Shining a gluon beam through quark-gluon plasma

Abstract

We compute the energy density radiated by a quark undergoing circular motion in strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills plasma. If it were in vacuum, this quark would radiate a beam of strongly coupled radiation whose angular distribution has been characterized and is very similar to that of synchrotron radiation produced by an electron in circular motion in electrodynamics. Here, we watch this beam of gluons getting quenched by the strongly coupled plasma. We find that a beam of gluons of momenta $\ensuremath{\sim}q\ensuremath{\gg}\ensuremath{\pi}T$ is attenuated rapidly, over a distance $\ensuremath{\sim}{q}^{1/3}(\ensuremath{\pi}T{)}^{\ensuremath{-}4/3}$ in a plasma with temperature $T$. As the beam propagates through the plasma at the speed of light, it sheds trailing sound waves with momenta $\ensuremath{\lesssim}\ensuremath{\pi}T$. Presumably these sound waves would thermalize in the plasma if they were not hit soon after their production by the next pulse of gluons from the lighthouselike rotating quark. At larger and larger $q$, the trailing sound wave becomes less and less prominent. The outward-going beam of gluon radiation itself shows no tendency to spread in angle or to shift toward larger wavelengths, even as it is completely attenuated. In this regard, the behavior of the beam of gluons which we analyze is reminiscent of the behavior of jets produced in heavy ion collisions at the LHC which lose a significant fraction of their energy without appreciable change in their angular distribution or their momentum distribution as they plow through the strongly coupled quark-gluon plasma produced in these collisions.