Finite-temperature effects on the threshold cusps in π π and D D ¯ * scatterings from relativistic heavy-ion collisions

We investigate how the temperature influences the threshold cusps in meson-meson scatterings, i.e., π π and D D ¯ * (or D * D ¯ ) scatterings, using the production rates and propagators obtained at finite temperature. The line shape of production rate of π π at different temperatures demonstrates that the cusp structure in π π scattering is mildly enhanced as the temperature increases. For the π π propagator, which includes isospin symmetry breaking, the line shape displays a unique plateaulike structure, and this structure will also be enhanced as the temperature increases. For comparison, the line shape of the D D ¯ * propagator including isospin symmetry breaking is also investigated at different temperatures. As the temperature increases, its line shape shows a similar plateaulike structure but with some different properties when the temperature modifications to the masses and widths of D and D ¯ * are considered.