Thermal Relaxation of Charm in Hadronic Matter

TL;DR

This paper calculates the thermal relaxation rate of open-charm mesons in hot hadronic matter, revealing significant effects on D-meson spectra in heavy-ion collisions and suggesting a continuous diffusion coefficient near the QCD critical temperature.

Contribution

It provides empirical estimates of D-meson relaxation times using scattering amplitudes, connecting hadronic and quark-gluon plasma phases.

Findings

Relaxation time of 25-50 fm/c at T=150-180 MeV in pion gas

Reduced relaxation time of 10-25 fm/c in hadron-resonance gas

Similar spatial diffusion coefficient near T_c for hadronic and QGP phases

Abstract

The thermal relaxation rate of open-charm ($D$) mesons in hot and dense hadronic matter is calculated using empirical elastic scattering amplitudes. $D$-meson interactions with thermal pions are approximated by $D^*$ resonances, while scattering off other hadrons ($K$, $\eta$, $\rho$, $\omega$, $K^*$, $N$, $\Delta$) is evaluated using vacuum scattering amplitudes as available in the literature based on effective Lagrangians and constrained by realistic spectroscopy. The thermal relaxation time of $D$-mesons in a hot $\pi$ gas is found to be around 25-50\,fm/$c$ for temperatures $T$=150-180\,MeV, which reduces to 10-25\,fm/$c$ in a hadron-resonance gas. The latter values, argued to be conservative estimates, imply significant modifications of $D$-meson spectra in heavy-ion collisions. Close to the critical temperature ($T_c$), the spatial diffusion coefficient ($D_s$) is surprisingly similar to recent calculations for charm quarks in the Quark-Gluon Plasma using non-perturbative $T$-matrix interactions. This suggests a possibly continuous minimum structure of $D_s$ around $T_c$.