Transcript Hydrodynamic Flow from Jets

Hydrodynamic Flow from Fast
Particles
Jorge Casalderrey-Solana.
E. V. Shuryak, D. Teaney
SUNY- Stony Brook
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.
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 
s  4h
 0.1 fm
3e  p 
The initial disturbance is:
dE dx s
 36  100  1
3
e s
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
Contains the information about


 T  J x
the deposition/themalization of
the energy and momentum

The functional form of J  x is
unknown. It is only constraint by
the energy loss, but it does not
determine it.
 
  x  r jet t 2 2 2
dE e
J 
dx 2 2



3/ 2
1,

dP
3


  d xJ  x 
dt
1, 0 0 
Function with
zero integral
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
  
X  x  x0
Far away from the fluid:
T '  u   
x0  vt0
Rotational flow
u '  h     R   U   R 
Mach cone
sound
propagating mode
   c    s  
2
t
2
s
2
2
diffuson
not propagating mode
3
 t Ri  s  2 Ri
4
Excitation Mechanisms
To study how the two modes are excited we study the flux
momentum. In the jet rest frame:
dS R j dE R j

 T
 T

d
d
d
d
dE j
dS j
dE j
dE
dPx
v

0
Fixed v 
dt
dt
d
 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
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
f
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.
Spectrum
• Cooper-Fry with equal time freeze out
dN
dpz d 2 pt
p z 0
• At low pt~Tf
dN
dpz d 2 pt
p z 0
dV

e
3
2 

pu

Tf
dV

e
3
2 
 
E E T pt v
 

Tf Tf Tf Tf
E
Tf
dep
dep


P
e
E
E
P
t
V 


cos(  f ) 
3 

2   T f 4 T f   p

• 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 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 f.
10  pt T  20
dN
dN

dyd f dyd f

jet
dN
dyd f
Non-trivial structure is
not observed.
dE
GeV
 12.6
dx
fm
inclusive
dE
GeV
2
dx
fm
Isentropic Interactions: Correlations
Non trivial correlation in f:
dN
dN

dyd f dyd f

jet
dN
dyd f
inclusive
 1 
f  arccos

 3
5  pt T  10
1  pt T  5
310  pt
T  15
1015  pt
T  20
Simple simulation
Static homogeneous baryon free fluid.
Ideal QGP equation of state.
Only one jet energy.
dE
 63T 2 T  0.75 sT  0.1
dx
dE 8
E
dx T
Experimental Correlation.
f +/-1.23=1.91,4.37
1  pt T  5
5  pt T  10
310  pt
T  15
1015  pt
T  20
 1 
f  arccos

 3
5  pt T  10
1  pt T  5
310  pt
T  15
1015  pt
T  20
Expansion effects
We study a simple dynamical model: A static liquid in a dynamic gravity field:
d  dt  Rt 
2
2
2
 

2
2
2
2
dx  Rh  dh  dx

Big Bang like
1/ 3
R is an external parameter, we choose it as
From the potential (in Fourier space)
h Mh G   M G  0
 k c
2 2
s
1
M 
RT

Gi  sTvi  isk i  k iG
2
2
 t0  t 
 , sR3  S
Rt   R0 
 t0 
Harmonic oscillator with time
dependent mass and frequency
M
1
M 2 
cs RTcs2
decreases with increasing R for c2s < 1/3

Expansion effects: Amplitude
We assume adiabatic changes:
1 dM
 kcs
M dh
1 dcs2
 kcs
2
cs dh
There is an (approximately) constant
of motion. The adiabatic invariant:
harmonic oscillator

2 Ics
I   pdq
Gk 
kM
vk
2kcs I
R
T
M
vk

T
T
t1
t2
vk

T
T 
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.
Expansion effects: Reflected Waves
If the deconfinement phase transition
is fist order then
cs  0
t<tM
t=tM
t>tM
t>>tM
(mixed phase)
A reflected wave appears  second cone
B
BC  tM 0.2
A
AB  tM
3
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
f  ar cos
AB  CB
 1.4
tM
Expansion effects: Reflected Waves
In central collisions no correlations are observed at f~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).
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 f   ).
Back up slides
Considerations about Expansion
• c2s is not constant through system evolution:
csQGP= 1 3 , cs= 0.2 in the resonance gas and cs~0 in
(Hung,E. Shuryak hep-ph/9709264)
the mixed phase.
•Distance traveled by sound is
reduced Mach direction changes
cs 
av
1
f
 dc ( )  0.33
s
• q = 1.23 rad =71o
p/e() = EoS along fixed nB/s lines
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 f.
1
dN
c(f ) :
Q dpz pt dpt df
dN
Q :
dpz pt dpt
p z 0
pt
p z 0
pt
No non-trivial structure is observed.