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 DisturbancesRight 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

fmpes 1.034

The initial disturbance is:

1100363

s

s

edxdE

background energy

Strong initial modifications !

We cannot do an accurate matching of the jet and the medium.

Coupling of the jet to hydroWe describe the excited medium through hydrodynamics

xJT

xJxddtdP

3

00,1,12

2/32

2 22

trx jetedxdEJ

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

xJ

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 0xxX

00 vtx

Mach cone

RURhu

uT

'

'

2222 sst c isit RR 2

43

soundpropagating mode

diffusonnot 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:

ddE

ddST

ddS

TddE j

Rj

Rjj

Fixed v 0ddE

dtdPv

dtdE j

x

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

f

t

ffff

z

Tvp

TT

TE

TE

Tup

ptz

edVedVpddp

dN

330

2 22

• At low pt~Tf

)cos(42 3

02

pP

TPE

TEVe

pddpdN dep

f

tdep

f

TE

ptz

f

z

• 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

Non Isentropic InteractionBoth 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.

inclusivejet dyddN

dyddN

dyddN

2010 Tpt fmGeV

dxdE 6.12

fmGeV

dxdE 2

Isentropic Interactions: Correlations

51 Tpt

105 Tpt

15103 Tpt

201510 Tpt

Non trivial correlation in inclusivejet dyd

dNdyddN

dyddN

263TdxdE

75.0T 1.0Ts

Simple simulationStatic homogeneous baryon free fluid.Ideal QGP equation of state.Only one jet energy.

TdxdEE 8

3

1arccos

Experimental Correlation. +/-1.23=1.91,4.37

51 Tpt

105 Tpt

15103 Tpt

201510 Tpt

3

1arccos

51 Tpt

105 Tpt

15103 Tpt

201510 Tpt

Expansion effectsWe study a simple dynamical model: A static liquid in a dynamic gravity field:

2222222 xddRxdtRdtd

Big Bang like

R is an external parameter, we choose it as ,3/1

0

00

tttRtR

From the potential (in Fourier space)

SsR 3

GkisksTvG iiii

02 GMGM

22

1

ss RTccMM 222

sck

Harmonic oscillator with time dependent mass and frequency

decreases with increasing R for c2s < 1/3

RTM 1

Expansion effects: Amplitude We assume adiabatic changes:

skcddM

M

1

ss

s

kcddc

c

2

2

1

There is an (approximately) constant of motion. The adiabatic invariant:

pdqI harmonic oscillator

kMIcG s

k2

MIkcR

Tv sk 2

For RHIC, the evolution changes the fireball radius (from ~6fm to ~15 fm) and the c2

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.

Tvk

Tvk

1t

2t

T

T

t<tM t=tM t>tM t>>tM

Expansion effects: Reflected Waves If the deconfinement phase transition is fist order then

0sc (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

3MtAB

2.0MtBC

A reflected wave appears second cone

4.1cos

MtCBABar

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/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.

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 ).

Back up slides

<= RHIC

• c2s is not constant through system evolution:

csQGP= , cs= in the resonance gas and cs~0 in the mixed phase.

p/e() = EoS along fixed nB/s lines

Considerations about Expansion

•Distance traveled by sound is reduced Mach direction changes

2.031

33.0)(1

sf

avs cdc

(Hung,E. Shuryak hep-ph/9709264)

• = 1.23 rad =71o

Non Isentropic InteractionBoth the vorticity and the entropy production lead to modification in the near field (non-hydrodynamic core).

tzppttz ddppdp

dNQ

c0

1:)(

tzppttz dppdp

dNQ0

:

The presence of the diffusion mode make the liquid to move preferentially along the jet direction. correlations at .

No non-trivial structure is observed.