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

TL;DR

This paper investigates how $t$-channel singularities affect charm meson reactions in an expanding hadron gas after heavy-ion collisions, revealing their impact on charm-meson ratios and reaction rates.

Contribution

It introduces a detailed analysis of $t$-channel singularities and thermal effects on charm meson reaction rates in an expanding hadron gas.

Findings

$t$-channel singularities are regularized by thermal $D$ widths.

Reaction rates from $t$-channel singularities are inversely related to pion density.

Charm-meson ratios are slightly altered by $t$-channel effects.

Abstract

We study the time evolution of the numbers of charm mesons after the kinetic freezeout of the expanding hadron gas produced by the hadronization of the quark-gluon plasma from a central heavy-ion collision. The $\pi D$ reaction rates have contributions from a $D^\ast$ resonance in the $s$ channel. The $\pi D^\ast$ reaction rates are enhanced by $t$-channel singularities from an intermediate $D$. The contributions to reaction rates from $D^\ast$ resonances and $D$-meson $t$-channel singularities are sensitive to thermal mass shifts and thermal widths. In the expanding hadron gas, the $t$-channel singularities are regularized by the thermal $D$ widths. After kinetic freezeout, the thermal $D$ widths are dominated by coherent pion forward scattering. The contributions to $\pi D^\ast$ reaction rates from $t$-channel singularities are inversely proportional to the pion number density, which decreases to 0 as the hadron gas expands. The $t$-channel singularities produce small but significant changes in charm-meson ratios from those predicted using the known $D^\ast$-decay branching fractions.