Angular Modulation of the Transverse Momentum of $\rho^0$ Mesons and their Decay Pions Relative to the Event Plane in Ultra-Peripheral Au+Au Collisions at $\sqrt{s_{NN}} = 200$~GeV

We present a detailed analysis of $\rho^0$ meson photoproduction in ultra-peripheral Au+Au collisions at $\sqrt{s_{NN}} = 200$~GeV, using data from the STAR experiment. In these events, strong electromagnetic fields generate linearly polarized photons, which interact with target to create $\rho^0$ mesons. Since photon polarization is not directly measurable, we use the first-order event plane ($\Psi_1$), reconstructed via neutron emission in the ZDC-SMD detectors, as a proxy for the photon polarization axis.

We study azimuthal angular distributions of the transverse momentum of $\rho^0$ mesons and their decay pions relative to $\Psi_1$. Weak modulation is observed at the $\rho^0$ level, consistent with interference effects, while the pions show a slightly larger anisotropy, suggesting sensitivity to photon polarization. These results demonstrate that final-state pions retain a clearer imprint of the initial photon polarization and introduce a new experimental approach for probing photon polarization, offering insights into the interplay between electromagnetic fields, spin dynamics, and collision geometry in photonuclear processes.