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We calculate the photoproduction of double $J/\psi$ ($\Upsilon$) to leadingorder based on the nonrelativistic quantum chromodynamics factorizationframework at the Large Hadron Collider with forward proton tagging. Thenumerical results of double $J/\psi$ photoproduction pp $\rightarrow$p$\gamma$p $\rightarrow$ $J/\psi$ + $J/\psi$ with different forward detectoracceptances ($\xi$) are presented. The total cross section of double $J/\psi$photoproduction is less than 200 fb with 0.1 $<$ $\xi$ $<$ 0.5, but can reachabout 1.37(1.27) pb with 0.0015 $<$ $\xi$ $<$ 0.5 ( 0.0015 $<$ $\xi$ $<$ 0.15). The double $J/\psi$ photoproduction may have the potential to be detectedand provide an interesting signature, thus is useful for studying the mechanismof heavy quarkonium production. We also predict the double $\Upsilon$photoproduction and find they are, unfortunately, small (with less than 10 fb).

Photoproduction of the double $J/\psi$ ($\Upsilon$) at the LHC with forward proton tagging