  We study the LHC sensitivity to new broad neutral resonances produced in
two-photon fusion and decaying to a top quark pair, $\gamma\gamma \to
t\bar{t}$. This is probed in central exclusive $t\bar{t}$ production in
proton-proton collisions, $pp \to p t\bar{t} p$. We use the tagging of the
intact protons by PPS (CMS) and AFP (ATLAS) and consider the semi-leptonic
$t\bar t$ channel. The sensitivity is also mapped onto a set of dimension-8
$\gamma\gamma t\bar{t}$ operators in the large mass limit. Using the
kinematical correlations between the intact protons and the reconstructed
$t\bar{t}$ system, we obtain a sensitivity to the couplings of the dimension-8
operators of $1.4 \cdot 10^{-11}~\mathrm{GeV}^{-4}$ at 95% CL. The sensitivity
to the anomalous couplings is significantly improved down to about $7\cdot
10^{-12}~\mathrm{GeV}^{-4}$ if the proton time-of-flight is known with a
precision of 20 ps in future measurements. The 95% CL sensitivity to broad
neutral resonances reaches masses of order $ 1500~\mathrm{GeV} $ when using
timing information.
