Polarization of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> meson in the hadronic phase with nucleon scatterings and a viscous hydrodynamic background

We extend our previous work on the spin alignment of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>ϕ</a:mi> </a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mtext>FLUID</b:mtext> <b:mi>u</b:mi> <b:mtext>M</b:mtext> </b:mrow> </b:math> , for different beam energies. We find that all the effects taken into account cannot explain the out-of-plane spin alignment of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>ϕ</c:mi> </c:math> meson observed experimentally.