Polarization of the $\phi$ meson in the hadronic phase with nucleon scatterings and a viscous hydrodynamic background

We extend our previous work on the spin alignment of the $\phi$ vector meson in the hadronic phase of the Quark Gluon Plasma, by including effects of nucleon scatterings. The emission rates are calculated in a realistic hydrodynamic background simulated with the code Fluid$u$m, for different beam energies. We find that all the effects taken into account cannot explain the out-of-plane spin alignment of the $\phi$ meson observed experimentally.