Transcript Slide 1
Mach Cones in
Quark Gluon Plasma
Jorge Casalderrey-Solana
Lawrence Berkeley Laboratory
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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
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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?
3
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
dtx rjet 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/dx12 Gev/fm
dN/dydD
5 pt T 10 Expanding medium the
necessary dE/dx1.5 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:
22 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?
22 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%
D13
D * 0
D *
2
D *
D12
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
14
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
16
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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