Analysis of the data on differential cross sections and spin density matrix elements for $\gamma p \to \rho^0 p$

The newly published data on spin density matrix elements from the GlueX Collaboration, along with the previously released differential cross-section data from the CLAS Collaboration and the other two experiments for the $\gamma p \to \rho^0 p$ reaction, are systematically investigated using an effective Lagrangian approach within the tree-level Born approximation. The model combines contributions from $t$-channel meson exchanges ($\pi$, $\eta$, and $f_2$), $s$-channel nucleon ($N$) and nucleon resonance ($N^\ast$) exchanges, $u$-channel $N$ exchange, and a generalized contact term to construct the scattering amplitudes. Regge propagators are employed for $t$-channel amplitudes to incorporate the contributions from mesons with various spins lying on the same trajectories. The analysis shows that the background contributions, dominated by the $f_2$-trajectory exchange, provide a satisfactory description of the data in the high-energy and forward-angle regions. The inclusion of specific nucleon resonances, such as $N(2100)1/2^{+}$, $N(2060)5/2^{-}$, or $\Delta(2000)5/2^{+}$, significantly improves the description of the differential cross-section data at near-perpendicular scattering angles in the low-energy region. Predictions of photon beam and target nucleon asymmetries are provided, offering valuable insights to discriminate reaction mechanisms when corresponding data become available in the future.