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The process $\gamma \gamma \to p \bar{p} K^+ K^-$ and its intermediateprocesses are measured for the first time using a 980~fb$^{-1}$ data samplecollected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$collider. The production of $p \bar{p} K^+ K^-$ and a$\Lambda(1520)^0~(\bar{\Lambda}(1520)^0)$ signal in the $pK^-$~($\bar{p} K^+$)invariant mass spectrum are clearly observed. However, no evidence for anexotic baryon near 1540~MeV/$c^2$, denoted as$\Theta(1540)^0$~($\bar{\Theta}~(1540)^0$) or$\Theta(1540)^{++}$~($\Theta(1540)^{--}$), is seen in the $pK^-$~($\bar{p}K^+$) or $pK^+$~($\bar{p} K^-$) invariant mass spectra. Crosssections for $\gamma \gamma \to p \bar{p} K^+ K^-$, $\Lambda(1520)^0 \bar{p}K^+ +c.c.$ and the products $\sigma(\gamma \gamma \to \Theta(1540)^0 \bar{p}K^+ +c.c.)\BR(\Theta(1540)^0 \to p K^{-})$ and $\sigma(\gamma \gamma \to\Theta(1540)^{++} \bar{p} K^- +c.c.)\BR(\Theta(1540)^{++}\to p K^{+})$ aremeasured. We also determine upper limits on the products of the $\chi_{c0}$ and$\chi_{c2}$ two-photon decay widths and their branching fractions to $p \bar{p}K^+ K^-$ at the 90\% credibility level.

First observation of $\gamma \gamma \to p \bar{p} K^+ K^-$ and search for exotic baryons in $pK$ systems