ of order one. For the DM modelswhich can consistently explain both the excesses,the predicted cross sectionsfor gamma-ray line are typically of$\mathcal{O}(10^{-31}-10^{-29})~\text{cm}^{3}\text{s}^{-1}$, which are close tothe current limits from the Fermi-LAT experiment.

Connecting the LHC diphoton excess to the Galatic center gamma-ray excess