Jet Tomography and Particle Correlations in Heavy-Ion Collisions

Jet Tomography and Particle Correlations

in Heavy-Ion CollisionsBarbara Betz

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

Phys. Rev. C 79, 034902 (2009); Nucl. Phys. A 830, 777c (2009); Phys.Rev. Lett. 105, 222301 (2010); arXiv:1012.4418 [nucl-th]

arXiv:1102.5416 [nucl-th]

HIC Facilities

initial state

pre-equilibrium

expanding fireball

hadronization

hadronic phaseand freeze-out

S. Bass, Talk Quark Matter 2001

03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

RHIC, BNL: 2000 – … p+p, d+Au, Cu+Cu,

Au+Au LHC, CERN: 2008/9 - … p+p, Pb+Pb FAIR, GSI: ~2016 - … accelerates ions from p

3 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

Tomography and Correlations

What can be extracted about medium proper-ties?

What do conical correlations tell us?

What is the role/impact of fluctuating initial

conditions?Test sensitivity of azimuthal dependenceof single and dihadron nuclear

modification factors

4 < pTtrigger < 6 GeV/c

0.15 < pTassoc < 4 GeV/c

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

PHENIX, Phys. Rev. Lett. 105, 142301 (2010)

The Medium

Initial Conditions

2 Major RHIC Results

Reproducing the elliptic flow v2

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

Medium behaves like an almostideal fluid

BNL press release, April 18 2005.

Particles don‘t interact,

expansion independent

of initial shape

Particles interact,expansion

determined by density gradient

„dust“ fluid

Data can be described by hydrodynamics

with small

Fluid-like Medium

Jet Quenching• Like in medicine, hard probes can be

used to investigate the medium properties

• If created matter is opaque, a jet depositing its energy should eventually disappear jet suppression

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

pTassoc > 2 GeV/c

What can the energy lost tell us about the medium properties

and the initial conditions?

Trigger particle

University Wuppertal, “Schul-Vorlesungen zur Physik”

The Medium

Jets in HIC I

By observation: Confirm fast

thermalization Study EoS of the fluid

Mach cone angle sensitive to EoS

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

IF the medium behaves like a fluid: Mach cones have to occur because

offluid dynamics

0.15 < pTassoc < 4 GeV/cAu+Au / p+p

= 200 GeVs

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

Jets in HIC II

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

Reflect interaction of jet with medium

• Redistribution of energy to lower pT-particles

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

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

Experimental Studies

Many more studies: path-length dependence, centrality dependence, energy

dependence11

STAR, Phys. Rev. C 82, 024912 (2010)see also PHENIX, Phys. Rev. C 77, 011901 (2008)

Position of away-side

peaks does not change

strongly with pTassocNot due to

Cherenkov gluonradiation

What happens to larger pT

trigger?

Jet - Studies in HIC I

A. Sickeles [PHENIX], Eur. Phys. J. C 61, 583 (2009); PHENIX, Phys. Rev. Lett. 97, 052301 (2006); J. Jia, Eur. Phys. J. C 62, 255 (2009)

Some caveats

Background Subtraction

How can one proof/disproof

the two-source model?J. Ulery [STAR], PoS LHC07, 036 (2007)

D. d’Enterria and BB., Springer Lecture Notes (2008)

Assumption (Two-source model) :

No correlations between flow anisotropy

and jets ZYAM (Zero Yield At Minimum) Subtraction of:estimated elliptic flow modulatedbackground can leads to:double peaked structure

Background:Particle

correlation from elliptic flowOther methods

A. Sickles et al, Phys. Rev. C 81, 014908 (2010)STAR, arXiv: 1102.2669 [nucl-ex]

3-Particle Correlations

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 methodC. Pruneau, Phys. Rev. C 79, 044907 (2009)

Deflected jet

Mach Cone

ptrigT>3 GeV, passoc

T=1 – 2 GeV

C. Pruneau, Talk at the Workshop on ‘Critical Asessment of Theory and Experiment on Correlations at RHIC’, BNL, February 2009

Theoretical Approach

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.

