Time Dependent q̂ from AdS/CFT

Abstract

We present the first ever AdS/CFT calculation of q̂ for a light quark jet as a function of position or, equivalently, time. Our result does not suffer from the gamma factor blow up of the usual time-independent AdS/CFT heavy quark setup and is qualitatively similar to, but differs by ∼O(1) factor from, the light flavor result of Liu, Rajagopal, and Wiedemann. Our findings can be immediately implemented into any q̂-based energy loss model.Our q̂ derivation relies on our calculation of the average distance squared, s2(t), travelled by the endpoint of a string falling in an AdS3-Schwarzschild spacetime. The early time behavior is ballistic, s2(t)∼t2, but the late time behavior is the usual diffusive Brownian motion, s2(t)∼t. These late time dynamics are universal and depend only on the near-horizon physics, which allows us to generalize our results to arbitrary dimensions and thus make contact with the physics explored by RHIC and LHC.Additionally, we find that AdS/CFT predicts angular ordering for radiation in medium, just as in vacuum, and in contradistinction to weak-coupling, with its anti-angular ordering prediction. Finally, our results also imply, sensibly, that AdS/CFT predicts a smooth interpolation between the angular correlations of open heavy flavor and light flavor observables.