Photoproduction of $\omega$ mesons off nuclei and impact of polarization on meson-nucleon interaction

We consider photoproduction of $\omega$ mesons off complex nuclei to study interactions of transversely and longitudinally polarized vector mesons with nucleons. Whereas the total cross section for interactions of the transversely polarized vector mesons with nucleons $\sigma_T=\sigma(V_TN)$ can be obtained from coherent photoproduction, measurements of vector meson photoproduction in the incoherent region provide a unique opportunity to extract the total cross section for longitudinally polarized mesons interacting with nucleons $\sigma_L=\sigma(V_LN)$, which has not yet been measured and strongly depends on theoretical approaches. This work is stimulated by the construction of the new experiment GlueX at Jefferson Lab, designed to study the photoproduction of mesons in a large beam energy range up to 12 GeV.