Excitation function for global \Lambda polarization in relativistic heavy ion collisions with the Core Corona model

We compute the excitation function of the global $\Lambda$ polarization in semicentral heavy-ion collisions within a Core--Corona framework, where the interaction region is described as a dense core and a dilute corona separated by a critical value of the participant density. An important ingredient in the model are the intrinsic polarization functions in each of the two regions. These are computed from a field-theoretical approach where the vortical motion of the medium is included in an effective fermion propagator, which we derive explicitly. The interactions in the core and the corona are transmitted by suitable mediators at finite temperature and baryon chemical potential; gluons for the former and $\sigma$-mesons for the latter. The temperatures and baryon chemical potentials are related to the collision energies along the chemical freeze-out curve. By allowing the cross section for $\Lambda$ production in the nuclear environment to take on values below the nucleon-nucleon threshold cross section, the calculation describes the lowest energy polarization data point. For the centralities corresponding to the experimental data, we find that the contribution from the corona is the dominant one and that a lifetime, and correspondingly a volume of this region, which becomes larger for the smaller energies due to stopping, is an essential ingredient in the calculation. Overall, the model provides a good description of the excitation function across the full experimental range and predicts a robust maximum near $\sqrt{s_{NN}}\sim$ 3 GeV that remains stable under reasonable variations of the freeze-out curve and the proton-proton $\Lambda$ production threshold to account for subthreshold production in a nuclear environment.