Interactions of the deuteron with a hadronic medium

We investigate the interactions of the deuteron with light mesons during the hadronic phase in heavy-ion collisions. We treat the deuteron as a weakly bound state and employ the quasi-free approximation to describe the $d\pi$ interaction. The underlying elementary $N\pi$ amplitudes are described by a hybrid effective model, combining the non-resonant background from chiral perturbation theory with resonant contributions via Breit-Wigner parameterizations. These amplitudes are used to calculate the vacuum and thermally-averaged cross-sections for deuteron dissociation and production, namely, $d + \pi \rightarrow N + N' + \pi$ and the corresponding inverse reaction. We then use these cross sections in a rate equation to estimate the time evolution of the deuteron multiplicity. For the initial conditions we consider two models: the statistical hadronization model and the coalescence model, where the deuteron is treated as a hadronic molecule. Our findings suggest that the final deuteron yield does not retain a memory of its initial production mechanism.