mach cones in quark gluon plasma
DESCRIPTION
Mach Cones in Quark Gluon Plasma. Jorge Casalderrey-Solana Lawrence Berkeley Laboratory. 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). {. - PowerPoint PPT PresentationTRANSCRIPT
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Mach Cones in Quark Gluon Plasma
Jorge Casalderrey-Solana
Lawrence Berkeley Laboratory
2
Jet-Medium CouplingWhat happens to the energy lost by jets?
Leaves the interaction region being transferred to propagating modes:
Remains in the medium
Hydrodynamical behaviour the medium reacts collectively
• Described as a parton cascade (Ma et al.)
• Themalize (Stoecker , JCS, Teaney & Shuryak, Renk & Ruppert, Chaudhuri & Heinz)
• Plasma modes { Plasmon (Ruppert & Mueller)
Cherenkov ( Koch, Majumder & Wang, Dremin)
• Large angle induced radiation (Vitev, Polosa & Salgado)
3
Hydrodynamic Modes
Diffuson (Rμ)
00 tx
M Propagating mode, cs
sM ccos
Sound (φ)
Wave interference Mach cone at
Not propagating mode Remembers source direction
The strength of the two modes is set by the shape of the bullet
What sets relative mode amplitude in Jet-Medium interaction?
NR fluid dynamics
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Isentropic excitations: No significant entropy production. Medium excitation by sound wave emission. The Eloss is quadratic in the amplitude.
Non isentropic excitations: the main excitation mechanism is entropy production and the flow field introduces vorticity.
Excitation Mechanisms 00 J
2
2
2
tvx
ii e
dxdEsTvJ
2
2
22/322
1
tvxxt e
dxdE
vJJ
xxx RT
xv 1),(
x (fm)
ρ (f
m)
ρ (f
m)
x (fm)
dtdSR x
xJT
xJxddtdP
3
Depostion/thermaliztion process
One integral constraint
00,1,12
2/32
2 22
trx jetedxdEJ
Function with zero integral
The source is not unique:
Jet modification of hydro:
5
Spectrum
Excitation independent low passocT (T) angular dependence,
the distribution from different fluid cells overlaps
High passocT particles reflect the flow picture
Spectrum: Cooper-Fry
f
t
ff
TE
ptz Tvp
TT
TEedV
pddpdN f
z
exp2 3
02
)cos(42 3
02
pP
TPE
TEVe
pddpdN dep
f
tdep
f
TE
ptz
f
z
No large angle correlation at small passocT
The fluid picture is not directly observed
passocT fluid cell
velocity
Peaks at passocT ║ v but broad angle distribution at low pT
Peaks at back jetdirection
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Non Isentropic Excitations
2010 Tpt
fmGeV
dxdE 6.12
fmGeV
dxdE 2
Diffuson flow along jet direction
No large angle correlation
Chaudhuri & Heinz: Non linear hydro + source
dN/d
yd
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Isentropic Excitations
Static Medium Large dE/dx12 Gev/fm
The correlations develops as passoc
T increases
The magnitude of the correlation decreases exponentially.
Expanding medium the necessary dE/dx1.5 Gev/fm
(dilution of the medium)
51 Tpt
105 Tpt
1510 Tpt
2015 Tpt
3
1arccos
dN/d
yd
4.0<PTTrig<6.0 GeV/c0.15<PTAssoc<4.0 GeV/c
D
8
Expanding MediumThe underlying flow v affects the directionality of the Mach cone (Satarov 05)
Renk + Ruppert : studies in a realistic background + BDMPS radiative losses
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
Observed 3-p signal (strong radial expansion destroys the cone)
Dominated by Radial flow ║ Mach flow (Cooper-Fry)
Longitudinal flow Elongation in y Radial flow broadens the peaks (misalignment of flow and jet)
GeVp trigt 0.45.2
GeVpassoct 5.20.1
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Mach Angle from TransportAMPT Transport model:
Large angle correlation is observed
Hadronic re-scattering increases the magnitude of the correlation
Y. G. Ma, G. L. Ma et al. (06)
22 parton cascade + recombination
The signal has a partonic origin
3-particle analysis: the medium excitation is conical.
It requires “long” partonic phase
p > 1.5 fm
Large partonic σ Hydro limit?collective effects?
22 interaction Isentropic ? (no particle production)
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Cherenkov radiation:
At high T, plasma modes are time like cannot be excited by ω=vq
If there are bound states in the plama:
(space like gluon) 1n
pnc /1cos
Large angle radiation happens mostly at low passoc
t as opposed to Mach cone.
Koch, Majumder, Wang (05)
Processes like lead to
A similar mechanism in the plasmon (longitudinal gluon) can happen if it also becomes spacelike, εL>1 (Ruppert and Mueller)
Dremin (05)
p
n(ω) >1 for ω inter-level spacing
Heavy bound states are required for Cherenkov gluons at ω 1 GeV
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Radiation at Large AngleInduced gluon radiation is suppressed at small angle (interference)
Vitev (05)
Smearing:
Polosa + Salgado: since ptrigT passo
T 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
Inclusive distribution do not show large angle correlations
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Deflected JetsScattering of an energetic parton in the medium leads to a change in jet direction
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 correlationChiu and Hwa (06)
Follow path of the partons
Random deflection (gaussian)
α
At initial times σ/2=0.88 (large deflections)
(Armesto et al., Fries)
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Au+Au 0-12%
12
13
*
2
*
* 0
θ* = 120
GeVp trigt 0.45.2
GeVpassoct 5.20.1
%50 Cent
PHENIX Acceptance
Indications of abnormal jets
Star: signal along the off-diagonal consistent with conical structure
Three Particle Correlations
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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
Looking at T00 they found the shock waves in N=4 SYM
This is a dynamical model. No assumption about hydro- dynamical behavior is made!
),,(00 kkvkT LL = Energy Density
0 2 4KL
1K┴
2
0 2 4KL
1K┴
2
0 2 4KL
1K┴
2
0 2 4KL
1K┴
2
Mach c
one
v=0.75 v=0.9
v=0.95 v=0.99
Drag { Herzog et al.JCS & TeaneyGubser
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2T
MNg
dtdp c
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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. pT
asso dependence of D:
Deflected Jets Different three particle correlation.
Cherenkov: decreases (unless heavy bound states) Mach cone and gluon radiation: increases
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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
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 necessary dE/dx 1.5 GeV/fm.
Expanding medium: also the fluids temperature lowers with .
The spectrum is controlled by v/T
velocity field v1 > v2
T1 < T2
T1 T2
v1 v2<
t1 t2
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From STAR highlights :