Jet Energy Loss and Mach Cones, Jet-Medium Interactions ... · Jet-Medium Interactions, Jets in Hydrodynamics Barbara Betz ... • Generation of Mach cone pattern ... Mach cone for

Jet Energy Loss and Mach Cones,Jet-Medium Interactions,Jets in Hydrodynamics

Barbara Betz

Thanks to: Miklos Gyulassy, Jorge Noronha, Dirk Rischke,

Giorgio Torrieri

Phys. Rev. C 79, 034902 (2009), Phys. Lett. B 675, 340 (2009),

Nucl. Phys. A 830, 777c (2009), arXiv:1005.5461

Towards a Consistent Picture of Mach Cones in Heavy-Ion Collisions

From the Static Medium toJet Reconstruction Algorithms

3 06/24/10 INT Workshop Seattle Barbara Betz

The Medium created in a HIC

Data described by hydrodynamics

Small

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

Medium behaves like an almost

ideal fluid

/s

IF the medium behaves like a fluid

Mach cones have to occurbecause of fluid dynamics


Jet - Studies in HIC

• Generation of Mach cone pattern

Redistribution of energy to lower pT-particles

• 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 mediumPHENIX, Phys. Rev. C 77, 011901 (2008)

Au+Au / p+p

= 200 GeVs

H. Stöcker, Nucl. Phys. A 750, 121 (2005), J. Casalderrey-Solana et al. Nucl. Phys. A 774, 577 (2006)


Jet - Medium Interaction

• First-order phase transition

• Expanding (2+1)d hydro (AZHYDRO)

• Quenched jet

• Isothermal Freeze-out

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

Where does the double-peaked structurecome from?


Extended Jet - Studies in HIC

STAR, arXiv: 1004.2377

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

Position of away-sidepeaks does not changestrongly with pT

assoc

Not due toCherenkov gluonradiation

What happens to larger pT

trigger?

7

Some Caveats

ZYAM (Zero Yield At Minimum):Can lead to a double-peaked structure

Two-source model:Can one assume that the correlationsfrom flow anisotropy and jets areuncorrelated? J. Ulery [STAR], PoS LHC07, 036 (2007)

How can one proof/disproof the two-source model?

06/24/10 INT Workshop Seattle Barbara Betz

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

ptrigT=3 – 4 GeV, passoc

T=1 – 2 GeV Three-particle correlations seem to

corroborate Mach cone idea

What’s the effect of ZYAM?

No agreement with 3-particle cumulant method C. Pruneau, Phys. Rev. C 79, 044907 (2009)


A little bit of Theory


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

mainly flow driven

Conversion into particles Freeze-out:

Jets can be modelled using (ideal) hydrodynamics:

e+p v.


The Static Medium


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

Assume: Near-side jet is not modified by medium

Maximal fluid response

Jet decelerating from v=0.999according to Bethe-Bloch formalism

a=-1.36 GeV/fm

Simplest back-reaction from the medium

Bragg Peak

adjusts path length

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


Stopped Jet II

Mach cone forsound waves Diffusion wake

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)


Stopped Jet III

Diffusion wake causespeak 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)

Any conclusions about deposition mechanism???


Different Jet-Energy Loss Modells


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


Non-Mach correlations

caused by Neck region

Jets in AdS/CFT

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


Heavy Quark Jets


Heavy Quark JetsCompare 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 )


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 fm

S. 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)


The Expanding Medium


Expanding Medium I

Satarov et al, PLB 627:64 (2005)

• Consequences of expansion?

Transverse flow causes distortion

Expansion broadens Mach cone angle

• Predictions:

Radial flow, Elliptic flow

Mach cones are sensitive to the background flow

• Qualitative, model-independent effect


Expanding Medium II

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):

