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We study the time evolution of the numbers of charm mesons after the kineticfreezeout of the expanding hadron gas produced by the hadronization of thequark-gluon plasma from a central heavy-ion collision. The $\pi D$ reactionrates have contributions from a $D^\ast$ resonance in the $s$ channel. The $\piD^\ast$ reaction rates are enhanced by $t$-channel singularities from anintermediate $D$. The contributions to reaction rates from $D^\ast$ resonancesand $D$-meson $t$-channel singularities are sensitive to thermal mass shiftsand thermal widths. In the expanding hadron gas, the $t$-channel singularitiesare regularized by the thermal $D$ widths. After kinetic freezeout, the thermal$D$ widths are dominated by coherent pion forward scattering. The contributionsto $\pi D^\ast$ reaction rates from $t$-channel singularities are inverselyproportional to the pion number density, which decreases to 0 as the hadron gasexpands. The $t$-channel singularities produce small but significant changes incharm-meson ratios from those predicted using the known $D^\ast$-decaybranching fractions.

Charm-Meson $t$-channel Singularities in an Expanding Hadron Gas