jet propagation and mach-cone formation in (3+1)-dimensional ideal hydrodynamics barbara betz...

Jet Propagationand Mach-Cone Formationin (3+1)-dimensional Ideal

Hydrodynamics

Barbara Betz

DisputationsvortragJohann Wolfgang Goethe-Universität

Frankfurt am Main13/10/2009

Phys. Lett. B 675, 340 (2009), Prog. Part. Nucl. Phys. 62, 556 (2009),

Phys. Rev. C 79, 034902 (2009), arXiv: 0907.2516 [nucl-th] (Nucl. Phys. A in press)

Barbara Betz Disputationsvortrag

2 13/10/2009

proton

The QCD Phase Diagram

initial state

pre-equilibrium

expanding fireball

hadronization

hadronic phaseand freeze-out

S. Bass, Talk Quark Matter 2001

Insights into theory of strong

interactions (QCD) Medium created in

heavy-ion (HIC) collisions similar to the one created after Big Bang

Explore the phase diagram of QCD with HIC


3 13/10/2009

„dust“

The Expanding Medium From first principles, it is unclear if medium is …

fluid

Data described by hydrodynamics Small

P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99,172301 (2007)

Hydrodynamics: azimuthal anisotropy of emitted particles, parametrized by v2

Medium behaves like an almostideal fluid

/s

Particles interact,expansion determined by density gradient

Particles don‘t interact, expansion independent of initial shape


4 13/10/2009

Jet - Studies in HIC I • Jet moving through dense matter,

depositing its energy

should eventually disappear

• Jet suppression: signal for creation of opaque matter (Quark-Gluon Plasma)

STAR, Phys. Rev. Lett. 91 (2003) 072304

4 < pTtrigger < 6 GeV/c

pTassoc > 2 GeV/c

Can energy lost by jets tell us something about medium properties?

Trigger particle


5 13/10/2009

PHENIX, Phys. Rev. C 77, 011901 (2008)

Au+Au / p+p

= 200 GeVs

• Redistribution of energy to lower pT-particles

Generation of Mach cone pattern

• Re-appearance of the away-side for low and intermediate pT

assoc

• Mach cone angle sensitive to EoS:

STAR, Nucl. Phys. A 774, 129 (2006)

4 < pTtrigger < 6 GeV/c

0.15 < pTassoc < 4 GeV/c

Reflect interaction of jet with medium

Jet - Studies in HIC II


6 13/10/2009

Hydrodynamics I Medium created in a HIC can be described using hydrodynamics

• Hydrodynamics represents (local) conservation of

energy-momentum

(local) charge

• For ideal hydrodynamics in local thermodynamical equilibrium

• Equation of State

,

, ,

• For viscous hydrodynamics (Eckart frame)

,


7 13/10/2009

Hydrodynamics II

BB, D. Henkel and D. H. Rischke, Prog. Part.. Nucl. Phys. 62, 556 (2009)

W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979)W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979)A. Muronga, Phys. Rev. C 76, 014909 (2007)A. Muronga, Phys. Rev. C 76, 014909 (2007)BB, D. Henkel, and D. H. Rischke, Prog. Part. Nucl. Phys. 62, 556 (2009)

Deriving the transport equations for viscous quantities up to 2nd order in

gradients, starting from the Boltzmann equation


8 13/10/2009

Modelling of Jets

STAR, Phys. Rev. Lett. 95, 152301 (2005)

residue of energy and momentum given by the jet

• Assumption of isochronous/isothermal freeze-

out

• No interaction afterwards

p·ve+r r

:mainly flow driven

Conversion into particles Freeze-out:

Jets can be modelled using (ideal) hydrodynamics:


9 13/10/2009

Stopped Jet IApplying a static medium and an ideal Gas EoS for massless gluons

Assume: Near-side jet is not modified by medium

dE dM GeV(0) v (0) 1.5

dt dt fm= =

t=4.5/v fmdE GeV dM GeV

(0) 1.5 (0) 0dt fm dt fm

= =

BB et al., Phys. Rev. C 79, 034902 (2009)

Bragg Peak

Jet decelerates according to Bethe-Bloch formalism

Mach cone Diffusion wake


10 13/10/2009

Stopped Jet II

Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity

Energy Flow Distribution

Assuming: Particles in subvolume will be emitted into the same direction

pT = 5 GeV

BB et al., Phys. Rev. C 79, 034902 (2009)