Medium created in a HIC can be described using hydrodynamics

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

dE dM GeV(0) v (0) 1.5dt 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 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)

Any conclusions about deposition mechanism???03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara

The Expanding Medium

Expanding Medium I

Consider different jet paths

• Apply Glauber initial conditions and an ideal Gas EoS for massless gluons• Focus on radial flow contribution

Experimental results based

on many eventsA. K. Chaudhuri, Phys. Rev. C 75, 057902

(2007) ,A. K. Chaudhuri, Phys. Rev. C 77, 027901

(2008)

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

near-side jet

dE/dt = 1 GeV/fm

Jet 150

Etot = 5 GeV

Expanding Medium IIEtot = 5 GeV

broad away-side peak double peaked structure

due to non-central jets

pTtrig = 3.5

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

vjet =0.999

BB et al., Phys. Rev. Lett. 105, 222301 (2010)

Expanding Medium IIIEtot = 10

Strong impact of the Diffusion wake

broad away-side peak double peaked structure

Causes smaller dip for pT=2 GeV

pTtrig = 7.5

6 < pTtrigger < 10

1.5 < pTassoc < 2.5

dPath length dependence Centrality

dependence03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

STAR, Phys. Rev. C 82, 024912 (2010)

BB, arXiv:1012.4418[nucl-th]

Expanding Medium IV

Conical emission angle also appears for subsonic jets

Not a Mach cone

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

(energy-momentum deposition scenario) pTassoc = 2.0

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

assoc = 3 GeV

PHENIX, PRL98, 232302 (2007)

BB et al., Phys. Rev. Lett. 105, 222301 (2010)

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., J. Phys. G 37, 094043 (2010)

Hot Spots IICheck with one single hot

Au, De/e0 = 2

Hot Spots IIICan hot spots explain

everything?

There is a superposition of jets and fluctuating initial conditions

pTassoc= 2.0 GeV pT

trig = 8.0 GeV

pTtrig = 3.5

Both lead to double-peak structure

Coalesced peak only for jet events

Heavy quark jets need to be studied

BB, arXiv:1012.4418 [nucl-th]

Heavy-flavor results

e-h correlations from heavy-flavordecay show a double-peak

structure on the away-sideClear indication that the signal is not just background fluctuation

A. Adare et al. [PHENIX], arXiv: 1011.1477[nucl-ex]

Why v3 deformations cannot be the whole story

ptrigT=3 – 4 GeV, passoc

T=1 – 2 GeV

What are the consequences of triangular flow?

The latter case should not be subtracted!

v3 could be due to initial conditions (hot spots)

OR due to a jet traversing the medium

- Correlation in Df1-Df2

Df1/2 120°- No correlation in D1-

D2B. Alver et al., Phys. Rev. C 81, 054905 (2010)

Shock front??

~ 120J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007)

B. Alver, Talk at the Glasma Workshop, BNL, May 2010

Fluctuating Initial Conditions

Initial Conditions Studying heavy-ion collisions requires a good understanding

of the role of the initial conditions:- Glauber model:

incoherent superposition of p+p collisions

- Color Glass Condensate (CGC): saturation effects are included

They differ:- initial temperature gradients- initial high-pT parton distribution- distance travelled by each partonLeads to a different opacity estimate

Glauber

L. McLerran, Talk at a the CP Violation Workshop, BNL, April 2010

Opacity of the Medium Exploring the properties of the

strongly-coupled sQGPjet quenching: signal for creation of opaque matter

S. Bass et. al., PRC 79 (2009), 024901

defined via:

