Evolution of charm-meson ratios in an expanding hadron gas

We study the time evolution of the number of charm mesons after the kinetic freeze-out of the hadron gas produced by a central heavy-ion collision. The $\pi$ D${}^{\ast }$ $\to$ $\pi$ D${}^{\ast }$ reaction rates have $t$-channel singularities that give contributions inversely proportional to the thermal width of the D. The ratio of the D${}^0$ and D${}^{+}$ production rate can differ significantly from those predicted using the measured D${}^{\ast }$ branching fractions.