The $\cos 2\phi$ azimuthal asymmetry in $\rho^0$ meson production in ultraperipheral heavy ion collisions

We present a detailed study of vector meson photoproduction in ultraperipheral heavy ion collisions (UPCs). Using the dipole model, we develop a framework for the joint impact parameter and transverse momentum dependent cross sections. We compute the unpolarized cross section and $\cos 2\phi$ azimuthal angular correlation for $\rho^0$ photoproduction with $\phi$ defined as the angle between the $\rho^0$'s transverse momentum and its decay product pion meson's transverse momentum. Our result on unpolarized coherent differential cross section gives excellent description to the STAR experimental data. A first comparison between theoretical calculation and experimental measurement on the $\cos 2\phi$ azimuthal asymmetry, which results from the linearly polarized photons, is performed and reasonable agreement is reached. We find out the characteristic diffractive patterns at both RHIC and LHC energies and predict the impact parameter dependent $\cos 2\phi$ azimuthal asymmetries for $\rho^0$ photoproduction by considering UPCs and peripheral collisions. The future experimental measurements at RHIC and LHC relevant to our calculations will provide a tool to rigorously investigate the coherent and incoherent production of vector meson in UPCs, as well as to probe the nuclear structure in heavy ion collisions.