near-side jet

dE/dt = 1 GeV/fm

Jet 150

Etot = 5 GeV

23

Expanding Medium IIIEtot = 5 GeV

broad away-side peak double peaked structure

due to non-central jets

pTtrig = 3.5 GeV

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


vjet =0.999

BB et al., arXiv: 1005.5461


Expanding Medium IVEtot = 10 GeV

Strong impact of the Diffusion wake

broad away-side peak double peaked structure

Causes smaller dip for pT=2 GeV

pTtrig = 7.5 GeV

6 < pTtrigger < 10

1.5 < pTassoc < 2.5

STAR, arXiv: 1004.2377f

Yie

ld

25

Expanding Medium V


Comparing different deposition scenarios, one sees that

„cone“ angle approximately the same for different deposition scenarios

pTassoc = 2.0 GeV: No double-peaked structure for pure energy

deposition scenario due to thermal smearking

pTtrig = 3.5 GeV

pTassoc = 3.0 GeVpT

assoc = 2.0 GeV

vjet =0.999 BB et al., arXiv: 1005.5461

26

Expanding Medium VI


Conical emission angle also appears for subsonic jets Not a Mach cone

Considering a bottom quark (M=4.5 GeV), propagating at vjet < cs

(on-shell energy-momentum deposition scenario)

pTassoc = 2.0 GeV

Cu+Cu: Similar away-side shoulder width, double-peak structure reappars for pT

assoc = 3 GeV

BB et al., arXiv: 1005.5461 PHENIX, PRL98, 232302 (2007)


Some other models

28

MARTINI + MUSIC


MARTINI: Modular Algorithm for Relativistic Treatment of Heavy

IoN Interactions

Incorporating an event-averaged MARTINI source term into the

(3+1)d hydro evolution MUSIC (MUScl – Monotonic Upstream CenteredStream [for conservaion laws] - for Ion Collisions)B. Schenke et al., Phys. Rev. C 80, 054913 (2009), B. Schenke et al., arXiv:1004.1408

B. Schenke, Talk at the RHIC & AGS Annual User’s Meeting, BNL, June 2010 Qualitative similar result


Mach Cones in Transport Theorylocal energy density

“perturbative” scenario

momentum density

“pure energy” scenario

Diffusion wake

D. Molnar, AIP Conf. Proc. 1182 ,791 (2009)

30

BAMPS


BAMPS: Boltzmann Approach of MultiParton Scatterings

A transport algorithm solving the Boltzmann equations for on-shellpartons with pQCD interactions

C. Greiner, Talk at the Opening Symposium of the JET Collaboration, Berkeley, June 2010

Box scenario, no expansion, massless Boltzmann gas interactions, 2 -> 2

The shock front (Mach front) gets broader and vanish with more dissipation


Jets in pQCD


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

1

s 4

=

3

s 4

=

6

s 4

=

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

Signal dissolves with viscosity


Jets in pQCD

R. Neufeld and T. Renk, arXiv:1001.5068.

Crescendo Deposition Scenario1 can lead to adouble-peaked structure, depending on l2

and /s

Deflection due to background flow and averaging matters and can lead to the double-peaked away-side structure dependingon cross-section H. Li et al., arXiv: 1006.2893.

Likewise, a jet shower can result in a double-peaked away-side

H. Li et al., arXiv: 1006.2893.

Static medium

1Increasing number of radiated gluons deposit energy Ep >> DEtot2local medium excitation parameter


Some more caveats


Hot Spots ICan fluctuating initial condition explain the 2+3-particle correlations?

Takahashi et al, PRL 103, 242301 (2009)

F. Grassi, Talk at the Glasma Workshop, BNL, May 2010

R. Andrade et al., arXiv: 0912.0803


Hot Spots IICheck with one single hot spot

Can exp. data be corrected? Heavy quark jets are not affected

t=9.36 fmt=0 fm


Full Jet Reconstruction

What happened to the Mach cone?

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

Strong diffusion wake!

Flow profile at freeze-out after background subtraction

Jet 150

Test Proposal:Take a hydro-jet event, apply different jet reconstructionalgorithms and compare them

Jet 180

Summary Different source terms may lead to different structures on the away-side

(pQCD, AdS/CFT, …)

„Conical“ signal can be created:

by averaging over wakes created by jets in different events.

There is a deflection of particles emitted due to collectivetransverse flow.

Structure cannot directly be related to EoS, but is a measure for the flow

Quite insensitive to deposition mechanism, jet velocity (evenfor subsonic jets), and system size

Necessary to study heavy-flavor tagged jets.


Measured away-side structure may be due to initial fluctuations

Mach cones have to occur in heavy-ion collisions if there is a fluid

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Jet Energy Loss and Mach Cones, Jet-Medium Interactions ... · Jet-Medium Interactions, Jets in Hydrodynamics Barbara Betz ... • Generation of Mach cone pattern ... Mach cone for