Strong influence of the Diffusion wake


11 13/10/2009

Modelling Jets using …

Conclusion about Mach cones?

pQCD

AdS/CFT

P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008)

R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)

Strongly-coupled theory

Pointing vector perturbation

Momentum density perturbationEnergy density perturbation

Energy density perturbation

Weakly-coupled theory

v=0.75

v=0.99955


12 13/10/2009

Heavy Quark Jets in pQCD vs AdS/CFT Compare weakly and strongly coupled models using heavy punch-through jet

pQCD: Neufeld et al. source for a heavy quark

AdS/CFT: Stress tables with/s=1/(4 ) R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)

pT = 3.14 GeV

BB et al., Phys. Lett. B 675, 340 (2009)

No Mach-like peaks:

AdS/CFT: Strong influence of the Neck region

Static medium and isochronous freeze-out needed for comparison

t=4.5/v fmS. Gubser et al, Phys. Rev. Lett. 100, 012301 (2008)


J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)


13 13/10/2009

L. Satarov et al, Phys. Lett. B 627, 64 (2005)

Expanding Medium I

Consider different jet paths

b=0

• Apply Glauber initial conditions and an ideal Gas EoS for massless gluons

• Focus on radial flow contribution

Experimental results based on many events

A. K. Chaudhuri, Phys. Rev. C 75, 057902 (2007) ,

A. K. Chaudhuri, Phys. Rev. C 77, 027901 (2008)

• Two-particle correlation (Tfreeze-out < Tcrit = 130 MeV):

represents near-side jet

Jet 150

Etot = 5 GeV


14 13/10/2009

Expanding Medium IIEtot = 5 GeV

broad away-side peak double peaked structure

due to non-central jets

pTTtrig trig = 3.5 GeV

BB et al., Nucl. Phys. A in press (arXiv:0907.2516 [nucl-th])

PHENIX, Phys. Rev. C 77, 011901 (2008)


15 13/10/2009

Summary Investigation of jet-medium interactions using (3+1)d ideal

hydrodynamics for different energy and momentum loss scenarios (schematic source term, pQCD, AdS/CFT)

Diffusion wake is always created if dM/dx > threshold

Different impacts of pQCD and AdS/CFT source terms

Experimentally observed signal can be obtained from different contributions of several jets in an expanding medium

Deflection of Mach cones

Structure unrelated to EoS

Single jet events

Transport equations for dissipative hydrodynamics to 2nd order in gradients

Fundamental for any numerical application of viscous effects


16 13/10/2009

Backup


17 13/10/2009

t=4.5/v fm v=0.999

Punch – Through Jet I Applying a static medium and an ideal Gas EoS for massless gluons

dM dE GeV1.5

dt dt fm= =

dE GeV dM GeV1.5 , 0

dt fm dt fm= =

Maximal fluid response

BB et al., Phys. Rev. C 79, 034902 (2009)

Assume: Near-side jet is not modified by medium


18 13/10/2009

Punch – Through Jet II

Diffusion wake causes peak in jet direction


Energy Flow Distribution


pT = 5 GeV

BB et al., Phys. Rev. C 79, 034902 (2009)


19 13/10/2009

Creation of Bow Shock for smaller v strengthens peak in jet direction

Does the jet-pattern reproducethe features of a Mach cone?

Velocity dependence of the emission angle

pT = 5 GeV

Punch – Through Jet IIIBB et al., Phys. Rev. C 79, 034902 (2009)


20 13/10/2009

Still influence of diffusion wake

• Transverse momentum deposition:

from explosion of matter

t=4.5/v fm

L TdM dM1=

dt 4 dt

TdMdE=

dt dt

Vorticity conservation

Punch – Through Jet IV

BB et al., Phys. Rev. C 79, 034902 (2009)


21 13/10/2009

Punch – Through vs Stopped Jet

Similar freeze-out patterns

pT = 5 GeV

BB et al., Phys. Rev. C 79, 034902 (2009)

pT = 5 GeV

Punch-Through Jet Stopped Jet


22 13/10/2009

Punch – Through Jet: Velocity Scan

t=4.5/v fm


23 13/10/2009

Near-side Jet

t=4.5/v fm

• Assuming energy-momentum conversation and the disapparance of the near-side jet after t=0.5fm

Reduction of diffusion

wake

Not strong enoughto be seen in the freeze-out pattern


24 13/10/2009

The Diffusion Wake

G. Burau, Genua Harbour, September 2008

The diffusion wake exists!


