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We present a study of photon-photon scattering in the mass range$W_{\gamma\gamma} < 5$ GeV. We extend earlier calculations of this crosssection for $W_{\gamma\gamma}>$ 5 GeV into the low mass range wherephotoproduction of the pseudoscalar resonances $\eta$, $\eta^{'}(958)$contributes to two-photon final states. We present the elementary photon-photoncross section as a function of diphoton mass $M_{\gamma\gamma}$ arising fromlepton and quark loop diagrams, and the visible cross section obtained with thegamma-gamma decay branching fractions of the resonances $\eta$,$\eta^{'}(958)$, $\eta_c(1S)$, $\eta_c(2S)$, $\chi_{c0}(1P)$. We derive thecorresponding cross sections in ultra-peripheral Pb-Pb collisions at$\sqrt{s_{NN}}$ = 5.02 TeV by folding the elementary cross section with theheavy-ion photon fluxes. We consider the dominating background of thetwo-photon final state which arises from gamma decays of photoproduced$\pi^{0}$-pairs. Such $\pi^{0}$-pairs contribute to the background when onlytwo of the four decay photons are within the experimental acceptance, while theother two photons escape undetected. We reduce this background by applying cutson asymmetries of transverse momenta of the two photons and indicate how thebackground can be further suppressed using a multivariate sideband analysis. Wepresent the cross section for the signal and the background at midrapidity$|\eta| <$ 0.9, and in the forward rapidity range 2.0 $< \eta <$ 4.5.

Light-by-light scattering in ultra-peripheral heavy-ion collisions at low diphoton masses