Charm diffusion in a pion gas implementing unitarity, chiral and heavy quark symmetries

Abstract

We compute the charm drag and diffusion coefficients in a hot pion gas, such as is formed in a heavy ion collision after the system cools sufficiently to transit into the hadron phase. We fully exploit heavy quark effective theory (with both D and D∗ mesons as elementary degrees of freedom during the collision) and chiral perturbation theory, and employ standard unitarization to reach higher temperatures. We find that a certain friction and shear diffusion coefficients are almost p2-independent at a fixed temperature which simplifies phenomenological analysis. At the higher end of reliability of our calculation, T ≃ 150 MeV, we report a charm relaxation length λc ≃ 40 fm, in agreement with the model estimate of He, Fries and Rapp. The momentum of a 1 GeV charm quark decreases about 50 MeV per fermi when crossing the hadron phase.