Current description commonly based on pQCD though medium is supposedly sQGP

D. D’Enterria, Lect. Notes Phys.785 (2010), 285

S. Bass et. al., PRC 79 (2009), 024901

Caveat pQCD descriptions disagree in their

prediction of the azimuthal anisotropy of high-pT hadrons, characterizing

due to v2=v2(l) v2 is sensitive to the path length

dependence of energy loss, scaling as dE/dx ~ lz:z=1 : pQCD z=2 : AdS/CFT (on-shell partons) z>2 : AdS/CFT (off-shell partons)

M. Gyulassy et. al., PRL 85 (2000), 5535

S. Gubser et. al., JHEP 0810 (2008), 052;P. Chesler et.al., PRD 79 (2009) 125015

Energy-Loss Mechanisms

A. Adare et al, Phys. Rev. Lett. 105, 142301 (2010)

First investigation of v2(Npart) and RAA(Npart) for pT > 5 GeV hadrons is based onJ. Jia et. al., PRC 82 (2010),

024902

simple jet absorption model

Once RAA(Npart=350) ~ 0.18 for 0-5% p0 data - pQCD-like energy loss

fails to reproduce v2(Npart)

- AdS/CFT-like energy loss describes data for CGC initial conditions

pQCD-like AdS/CFT-like

Generic Energy Loss Model

Choosing an ansatz for the energy loss

t0 = 2fm, one can determine the RAA(Npart), vn(Npart)

P: momentum of the jet(s)a,z: parameters controlling the jet-energy and path-length

dependencek: being fixed thus that RAA(Npart=350) ~ 0.18 for most central

data and considering Bjorken expansion via

CGC/KLN: H. Drescher et. al., PRC 76 (2007) 024905

Glauber: B.Betz et.al., arXiv:1102.5416 [nucl-th]

RAA and v2

z=1 z=2Having fixed k forRAA(Npart=350) ~

0.18 RAA(Npart) can be reproduced z=1: v2 not

reproducedz=2: v2 reproduced

for CGC initial cond.

B.Betz et.al., arXiv:1102.5416 [nucl-th]

Small fluctuations for

RAA(Npart)large fluctuations

for v2(Npart)Not straightforward to distinguish between initial conditions

RAA vs. IAA, and vn vs. vnIAA

Extend to dijet analysis, but considering kaway = k

In contrast to Jia’s model, we

fit the RAA vs. IAA

vn vs. vnIAA:

- clear shift between Glauber and CGC model

- saturation effect for larger z

J. Jia et.al., arXiv:1101.0290 [nucl-th]

It is necessary to alwaysdetermine the mean andthe with of a correlation!

Higher Harmonics

z=1 z=2

- v3≠0 event-by-event,

- v4 similar for average and event-by-event initial conditionsNot suitable to distinguish betweenGlauber and CGC initial conditions

Higher harmonics are more sensitive to local gradients, but also to event-

by-event fluctuations larger v3,4 fluctuations

Path-length dependence

Study the path-length dependence at b=8fm:- Once RAA is

fixed via k,- sensitivity

remains mostly for v2 and v3

saturation effect occurs for larger zdescribed by AdS/CFToff-shell partons

S. Gubser et. al., JHEP 0810 (2008), 052;P. Chesler et.al., PRD 79 (2009) 125015

Measurement of virtuality in jet-photon collisions & v2,3 could lead to signature of AdS/CFT dynamics & microscopic mechanism of energy loss.

Summary „Conical“ signal can be created (general effect):

by averaging over deflected wakes created by jets.

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

even for subsonic jets

Necessary to study heavy-flavor tagged jets.

