Photoproduction and detection of $\rho'\rightarrow\pi^+\pi^-\pi^+\pi^-$ decays in ultra-peripheral collisions and at an electron-ion collider

Abstract

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 $\rho'$ is of interest as an intermediate mass state (between the $\rho$ and $J/\psi$) that is easier to detect than the $\phi$. 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). We compare the UPC projections with ALICE data, and constrain the branching ratio divided by the square of the photon-$\rho'$ coupling. The data prefer large couplings and small branching ratio, probably less than 25\%. The photon-meson coupling predicted by generalized vector meson dominance does not fit the data. The HERA $ep$ and ALICE UPC $e$Pb data exhibit very similar $4\pi$ 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 $\rho'\rightarrow\pi^+\pi^-\pi^+\pi^-$ 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.