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

TL;DR

This paper calculates charm quark diffusion in a hot pion gas using effective theories and unitarization, revealing temperature-independent coefficients and a charm relaxation length consistent with previous models.

Contribution

It introduces a comprehensive method combining Heavy Quark Effective Theory and Chiral Perturbation Theory with unitarization to compute charm diffusion coefficients in a pion gas.

Findings

Charm diffusion coefficients are nearly independent of momentum at fixed temperature.

Charm relaxation length at T≈150 MeV is about 40 fm.

A 1-GeV charm quark loses approximately 50 MeV per fm crossing the hadron phase.

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 p-independent at fixed temperature which simplifies phenomenological analysis. At the higher end of reliability of our calculation, T about 150 MeV, we report a charm relaxation length of some 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.