Photoproduction and detection of ρ'→π⁺π⁻π⁺π⁻ decays in ultra-peripheral collisions and at an electron-ion collider

Vector meson photoproduction is an important probe of nuclear structure. Light vector mesons are most sensitive to low$-x$ structure, as long as they are not too light for perturbative QCD calculations. The ρ' is of interest as an intermediate mass state (between the ρ and J/ψ) that is easier to detect than the φ. Using HERA data on proton targets, we make projections for lead/gold targets in UPCs at the Large Hadron Collider and RHIC, and for $ep$ and $eA$ collisions at a future Electron-Ion Collider (EIC). These projections for ion targets depend on the largely-unknown ρ'→π⁺π⁻π⁺π⁻ branching ratio, and use existing data to constrain that branching ratio. Current data points to a relatively low branching ratio, less than 50%. The HERA $ep$ and ALICE UPC ePb data exhibit very similar 4π mass spectra, indicating that, if the system is composed of two resonances, the products of their photon couplings with their four-pion branching ratios are similar. The predicted rates are high for both UPCs and the EIC. The ρ'→π⁺π⁻π⁺π⁻ decay can be observed at the EIC with high efficiency. In $ep$ collisions at the highest energy, the forward B0 detector is needed to observe this channel down to the lowest achievable Bjorken$-x$ values.