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

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