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Ultra-peripheral collisions (UPCs) of relativistic ions are an important toolfor studying photoproduction at high energies. Vector meson photoproduction isan important tool for nuclear structure measurements and other applications. Afuture electron-ion collider (EIC) will allow additional studies, using virtualphotons with a wide range of $Q^2$. We propose a significant expansion of theUPC and EIC photoproduction physics programs to include charged final stateswhich may be produced via Reggeon exchange. We consider two examples:$a_2^+(1320)$, which is a conventional $q\overline q$ meson, and the exotic$Z_c^+(4430)$ state (modeled here as a tetraquark). The $Z_c^+(4430)$cross-section depends on its internal structure, so photoproduction can testwhether the $Z_c^+(4430)$ is a tetraquark or other exotic object. We calculatethe rates and kinematic distributions for $\gamma p\rightarrow X^+n$ in $pA$UPCs and $ep$ collisions at an EIC and in UPCs. The rates are large enough fordetailed studies of these final states. Because the cross-section for Reggeonexchange is largest near threshold, the final state rapidity distributiondepends on the beam energies. At high-energy colliders like the proposed LHeCor $pA$ collisions at the LHC, the final states are produced at far forwardrapidities. For lower energy colliders, the systems are produced closer tomid-rapidity, within reach of central detectors.

Photoproduction of charged final states in ultra-peripheral collisions and electroproduction at an electron-ion collider