Time Dependent $\hat{q}$ from AdS/CFT

W. A. Horowitz
2017 Journal of Physics, Conference Series  
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
more » ... e distance squared, s^2(t), travelled by the endpoint of a string falling in an AdS_3-Schwarzschild spacetime. The early time behavior is ballistic, s^2(t)∼ t^2, but the late time behavior is the usual diffusive Brownian motion, s^2(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.
doi:10.1088/1742-6596/878/1/012021 fatcat:7ljp2kysqrel7daq545plm6lfm