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This Letter reports a measurement of the exclusive $\gamma\gamma\rightarrow\ell^+\ell^- (\ell=e, \mu)$ cross-section in proton-proton collisions at acentre-of-mass energy of 7 TeV by the ATLAS experiment at the LHC, based on anintegrated luminosity of $4.6$ fb$^{-1}$. For the electron or muon pairssatisfying exclusive selection criteria, a fit to the dilepton acoplanaritydistribution is used to extract the fiducial cross-sections. The cross-sectionin the electron channel is determined to be $\sigma_{\gamma\gamma\rightarrowe^+e^-}^{\mathrm{excl.}} = 0.428 \pm 0.035 (\mathrm{stat.}) \pm 0.018(\mathrm{syst.})$ pb for a phase-space region with invariant mass of theelectron pairs greater than 24 GeV, in which both electrons have transversemomentum $p_\mathrm{T}>12$ GeV and pseudorapidity $|\eta|<2.4$. For muon pairswith invariant mass greater than 20 GeV, muon transverse momentum$p_\mathrm{T}>10$ GeV and pseudorapidity $|\eta|<2.4$, the cross-section isdetermined to be $\sigma_{\gamma\gamma\rightarrow \mu^+\mu^- }^{\mathrm{excl.}}= 0.628 \pm 0.032 (\mathrm{stat.}) \pm 0.021 (\mathrm{syst.})$ pb. When protonabsorptive effects due to the finite size of the proton are taken into accountin the theory calculation, the measured cross-sections are found to beconsistent with the theory prediction.

Measurement of exclusive $\gamma\gamma\rightarrow \ell^+\ell^-$ production in proton-proton collisions at $\sqrt{s} = 7$ TeV with the ATLAS detector