„Conical“ correlations could arise from multiple non-Mach sources

Investigated higher Fourier harmonics of jet quenchingShowing that they are remarkably insensitive to theGlauber and KLN/CGC model initial conditions

Studied the path-length dependence for larger exponentsa saturation effect occurs for larger exponentsfavoring an AdS/CFT energy loss

Backup

Investigation of path length dependence:Double-peaked structure becomes

morepronounced out-of-plane

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

Jet - Studies in HIC

Could be due to deflection

Centrality dependence:

double-peaked structure for central collisions

one peak structure for very peripheral collisions

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

J. Jia, Eur. Phys. J. C 62, 255 (2009)

Jet - Studies in HIC

Energy Scan:

double-peaked structure occurs at about the same angle for different collision energies Mach cone???03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara

Stopped Jet • Jet stops after t=4.5/v

dE GeV(0) 1.5dt fmdM GeV(0) 0dt fm

dE GeV(0) 1.5dt fmdM GeVv (0) 1.5dt fm

Vorticity conservation

tFO=4.5/v fm

tFO=6.5/v fm

tFO=8.5/v fmDiffusion wake still

present

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

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

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

BAMPS: Boltzmann Approach of MultiParton ScatteringsA 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 dissipation03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara

Mach Cones in Transport

Different Jet-Energy Loss Modells

Modelling Jets using …

Conclusion about Mach cones?

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 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)

Heavy Quark Jets

Heavy Quark JetsCompare weakly and strongly coupled models using heavy punch-

through jetpQCD: Neufeld et al. source for a heavy quark

AdS/CFT: Stress tables with/s=1/(4 ) pR. 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)

Expanding Medium 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

assoc = 2.0 GeV

vjet =0.999

BB et al., arXiv: 1005.5461

Initial Fluctuations IP. Sorensen J. Phys. G 37, 094011 (2010), B. Alver et al., Phys. Rev. C 81, 054905 (2010)

Glauber initial conditions:

due to symmetry, odd Fourier components vanish

higher Fourier components may occur

Fluctuating initial conditions: B. Alver, Talk at the Glasma Workshop, BNL, May 2010

Initial Fluctuations II

B. Alver et al., arXiv: 1007.5469

B. Alver et al., Phys. Rev. C 81, 054905 (2010), B. Alver et al., arXiv: 1007.5469H. Petersen et al., arXiv: 1008.0625

v3 not negligable small

• v3 is extensively studied

Calculating v3 using a viscous hydro model with initial conditions deformed

according to the eccentricities from a Glauber and a KLM (CGC) model

Insensitivity of higher vn‘s

Why are the vn‘s at high-pT so insensivite to initial conditions while the vn‘s of soft particles are?- viscous forces are driven by local gradients- jet absorption is driven by global differences in the

integrated

These two effects are different, especially event-by-event- Glauber and CGC in. cond. are tuned to reproduce the observed multiplicites<T> is similar, even if local gradients of T are different

Hydrodynamics and tomography lead to very different results.

Flow Subtraction

Subtraction of v2 and v3

leads to double-peak structure

Jun Xu et al, Phys. Rev. C 83, 021903 (2011)

Subtraction of larger vn onlyleads to one broad away-

side peak

0.15 < pTassoc < 4 GeV/c

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

simila

(2+1)d correlations

H. Agakishiev et al. [STAR], arXiv:1102.2669[nucl-ex]

2 trigger, opposite to each other

+ 1 associated jetStill using ZYAM

Trigger particle

It needs to be shown that jet quenching results can be reproduced

for larger pTassoc

Structure on the away-side

1.5 GeV < pTassoc < pT

5 < pTtrig1 < 10 GeV/c

pTtrig2 < 4 GeV/c

Full Jet Reconstruction I

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

Full jet reconstruction

questions ZYAM

Full Jet Reconstruction II

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

Full Jet Reconstruction III

Jet-hadron away-side significantly narrower

n ~ 6: spectral indexK = k (1-a)

Nuclear modification factor

TAA : GlauberTAA = r2/ P0

2 : CGCH. Drescher et. al., PRC 76 (2007) 024905

Having fixed k, the harmonics can be calculated

determining the angle with the reaction plane

and the Fourier density components are given by

Jet Tomography and Particle Correlations in Heavy-Ion Collisions

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