Transcript Slide 1

Mach Cones in
Quark Gluon Plasma
Jorge Casalderrey-Solana
Lawrence Berkeley Laboratory
1
Jet-Medium Coupling
What happens to the energy lost by jets?
Leaves the interaction region being
transferred to propagating modes:
• Large angle induced radiation (Vitev, Polosa & Salgado)
• Plasma modes
{
Plasmon (Ruppert & Mueller)
Cherenkov
( Koch, Majumder & Wang, Dremin)
Remains in the medium
• Described as a parton cascade (Ma et al.)
• Themalize (Stoecker , JCS, Teaney & Shuryak,
Renk & Ruppert, Chaudhuri & Heinz)
Hydrodynamical behaviour  the medium reacts collectively
2
Hydrodynamic Modes
M
Sound (φ)
x0  t0
Propagating mode, cs
Wave interference 
Mach cone at cos M   cs
Diffuson (Rμ)
Not propagating mode
Remembers source direction
NR fluid dynamics 
The strength of the two modes is set by the shape of the bullet
What sets relative mode amplitude in Jet-Medium interaction?
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Excitation Mechanisms
0
J
0
x
JetJmodification
of
hydro:
  2
1
dE 
t
x v t
2 2
J 

e
v
dE 
i
3/ 2
2 2
2
J 
sT process
ie
 vT 2
 J xdx Depostion/thermaliztion

dx
  2
x v t

dE e
J 
dx 2 2

x (fm) 
3/ 2
1,
dP
3


  d xJ  x 
dt
ρ (fm)
ρ (fm)
One
x integral1constraint
v ( x,  )   x  R x
T not unique:
The source
is
dS
x
R 
dtx  rjet t 2 2 2

1, 0 0
Non isentropic excitations: the
main excitation mechanism is
entropy production and the
flow field introduces vorticity.
Function with
 zero integral
x (fm)
Isentropic excitations: No
significant entropy production.
Medium excitation by sound
wave emission. The Eloss is
quadratic in the amplitude. 4
Spectrum

0
The fluid picture is not directly observed
Spectrum: Cooper-Fry
passocT
fluid cell

dN
dpz d 2 pt
p z 0

dV
e
3
2 

E
Tf
 

 E T pt v 
exp


Tf 

T f T f

velocity
Peaks at passocT ║ v but broad angle distribution at low pT
Excitation independent low passocT (T) angular dependence,
the distribution from different fluid cells overlaps

dN
dp z d 2 pt
p z 0
E
Tf
dep
dep


P
e
E
E
P
t


V

cos(   ) 
3 

2   T f 4 T f   p

Peaks at
back jet
direction
No large angle correlation at small passocT
High passocT particles reflect the flow picture
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Diffuson 
flow along jet direction
No large angle correlation
dN/dydD
Non Isentropic Excitations
dE
GeV
 12.6
dx
fm
10  pt T  20
dE
GeV
2
dx
fm
D

Chaudhuri & Heinz:
Non linear hydro + source
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Isentropic Excitations
4.0<PTTrig<6.0 GeV/c
 1 
D  arccos