25 13/10/2009

Why linearized Hydro is not so good

Head wave pile-up- Non-linear hydrodynamics- Signal not well understood- Non-Mach cone angle

Source- Non-linear hydrodynamics- Non-thermalized

Diffusion Wake - Proportional to source- Not seen experimentally

Mach Cone- Linear hydrodynamics- Connected to EoS


26 13/10/2009

Momentum Deposition

BB et al., J. Phys. G 35, 104106 (2008)

dE/dx = 1.4 GeV/fm

Static medium for differentenergy and momentum lossrates:

Cooper-Frye freeze-outafter t=7.2fm

Double-peaked structure visible for (dM/dx)/(dE/dx) 12.8%»


27 13/10/2009

Stopped Jet • Jet stops after t=4.5/v fm

dE GeV(0) 1.5

dt fmdM GeV

(0) 0dt fm

=

=

dE GeV(0) 1.5

dt fmdM GeV

v (0) 1.5dt fm

=

=

Vorticity conservation

tFO=4.5/v fm tFO=6.5/v fm tFO=8.5/v fm

Diffusion wake still present

BB et al., Phys. Rev. C 79, 034902 (2009)


28 13/10/2009

Stopped Jet

tFO=4.5/v fm tFO=6.5/v fm tFO=8.5/v fm

Diffusion wake causes peak in jet direction

Larger impact of thermal smearing

BB et al., Phys. Rev. C 79, 034902 (2009)


29 13/10/2009

Different Contributions

EMach 53.9% PxMach 6.5%

EDiff -12.3% PxDiff 18.7%

ENeck 57.4% PxNeck 73.7%

EHead 1.0% PxHead 1.0%

dE dM GeV(0) v (0) 1.5

dt dt fm= =

t=4.5/v fm

BB et al., Phys. Rev. C 79, 034902 (2009)

pT =2. 5 GeV


30 13/10/2009

Energy-Momentum Relation

dEdM d+E

ddM dx dM

= = =xdt dx dt dx dx

æ ö÷ç ÷ç ÷÷çè ø

m

M m

=

= =

E

E

22

3

3

1

d 1 d2 2

dx dx

d 1 dE 1dx

=1-

dx m

=

=

22 2

22

22

dE 11

dx

dE 1= 1

dx 1

dE 1=

dx 1

=

1/

æ ö÷ç + ÷ç ÷ç ÷è ø

æ ö÷ç + ÷ç ÷ç ÷-è ø

æ ö÷ç ÷ç ÷ç ÷-è ø

dM dE=

dt dx dM dE(t) > (t)

dt dtdE dM

(t) = v(t) (t)dt dt

dM dE(t)= (t)

dt dxgeneral:


31 13/10/2009

Jet – Energy Loss Studies

fm

GeV2

dx

dE

GeV/c 5 Tp2

fm

GeV12.6

dx

dE

GeV/c 3 Tp2

GeV/c 2 Tp1

GeV/c 4 Tp3

GeV/c 1 Tp0.2

GeV/c 3 Tp2

GeV/c 2 Tp1

GeV/c 4 Tp3

GeV/c 1 Tp0.2

• Jet deposits energy and momentum along a trajectory

• Applying linearized hydrodynamics

Mach cone forsound wavesDiffusion wake

J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)


32 13/10/2009

Jets in AdS/CFT I

Heavy Quark String

N=4 SYM Thermal Background Black hole in AdS space

R. Fries et al, Phys. Rev. D 75, 106003 (2007)

Analogues:

Mach cone in coordinate space

S. Gubser et al., Phys. Rev. Lett. 100, 012301 (2008)


33 13/10/2009

Jets in AdS/CFT II

Pattern similar to pQCD

P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008)

Jet travelling at v=0.75

Poynting vector perturbationEnergy density perturbation

Diffusion Wake contribution

Attention: No clear Mach cone signal


34 13/10/2009

Non-Mach correlations caused by Neck region

Jets in AdS/CFT III



35 13/10/2009

Jets in pQCD I

R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)

