Collisional energy loss of a fast heavy quark in a quark-gluon plasma

Abstract

We discuss the average collisional energy loss $dE/dx$ of a heavy quark crossing a quark-gluon plasma, in the limit of high quark energy $E\ensuremath{\gg}{M}^{2}/T$, where $M$ is the quark mass and $T\ensuremath{\ll}M$ is the plasma temperature. In the fixed coupling approximation, at leading order $dE/dx\ensuremath{\propto}{\ensuremath{\alpha}}_{s}^{2}$, with a coefficient which is logarithmically enhanced. The soft logarithm arising from $t$-channel scattering off thermal partons is well known, but a collinear logarithm from $u$-channel exchange had previously been overlooked. We also determine the constant beyond those leading logarithms. We then generalize our calculation of $dE/dx$ to running coupling. We estimate the remaining theoretical uncertainty of $dE/dx$, which turns out to be quite large under Relativistic Heavy Ion Collider conditions. Finally, we point out an approximate relation between $dE/dx$ and the QCD Debye mass, from which we derive an upper bound to $dE/dx$ for all quark energies.