3


1  pt T  5
0.15<PTAssoc<4.0 GeV/c
Static Medium 
Large dE/dx12 Gev/fm
dN/dydD
5  pt T  10 Expanding medium the 
necessary dE/dx1.5 Gev/fm
10  pt T  15
15  pt T  20
D
(dilution of the medium)
The correlations develops
as passocT increases
D
The magnitude of the
correlation decreases
exponentially.
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Expanding Medium
The underlying flow v affects the directionality of the Mach cone (Satarov 05)
Longitudinal flow  Elongation in y
Radial flow broadens the peaks
(misalignment of flow and jet)
Renk + Ruppert : studies in a realistic background + BDMPS radiative losses
2.5  pttrig  4.0 GeV
1.0  ptassoc  2.5 GeV
Fraction f=0.75 of energy into θM
θM updated with local cs
Rapidity distribution of Back Jet P(y)
Elongation due to longitudinal flow
Dominated by Radial flow ║ Mach
flow (Cooper-Fry)
Observed 3-p signal (strong radial expansion destroys the cone)
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Mach Angle from Transport
Y. G. Ma, G. L. Ma et al. (06)
AMPT Transport model:
22 parton cascade + recombination
Large angle correlation is observed
The signal has a partonic origin
Hadronic re-scattering increases the
magnitude of the correlation
3-particle analysis: the medium
excitation is conical.
It requires “long” partonic phase
tp > 1.5 fm
Large partonic σ  Hydro limit?
collective effects?
22 interaction  Isentropic ?
(no particle production)
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Cherenkov radiation:
Koch, Majumder, Wang (05)
Dremin (05)
At high T, plasma modes are time like  cannot be excited by ω=vq
If there are bound states in the plama:
Processes like
lead to
n   1
n(ω) >1 for ω  inter-level spacing
Heavy bound states are required for
Cherenkov gluons at ω  1 GeV

Large angle radiation happens mostly at
low passoct as opposed to Mach cone.
(space like gluon)
cos  c  1 / n p 
p
A similar mechanism in the plasmon (longitudinal gluon) can happen if
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it also becomes spacelike, εL>1 (Ruppert and Mueller)
Radiation at Large Angle
Vitev (05)
Induced gluon radiation is suppressed at small
angle (interference)
Smearing:
Inclusive distribution do not show large angle
correlations
Polosa + Salgado: since ptrigT  passoT only one gluon can be radiated
Exclusive process  Sudakov  Stronger angular dependence than inclusive
distribution. After smearing:
Centrality dependence of the splitting
parameter is reproduced.
For low passocT becomes inclusive 
no large angle correlations
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Deflected Jets
(Armesto et al., Fries)
Scattering of an energetic parton in the medium leads to
a change in jet direction
α
The collinear fragmentation along the back jet is the
source of off π.
At each event there are particle in only one side
Clearly distinguishable through 3 particle correlation
Chiu and Hwa (06)
Follow path of the partons
Random deflection (gaussian)
At initial times σ/2=0.88
(large deflections)
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Three Particle Correlations
2.5  pttrig  4.0 GeV
1.0  ptassoc  2.5 GeV
PHENIX Acceptance
Au+Au 0-12%
D13
D *  0
D * 

2
D *  
D12
Cent 0  5%
Indications of abnormal jets
Star: signal along the off-diagonal consistent with conical
structure
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Conical Flow in AdS/CFT
(Friess, Gubser, Michalogiorgakis, Pufu hep-th/0607022)
String theory study of Heavy Quark
motion in strongly coupled N=4 SYM
Drag
{
Herzog et al.
2

g
Nc 2
dp
JCS & Teaney

T
dt
2M
Gubser
T 00 (  vkL , k L , k ) = Energy Density
v=0.75
T00
Looking at
they found the
shock waves in N=4 SYM
2
1
0
2
KL 4
v=0.95
1
0
2
KL
4
1
0
2
0
2
2
K┴
2
K┴
This is a dynamical model.
No assumption about hydrodynamical behavior is made!
v=0.9
K┴
K┴
2
KL 4
v=0.99
1
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KL
4
CONCLUSIONS
 Hydrodynamic description of deposited jet energy:
Mach cone formation.
 Particle spectrum reflects the cone (initial conditions!).
 Transport calculations: compatible with the Mach cone
 Mach like signals for plasma modes if n>1.
 Large angle correlations from one gluon radiation.
 pTasso dependence of D:
 Cherenkov: decreases (unless heavy bound states)
 Mach cone and gluon radiation: increases
 Deflected Jets  Different three particle correlation.
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Buck up
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Expansion effects: Amplitude
Static fluid  the amplitude of sound waves decrease like v α 1/r
v1 > v2
t1
velocity field
t2
v1
T1
<
v2
T2
T1 < T2
Expanding medium: also the fluids temperature lowers with t.
The spectrum is controlled by v/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  necessary dE/dx  1.5 GeV/fm.
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From STAR highlights :
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