Considering a static medium and linearized hydrodynamicsfor a punch-though jet

Mach cone signal & Diffusion Wake


36 13/10/2009

Jets in pQCD II

1s 4

=

3s 4

=

6s 4

=

Contour plots of magnitude of perturbed momentum density

Strong flow in jet-direction

R. Neufeld et al., Phys. Rev. C 79, 054909 (2009)


37 13/10/2009

pQCD Source Term IIdea: External color field generated by fast parton propagating through QGP

with

Since

Lorentz forced

considered to lowest order in coupling g


38 13/10/2009

pQCD Source Term IIFor a parton moving with v=const. and omitting dielectric screening:

with


39 13/10/2009

pQCD Source Term III

For ultraviolett and infrared cut-off:

Ep energy of fast parton


40 13/10/2009


The Neck Zone in pQCD vs AdS/CFT

Strong transverse flow No strong transverse flow

pQCDAdS/CFT



41 13/10/2009

Heavy Quark Jets in pQCD vs AdS/CFT I

Idea: Compare weakly and strongly coupled models

Using heavy quark punch-through jet

pQCD: Neufeld et al. source for a heavy quark

AdS/CFT: Stress tables provided by S. Gubser, A. Yarom and S. Pufu with

Applying ideal hydrodynamics for a staticmedium and an ideal gas EoS of masslessgluons

Assume that the near-side jet is not modified by the medium

/s=1/(4 )


t=4.5/v fm

Neufeld et al, Phys. Rev. C 78, 041901 (2008)


42 13/10/2009

No Mach-like peaks:

Isochronous freezeout needed to compare pQCD and AdS/CFT


pT = 3.14 GeVStrong influence of the Neck region



Heavy Quark Jets in pQCD vs AdS/CFT II


43 13/10/2009

Mach-like peaks &

Momentum Flow Distribution

Independent of pT - cut

Strong impact of diffusion wake



Heavy Quark Jets in pQCD vs AdS/CFT III


44 13/10/2009

Expanding Medium

Jet 90 Jet 120

Jet 150 Jet 180


45 13/10/2009

Expanding Medium

Jet 150 Jet 180

Jet 120


46 13/10/2009

Expanding Medium Etot = 5 GeV



PHENIX, Phys. Rev. C 77, 011901 (2008)


47 13/10/2009


Strong impact of the Diffusion wake


due to non-central jets

Causes smaller dip for pT=2 GeV PHENIX, Phys. Rev. C 77, 011901 (2008)



48 13/10/2009


broad away-side peak broad away-side peak

Pure energy deposition No conical distribution in expanding medium

Jet 180: No peaks on away-side



49 13/10/2009

Expanding Medium

en. and mom. loss en. and mom. loss pure energy loss

Etot = 10 GeV


Etot = 5 GeV


Etot = 5 GeV



50 13/10/2009

Expanding Medium

Etot = 4.3 GeV

broad away-side peak broad away-side peak



51 13/10/2009

Expanding Medium

• Jet deposition stopped

Etot = 5 or 10 GeV pTTtrig trig = 3.5 and 7.5 GeV


52 13/10/2009

Expanding Medium

For b=6 fm

Distortion of the conical structure

Dependence on background flow(centrality)


53 13/10/2009

Cooper-Frye Freeze-out:

The Caveat: Freeze-out Prescription

• Assumption of isochronous/isothermal freeze-

out

• No interaction afterwards

p·ve+r r

:

mainly flow driven

http://www.rnc.blb.gov/ssalur/www/Research3.html


54 13/10/2009

Isothermal and isochronousfreeze-out lead to very similarresults

Isothermal Freeze-out

Beak occurs for non-central jets Jet 150

Jet 180


55 13/10/2009

Backup

(General)


56 13/10/2009

Jet - Studies in HIC

Assumption :Correlations from flow anisotropyand jets are uncorrelated

ZYAM (Zero Yield At Minimum)

Subtraction of:estimated elliptic flow modulatedbackground

can leads to:double peaked structure

Background:Particle correlation from elliptic flow

J. Ulery [STAR], PoS LHC07, 036 (2007)

Two-source model:


57 13/10/2009


pT-dependence (associated jet): double peaked structure seems to get broader (but within errorbars)

pT-dependence (trigger jet): one peak structure evolves (possible punch-through)

PHENIX, Phys. Rev. C 77, 011901 (2008)


58 13/10/2009


J. Putschke, Talk at RHIC and AGS Users Meeting 2009


59 13/10/2009


Centrality dependence: double peaked structure for central collisions

one peak structure for very peripheral collisions

PHENIX, Phys. Rev. Lett. 97, 052301 (2006)


