Searches for exclusively produced $W$ boson pairs in the process $pp(\gamma\gamma) \rightarrow pW^+W^-p$ and exclusively produced Higgs boson in the process $pp(gg) \rightarrow pHp$ have been performed using $e^{\pm}\mu^{\mp}$ final states. These measurements use 20.2 fb$^{-1}$ of $pp$ collisions collected by the ATLAS experiment at a center-of-mass energy $\sqrt{s}=8$ TeV at the LHC. Exclusive production of $W^+W^-$ consistent with the Standard Model prediction is found with 3.0$\sigma$ significance. The exclusive $W^+W^-$ production cross-section is determined to be $\sigma (\gamma\gamma\rightarrow W^{+}W^{-}\rightarrow e^{\pm}\mu^{\mp} X) = 6.9 \pm 2.2 (\mathrm{stat.}) \pm 1.4 (\mathrm{sys.})$ fb, in agreement with the Standard Model prediction. Limits on anomalous quartic gauge couplings are set at 95\% confidence-level as $-1.7 \times 10^{-6} < a_0^W/\Lambda^2 < 1.7 \times 10^{-6}$ GeV$^{-2}$and $-6.4 \times 10^{-6} < a_C^W/\Lambda^2 < 6.3 \times 10^{-6}$ GeV$^{-2}$. A 95\% confidence-level upper limit on the total production cross-section for exclusive Higgs boson is set to 1.2 pb.

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