Hydrodynamic Flow from Fast Particles

1. Hydrodynamic Flow from Fast Particles Jorge Casalderrey-Solana. E. V. Shuryak, D. Teaney SUNY- Stony Brook

2. Where does the energy go? Parton propagation in the QGP leads to energy loss but what happens to the energy? The energy can be radiated out of the interaction medium. Energy then means degradation of the energy into (medium induced) gluons. The energy can be absorbed into the medium, either by absorption of the radiated gluons or because of collision loses. We assume that most of the energy is absorbed and thermalized. This energy incorporates to the hydrodynamic evolution of the medium and leads to jet induced collective effects.

3. Large initial Disturbances Right after the jet passage, the deposited energy needs to thermalize. This is a non dissipative process We assume that the typical scale for this process is set by h The initial disturbance is: background energy Strong initial modifications ! We cannot do an accurate matching of the jet and the medium.

4. Coupling of the jet to hydro Function with zero integral We describe the excited medium through hydrodynamics Contains the information about the deposition/themalization of the energy and momentum The functional form of is unknown. It is only constraint by the energy loss, but it does not determine it. We try to characterize different flows consistent with the energy loss constraint (without an explicit source). We do this in the region far from the jet, where the perturbation is small and we can use linearized hydro.

5. Linearized Modes Far away from the fluid: Rotational flow Mach cone sound propagating mode diffuson not propagating mode

6. Excitation Mechanisms To study how the two modes are excited we study the flux momentum. In the jet rest frame: Fixed v   Isentropic interactions: The fluid is mainly potential (irrotational). On shell propagation requires that no significant entropy is produced and there is no vorticity. The Eloss is quadratic in the amplitude of the perturbation.  Non isentropic interactions: the main excitation mechanism is entropy production and the flow field introduces vorticity.

7. f Jet Induced Flow: Correlations Regardless of the excitation mechanisms, shock waves are formed in the medium. We want to study their effect in the particle production. Two particle correlation experiments: trigger in a high energy particle and look at correlated softer particles. Jet Quenching biases trigger jets to be produced next to the interaction region surface. The back jet travels preferentially though the whole interaction region. The back jet modifies the fluid by the energy/momentum loss until it is absorbed.

8. Spectrum • Cooper-Fry with equal time freeze out • At low pt~Tf • Pt >>the spectrum is more sensitive to the “hottest points” (shock and regions close to the jet) • If the jet energy is enough to punch through,  fragmentation part on top of “thermal” spectrum

9. Non Isentropic Interaction Both the vorticity and the entropy production lead to modification in the near field (non-hydrodynamic core). The presence of the diffusion mode make the liquid to move preferentially along the jet direction.  correlations atf=p. Non-trivial structure is not observed.

10. Isentropic Interactions: Correlations Non trivial correlation in Df: Simple simulation Static homogeneous baryon free fluid. Ideal QGP equation of state. Only one jet energy.

11. Experimental Correlation. =+/-1.23=1.91,4.37

12. Expansion effects We study a simple dynamical model: A static liquid in a dynamic gravity field: Big Bang like R is an external parameter, we choose it as From the potential (in Fourier space) Harmonic oscillator with time dependent mass and frequency decreases with increasing R for c2s < 1/3

13. Expansion effects: Amplitude We assume adiabatic changes: There is an (approximately) constant of motion. The adiabatic invariant: harmonic oscillator For RHIC, the evolution changes the fireball radius (from ~6fm to ~15 fm) and the c2s from 1/3 to 0.2  the amplitude v/T grows by a factor 3. Energy loss quadratic in the amplitude  Since energy loss is quadratic in the amplitude, dE/dx could be reduced by a factor 9.

14. Expansion effects: Reflected Waves B t=tM t>tM t<tM t>>tM A If the deconfinement phase transition is fist order then (mixed phase) A reflected wave appears  second cone From hydro simulations, the QGP, mixed, and hadron gas phases last the same time t~4-5 fm. The second cone moves backwards  particle correlated in the trigger jet direction

15. Expansion effects: Reflected Waves In central collisions no correlations are observed at Df~1.4 rad In more peripheral, there is some correlation but looks like the shoulder of the Mach peak. If collective effects are the responsible of non trivial dihadron distributions: The non observation of the reflected peak seems to indicate that the QCD phase transition may not to be first order (experimentally).

16. Conical Flow in AdS/CFT? (Friess, Gubser, Michalogiorgakis, Pufu hep-th/0607022) Motion of a heavy quark in strongly coupled N=4 SYM The AdS/CFT provides the exact matching of the jet and the medium Looking at T00 they found the shock waves in N=4 SYM This is a dynamical model which allows to address how much energy is thermalized and how it incorporates into the hydro evolution.

17. Conclusions • We have used hydrodynamics to follow the energy deposited in the medium. • Finite cs leads to the appearance of a Mach cone (conical flow correlated to the jet) • Depending on the initial conditions, the direction of the cone is reflected in the final particle production. • Density decrease of expanding medium increases the Mach cone signal • First order phase transition reflected waves (correlations at Df < p ).

18. Back up slides

19. Considerations about Expansion • c2s is not constant through system evolution: csQGP= , cs= in the resonance gas and cs~0 in the mixed phase. (Hung,E. Shuryak hep-ph/9709264) • Distance traveled by sound is reduced Mach direction changes <= RHIC • q = 1.23 rad =71o p/e(e) = EoS along fixed nB/s lines

20. Non Isentropic Interaction Both the vorticity and the entropy production lead to modification in the near field (non-hydrodynamic core). The presence of the diffusion mode make the liquid to move preferentially along the jet direction.  correlations atf=p. No non-trivial structure is observed.