60 13/10/2009


Investigation of path length dependence:

Double-peaked structure becomes more

pronounced out-of-plane

A. Sickeles [PHENIX], Eur. Phys. J. C 61, 583 (2009)


61 13/10/2009


W. G. Holzmann [PHENIX], arXiv:0907.4833 [nucl-ex]

Geometry dependence, path length dependence

18 bins with 5 deg


62 13/10/2009

Experimental data show

superposition of Mach cone

structure and deflected jets

J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007)

Deflected jet Mach Cone


• Is the double-peaked structure due to a Mach cone formation?

ptrigT=3 – 4 GeV, passoc

T=1 – 2 GeV


63 13/10/2009

Jet - Studies in HIC N. N. Ajitanand [PHENIX], Nucl. Phys. A 783, 519 (2007)

Three-particle correlation shows

superposition of Mach cone

structure and deflected jets

Simulation for deflected

jets and Mach cone

High-pT trigger

Same-Side Jet

**


64 13/10/2009


Projection along =const.

shows away-side peak

N. N. Ajitanand [PHENIX], Poster Quark Matter 2009


65 13/10/2009

Heavy Quarks

B. Biritz [STAR], arXiv:0907.3937[nucl-ex]

3.0 < pttrig < 6.0 GeV

0.15 < pttrig < 0.5 GeV

Au+Au 200 GeV Cu+Cu 200 GeV

Non-photonic e-h correlations to probe heavy quark jet-medium

interactions


66 13/10/2009

Jet - Studies at SPS EnergiesCERES, Phys. Lett. B 687, 259 (2009)

Pb+Pb 158AGeV2.5 < pt

trig < 4.0 GeV1.0 < pt

assoc < 2.5 GeV


67 13/10/2009

Jet - Studies at SPS EnergiesCERES, Phys. Lett. B 687, 259 (2009)

Asymmetry: Hard scattering at SPS

dominated by large-x partonsPositive trigger: R-+ close to medium

value energy deposition


68 13/10/2009

Jet - Studies at SPS Energies

S. Kniege, PhD Thesis, Frankfurt (2009)

No sensitivity for three-particle correlations


69 13/10/2009

Jet - Studies Energy ScanJ. Jia, Eur. Phys. J. C 62, 255 (2009)

ptrigT=2.5 – 4 GeV, passoc

T=1 – 2.5 GeV

(PHENIX)=0.7, (CERES)=0.5

Trigger yield at SPS: stronger trigger bias, more non-trigger jets


70 13/10/2009

High pT-correlations

Effect of global momentum conservation?

Medium response???

Peaked away-side structure modelled by UrQMD

Pb+Pb (0-5%) 158AGeV

C. Blume, PoS(Confinement8) 110, 2008


71 13/10/2009

Full Jet Reconstruction I


Full jet reconstruction questions ZYAM


72 13/10/2009

Full Jet Reconstruction II

No apparent v2 modulation in jet-hadron vs. di-hadron correlations



73 13/10/2009

Full Jet Reconstruction III

Jet-hadron away-side significantly narrower



74 13/10/2009

Mach Cone Deformation

L. Satarov et al, Phys. Lett. B 627, 64 (2005)

Change in Mach angle dueto background flow


75 13/10/2009

Shock waves in A1+A2 Collisions

H. G. Baumgardt et al., Z. Physik A 273 (1975) 359

Sketch of a light nucleus penetrating through a heavier one:


76 13/10/2009

Shock waves in A1+A2 Collisions

H. G. Baumgardt et al., Z. Physik A 273 (1975) 359

Sketch of a non-central collision of

a light nucleus with a heavier one


77 13/10/2009

Shock waves in Ne+U Collisions I

P. Rau et al., to be published

(free streaming)or


78 13/10/2009

Shock waves in Ne+U Collisions II

(free streaming)or

P. Rau et al., to be published


79 13/10/2009

Boosted Thermal Distribution

Isotropically distributed thermal momentum (local rest frame)

gets peaked at small angles in the laboratory frame

P. Rau, private communication


80 13/10/2009

Smoke RingsBB et al, Phys. Rev. C 76, 044901 (2007)

Vorticity generated by a jet, t=11.52 fm, static medium


81 13/10/2009

Mach Cones in Transport Theory

D. Molnar, arXiv:0908.0299 [nucl-th]

local energy density

“perturbative” scenario

momentum density

“pure energy” scenario

Diffusion wake


82 13/10/2009

Energy Loss

Stopping power for muons in copper

PDG, J. Phys. G 33, 1 (2006)


