Gluon Bremsstrahlung in Weakly-Coupled Plasmas

I report on some theoretical progress concerning the calculation of gluon bremsstrahlung for very high energy particles crossing a weakly-coupled quark-gluon plasma. (i) I advertise that two of the several formalisms used to study this problem, the BDMPS-Zakharov formalism and the AMY formalism (the latter used only for infinite, uniform media), can be made equivalent when appropriately formulated. (ii) A standard technique to simplify calculations is to expand in inverse powers of logarithms $\ln(E/T)$. I give an example where such expansions are found to work well for $\omega/T \gtrsim 10$ where $\omega$ is the bremsstrahlung gluon energy. (iii) Finally, I report on perturbative calculations of $\hat q$.