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Mach Cones in Quark Gluon Plasma

Jorge Casalderrey-Solana

Lawrence Berkeley Laboratory

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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)

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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

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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:

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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

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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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