83 13/10/2009

The Ridge

Ridge: Long-ranged structure in

PHYTHIA simulation for p+p 0-30% Au+Au

PHOBOS, J. Phys. G 35, 104080 (2008)


84 13/10/2009

Geometry of HIC


85 13/10/2009

Mach Cone – Speed of Sound

Emission Angle of the Mach cone

Assuming vjet ~~ 1

massless QGP: cs ~ ~ 0.570.57 = 1.0 rad= 1.0 rad

Hadronic matter: cs ~ ~ 0.30.3 = 1.3 rad= 1.3 rad

1st order p.t.: cs ~ ~ 00 = 1.5 rad= 1.5 rad

F. Wang, Talk Quark Matter 2006


86 13/10/2009

Elliptic Flow and Viscosity I

M. Luzum and P. Romatschke, Phys. Rev. C 78:034915 (2008)

Initial conditions matter


87 13/10/2009

= 0.6S /s = 0.15

Z. Xu and C. Greiner, Phys. Rev. C 79:014904 (2009)

Initial conditions matter

= 0.3S /s = 0.08

Elliptic Flow and Viscosity II


88 13/10/2009

Viscous Hydrodynamics

W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979)W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979)A. Muronga, Phys. Rev. C 76, 014909A. Muronga, Phys. Rev. C 76, 014909BB, D. Henkel, and D. H. Rischke, Prog. Part. Nucl. Phys. 62, 556 (2009)BB, H. Niemi, and D. H. Rischke, in preparation

Deriving the transport equations for

starting from the Boltzmann equation


89 13/10/2009

Other Jet-Medium Models I

• Lattice QCD EoS

T. Renk and J. Ruppert, Phys. Rev. C 73, 034907 (2006)

Determines angular correlation pattern

• Fireball model

• BDMPS-like energy loss

f: „fraction … of energy lost to the medium [that] excites a collective mode“

(1-f): „remaining energy fraction … [that] in essence heats the medium and leads to some amount of the collective

drift along the jet axis…“

sound wave

diffusion

Mach cones only if dM/dx << dE/dx


90 13/10/2009

Other Jet-Medium Models II

A. Chaudhuri and U. Heinz, Phys. Rev. Lett. 97, 062301 (2006)

• First-order phase transition

Calculates the azimuthal distribution

• Expanding (2+1)d hydro(AZHYDRO)

jet 3jet

dxdES(x)= (x) (t)

dx dt(r-r )r r

(x)=S(x)(+1,-1S ,0,0)

00

dE s(x) dE=

dx s dx

• Source term:

Quenched jet Diffusion wake

• Isothermal Freeze-out


91 13/10/2009

Other Jet-Medium Models II

Hottest region at the head of the jet

Effect from diffusion wake

No Mach cone-like correlation ifdE/dx = dM/dx

A. Chaudhuri and U. Heinz, Phys. Rev. Lett. 97, 062301 (2006)


92 13/10/2009

Other Jet-Medium Models III

A. Chaudhuri, Phys. Rev. C 75, 057902 (2007)

AZHYDRO, for different jet paths:

Azimuthal distri-bution of pions for differentjet paths

Normalized, azimuthal distributionof pions, averaged over differentjet trajectories for b=3fm Au+Aucollisions


93 13/10/2009

Other Jet-Medium Models III

£

A. Chaudhuri, Phys. Rev. C 77, 027901 (2008)

jet may vary:

Implicit assumption: punch-through jets

Normalized, jet path averaged azimuthal distribution of pions for b=2.3fm, 4.1fm, 12.1fm Au+Au collisions

STAR: 0.15 passocT 4.0 GeV

4.0 ptrigT 6.0 GeV

PHENIX: 2.5 passocT 4.0 GeV

1.0 ptrigT 2.5 GeV

£

£

£

££

£

£

£


94 13/10/2009

Energy-Momentum Relation

On-shellness:222 mpE

/2ΔpΔx

λ

Heisenbergs uncertainty relation:

Large number of collisions

small small largeΔx Δp

2

Δm

22222 mΔp2pΔppm)Δp(pE2

jet propagation and mach-cone formation in (3+1)-dimensional ideal hydrodynamics barbara betz...

Documents