Energy loss of a heavy quark in the quark-gluon plasma

The energy loss $\frac{\mathrm{dE}}{\mathrm{dx}}$ for a heavy quark propagating through a quark-gluon plasma is calculated to leading order in the QCD coupling constant. Simple formulas for $\frac{\mathrm{dE}}{\mathrm{dx}}$ are obtained in the regions $E\ll \frac{M_Q^2}{T}$ and $E\gg \frac{M_Q^2}{T}$, where $M_Q$ is the mass of the heavy quark and $T$ is the temperature. The crossover energy between the two regions is determined to be approximately $1.8\frac{M_Q^2}{T}$. Under conditions relevant to ultrarelativistic heavy-ion collisions, charm quarks and bottom quarks lie on opposite sides of the crossover energy and therefore experience significantly different energy losses.