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Heavy Quark Propagation in an AdS/CFT plasma

Heavy Quark Propagation in an AdS/CFT plasma. Jorge Casalderrey-Solana LBNL. Work in collaboration with Derek Teaney. Outline. Langevin dynamics for heavy quarks. Calibration of the noise. Broadening from Wilson Lines. AdS/CFT computation. Broadening at finite velocity.

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Heavy Quark Propagation in an AdS/CFT plasma

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  1. Heavy Quark Propagation in an AdS/CFT plasma Jorge Casalderrey-Solana LBNL Work in collaboration with Derek Teaney

  2. Outline Langevin dynamics for heavy quarks Calibration of the noise Broadening from Wilson Lines AdS/CFT computation Broadening at finite velocity

  3. Langevin Dynamics Heavy Quark M>>T  moves slowly de Broglie w. l. HQ is classical Random (white) noise Einstein relations Medium properties

  4. Heavy Quarks at RHIC The Langevin model to is used to describe charm and bottom quarks Fits to data allow to extract the diffusion coefficient (Moore & Teaney, van Hees & Rapp)

  5. How to Calibrate the Noise In perturbation theory But we cannot use diagrams! M>>T  long deflection time  Thermal average

  6. Broadening from Wilson Lines E(t1,y1)Dt1dy1 E(t2,y2)Dt2dy2 Small fluctuation of the HQ path

  7. t y AdS/CFT computation Static Quark: straight string stretching to the horizon v=0 u=e We solve the small fluctuation problem (mechanical problem) u0=1 Horizon In terms of the classical solution

  8. Broadening and Diffusion in AdS/CFT In perturbation theory Depends explicitly on Nc. Different from h/s It is not universal! Putting numbers To compare with QCD => rescale the degrees of freedom (Liu, Rajagopal, Wiedemann)

  9. c(u)=v u=1/g Probe at finite velocity t Trailing string => work over tension x=vt x same k! Drag valid for all p ! (Herzog, Karch, Kovtun, Kozcaz and Yaffe ; Gubser) Broadening => repeat fluctuation problem Depends on the energy of the probe!

  10. Conclusions We have provided a “non-perturbative” definition of the momentum broadening as derivatives of a Wilson Line This definition is suited to compute k in N=4 SYM by means of the AdS/CFT correspondence. The calculated k scales as and takes much larger values than the perturbative extrapolation for QCD. The results agree, via the Einstein relations, with the computations of the drag coefficient. This can be considered as an explicit check that AdS/CFT satisfy the fluctuation dissipation theorem. The momentum broadening k at finite v diverges as .

  11. Back up Slides

  12. Computation of (Radiative Energy Loss) t L r0 (Liu, Rajagopal, Wiedemann) Dipole amplitude: two parallel Wilson lines in the light cone: Order of limits: String action becomes imaginary for For small transverse distance: entropy scaling

  13. Energy Dependence of (JC & X. N. Wang) From the unintegrated PDF Evolution leads to growth of the gluon density, In the DLA HTL provide the initial conditions for evolution. Saturation effects  For an infinite conformal plasma (L>Lc) with Q2max=6ET. At strong coupling

  14. Noise from Microscopic Theory HQ momentum relaxation time: Consider times such that microscopic force (random)  charge density electric field

  15. Heavy Quark Partition Function McLerran, Svetitsky (82) YM states YM + Heavy Quark states Integrating out the heavy quark Polyakov Loop

  16. Heavy Quark Partition Function McLerran, Svetitsky (82) YM states YM + Heavy Quark states Integrating out the heavy quark Polyakov Loop

  17. k as a Retarded Correlator k is defined as an unordered correlator: From ZHQ the only unordered correlator is Defining: In the w0 limit the contour dependence disappears :

  18. E(t1,y1)Dt1dy1 Since in k there is no time order: E(t2,y2)Dt2dy2 Force Correlators from Wilson Lines Integrating the Heavy Quark propagator: Which is obtained from small fluctuations of the Wilson line

  19. rab (-b/2, b/2; -T)A Final distribution Momentum Distribution -T/2 +T/2 v f0 (b) ff (b)

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