Observing light-by-light scattering at the large hadron collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the process pp→pγγp→pγγp\documentclass[12pt]{minimal}
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\begin{document}$${{pp}}\rightarrow {{p}}\gamma \gamma {{p}}\rightarrow {{p}}\gamma \gamma {{p}}$$\end{document} through graviton exchange in the large extra dimension (LED) model. Typically, when we do the background analysis, we also study the double Pomeron exchange of γγ\documentclass[12pt]{minimal}
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\begin{document}$$\gamma \gamma $$\end{document} production. We compare its production in the quark–quark collision mode to the gluon–gluon collision mode and find that contributions from the gluon–gluon collision mode are comparable to the quark–quark one. Our result shows, for extra dimension δ=4\documentclass[12pt]{minimal}
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\begin{document}$$\delta =4$$\end{document}, with an integrated luminosity L=200fb-1\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{L} = 200\,\mathrm{fb}^{-1}$$\end{document} at the 14 TeV LHC, that diphoton production through graviton exchange can probe the LED effects up to the scale MS=5.06(4.51,5.11)TeV\documentclass[12pt]{minimal}
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\begin{document}$${M}_{S}=5.06 (4.51, 5.11)\,\mathrm{TeV}$$\end{document} for the forward detector acceptance ξ1(ξ2,ξ3)\documentclass[12pt]{minimal}
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\begin{document}$$\xi _1 (\xi _2, \xi _3)$$\end{document}, respectively, where 0.0015<ξ1<0.5\documentclass[12pt]{minimal}
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\begin{document}$$0.0015<\xi _1<0.5$$\end{document}, 0.1<ξ2<0.5\documentclass[12pt]{minimal}
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\begin{document}$$0.1<\xi _2<0.5$$\end{document}, and 0.0015<ξ3<0.15\documentclass[12pt]{minimal}
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\begin{document}$$0.0015<\xi _3<0.15$$\end{document}.
