We study the photoproduction of exclusive $2\pi^+2\pi^-$ mesons in ultra-peripheral heavy-ion collisions at RHIC and LHC energies. Predictions in photon-nucleus interactions are calculated for various resonances at central and forward rapidities. The recent H1 preliminary data are utilized to improve the description of the poorly known $\gamma p \to 4\pi^\pm p$ process. We present the comparisons of our results to the available STAR data at RHIC, and made predictions for LHC energies.
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