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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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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)
,
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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:
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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)
BB et al., Phys. Lett. B 675, 340 (2009)
J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
16 13/10/2009
Backup
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
18 13/10/2009
Punch – Through Jet II
Diffusion wake causes peak in jet direction
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)
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
22 13/10/2009
Punch – Through Jet: Velocity Scan
t=4.5/v fm
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
24 13/10/2009
The Diffusion Wake
G. Burau, Genua Harbour, September 2008
The diffusion wake exists!
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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%»
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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:
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
34 13/10/2009
Non-Mach correlations caused by Neck region
Jets in AdS/CFT III
J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
38 13/10/2009
pQCD Source Term IIFor a parton moving with v=const. and omitting dielectric screening:
with
Barbara Betz Disputationsvortrag
39 13/10/2009
pQCD Source Term III
For ultraviolett and infrared cut-off:
Ep energy of fast parton
Barbara Betz Disputationsvortrag
40 13/10/2009
J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)
The Neck Zone in pQCD vs AdS/CFT
Strong transverse flow No strong transverse flow
pQCDAdS/CFT
BB et al., Phys. Lett. B 675, 340 (2009)
Barbara Betz Disputationsvortrag
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 )
BB et al., Phys. Lett. B 675, 340 (2009)
t=4.5/v fm
Neufeld et al, Phys. Rev. C 78, 041901 (2008)
Barbara Betz Disputationsvortrag
42 13/10/2009
No Mach-like peaks:
Isochronous freezeout needed to compare pQCD and AdS/CFT
Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity
pT = 3.14 GeVStrong influence of the Neck region
J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)
BB et al., Phys. Lett. B 675, 340 (2009)
Heavy Quark Jets in pQCD vs AdS/CFT II
Barbara Betz Disputationsvortrag
43 13/10/2009
Mach-like peaks &
Momentum Flow Distribution
Independent of pT - cut
Strong impact of diffusion wake
Assuming: Particles in subvolume will be emitted into the same direction
BB et al., Phys. Lett. B 675, 340 (2009)
Heavy Quark Jets in pQCD vs AdS/CFT III
Barbara Betz Disputationsvortrag
44 13/10/2009
Expanding Medium
Jet 90 Jet 120
Jet 150 Jet 180
Barbara Betz Disputationsvortrag
45 13/10/2009
Expanding Medium
Jet 150 Jet 180
Jet 120
Barbara Betz Disputationsvortrag
46 13/10/2009
Expanding Medium Etot = 5 GeV
broad away-side peak double peaked structure
pTTtrig trig = 3.5 GeV
PHENIX, Phys. Rev. C 77, 011901 (2008)
Barbara Betz Disputationsvortrag
47 13/10/2009
Expanding Medium Etot = 10 GeV
Strong impact of the Diffusion wake
broad away-side peak double peaked structure
due to non-central jets
Causes smaller dip for pT=2 GeV PHENIX, Phys. Rev. C 77, 011901 (2008)
pTTtrig trig = 7.5 GeV
Barbara Betz Disputationsvortrag
48 13/10/2009
Expanding Medium Etot = 5 GeV
broad away-side peak broad away-side peak
Pure energy deposition No conical distribution in expanding medium
Jet 180: No peaks on away-side
pTTtrig trig = 3.5 GeV
Barbara Betz Disputationsvortrag
49 13/10/2009
Expanding Medium
en. and mom. loss en. and mom. loss pure energy loss
Etot = 10 GeV
pTTtrig trig = 7.5 GeV
Etot = 5 GeV
pTTtrig trig = 3.5 GeV
Etot = 5 GeV
pTTtrig trig = 3.5 GeV
Barbara Betz Disputationsvortrag
50 13/10/2009
Expanding Medium
Etot = 4.3 GeV
broad away-side peak broad away-side peak
pTTtrig trig = 3.0 GeV
Barbara Betz Disputationsvortrag
51 13/10/2009
Expanding Medium
• Jet deposition stopped
Etot = 5 or 10 GeV pTTtrig trig = 3.5 and 7.5 GeV
Barbara Betz Disputationsvortrag
52 13/10/2009
Expanding Medium
For b=6 fm
Distortion of the conical structure
Dependence on background flow(centrality)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
55 13/10/2009
Backup
(General)
Barbara Betz Disputationsvortrag
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:
Barbara Betz Disputationsvortrag
57 13/10/2009
Jet - Studies in HIC
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)
Barbara Betz Disputationsvortrag
58 13/10/2009
Jet - Studies in HIC
J. Putschke, Talk at RHIC and AGS Users Meeting 2009
Barbara Betz Disputationsvortrag
59 13/10/2009
Jet - Studies in HIC
Centrality dependence: double peaked structure for central collisions
one peak structure for very peripheral collisions
PHENIX, Phys. Rev. Lett. 97, 052301 (2006)
Barbara Betz Disputationsvortrag
60 13/10/2009
Jet - Studies in HIC
Investigation of path length dependence:
Double-peaked structure becomes more
pronounced out-of-plane
A. Sickeles [PHENIX], Eur. Phys. J. C 61, 583 (2009)
Barbara Betz Disputationsvortrag
61 13/10/2009
Jet - Studies in HIC
W. G. Holzmann [PHENIX], arXiv:0907.4833 [nucl-ex]
Geometry dependence, path length dependence
18 bins with 5 deg
Barbara Betz Disputationsvortrag
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
Jet - Studies in HIC
• Is the double-peaked structure due to a Mach cone formation?
ptrigT=3 – 4 GeV, passoc
T=1 – 2 GeV
Barbara Betz Disputationsvortrag
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
**
Barbara Betz Disputationsvortrag
64 13/10/2009
Jet - Studies in HIC
Projection along =const.
shows away-side peak
N. N. Ajitanand [PHENIX], Poster Quark Matter 2009
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
68 13/10/2009
Jet - Studies at SPS Energies
S. Kniege, PhD Thesis, Frankfurt (2009)
No sensitivity for three-particle correlations
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
71 13/10/2009
Full Jet Reconstruction I
J. Putschke, Talk at RHIC and AGS Users Meeting 2009
Full jet reconstruction questions ZYAM
Barbara Betz Disputationsvortrag
72 13/10/2009
Full Jet Reconstruction II
No apparent v2 modulation in jet-hadron vs. di-hadron correlations
J. Putschke, Talk at RHIC and AGS Users Meeting 2009
Barbara Betz Disputationsvortrag
73 13/10/2009
Full Jet Reconstruction III
Jet-hadron away-side significantly narrower
J. Putschke, Talk at RHIC and AGS Users Meeting 2009
Barbara Betz Disputationsvortrag
74 13/10/2009
Mach Cone Deformation
L. Satarov et al, Phys. Lett. B 627, 64 (2005)
Change in Mach angle dueto background flow
Barbara Betz Disputationsvortrag
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:
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
77 13/10/2009
Shock waves in Ne+U Collisions I
P. Rau et al., to be published
(free streaming)or
Barbara Betz Disputationsvortrag
78 13/10/2009
Shock waves in Ne+U Collisions II
(free streaming)or
P. Rau et al., to be published
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
82 13/10/2009
Energy Loss
Stopping power for muons in copper
PDG, J. Phys. G 33, 1 (2006)
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
84 13/10/2009
Geometry of HIC
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
86 13/10/2009
Elliptic Flow and Viscosity I
M. Luzum and P. Romatschke, Phys. Rev. C 78:034915 (2008)
Initial conditions matter
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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)
Barbara Betz Disputationsvortrag
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
Barbara Betz Disputationsvortrag
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
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Barbara Betz Disputationsvortrag
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