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

The energy can be absorbed into the medium, either by absorption of the radiated gluons or because of collision loses. Where does the energy go? This energy incorporates to the hydrodynamic evolution of the medium and leads to jet induced collective effects. 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. We assume that most of the energy is absorbed and thermalized.

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   The initial disturbance is: background energy Strong initial modifications ! We cannot do an accurate matching of the jet and the medium.

Coupling of the jet to hydro We describe the excited medium through hydrodynamics Function with zero integral The functional form of is unknown. It is only constraint by the energy loss, but it does not determine it. Contains the information about the deposition/themalization of the energy and momentum 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.

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

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.

Jet Induced Flow: Correlations  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. Regardless of the excitation mechanisms, shock waves are formed in the medium. We want to study their effect in the particle production.

Spectrum Cooper-Fry with equal time freeze out At low p t ~T f P t >>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

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 at . Non-trivial structure is not observed.

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

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

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 c 2 s < 1/3

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 c 2 s 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.

t<t M t=t M t>t M t>>t M Expansion effects: Reflected Waves If the deconfinement phase transition is fist order then (mixed phase) 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 A B A reflected wave appears  second cone

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

Conical Flow in AdS/CFT? (Friess, Gubser, Michalogiorgakis, Pufu hep-th/ ) 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 T 00 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.

Conclusions We have used hydrodynamics to follow the energy deposited in the medium. Finite c s 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  ).

Back up slides

<= RHIC c 2 s is not constant through system evolution: c sQGP =, c s = in the resonance gas and c s ~0 in the mixed phase. p/e(  ) = EoS along fixed n B /s lines Considerations about Expansion Distance traveled by sound is reduced  Mach direction changes (Hung,E. Shuryak hep-ph/ )  = 1.23 rad =71 o

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 at . No non-trivial structure is observed.