Jet-medium interaction in heavy-ion collisions

Rudolph C. HwaUniversity of Oregon

Hua-Zhong Normal University, Wuhan, China

April, 2009

2

Outline

1. Introduction

2. Ridges

3. Dependence of ridge yield on trigger azimuth

4. Hadron correlation in back-to-back jets

5. Conclusion

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1. Introduction

Jet-medium interaction has one well-known consequence: Jet Quenching

--- studied in pQCD at high pT.

One way to learn about the dense, hot medium created in heavy-ion collision is to probe it with hard partons.

There are other ways of studying the jet-medium interaction that reveal a broad variety of its nature.

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High pT particles are suppressed.

ησηddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

=

high pT

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pT2 6

low intermediate

high

pQCDhydro

no rigorous theoretical framework

But that is where abundant experimental data exist,

especially on hadronic correlations that characterize the interaction between jets and medium.What can we learn from the abundant data?

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pT distributions of and p

At intermediate pT recombination model has been successful.

dN

pTdpT

=1

p0pT

dq1q1∫

dq2q2

Fqq(q1,q2 )R (q1,q2 , pT )

dN p

pTdpT

=1

p0pT

dq1q1∫

dq2q2

dq3q3

Fuud(q1,q2 ,q3)Rp(q1,q2 ,q3, pT )

Fqq =TT +TS+SS

Fuud =TTT +TTS+TSS+SSS

Parton distributions

fragmentation

medium effect

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/K

QuickTime™ and aTIFF (LZW) decompressor

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STAR4

3

2

1

0

Strong evidence in support of the recombination/coalescence model (Reco), since no other model can explain it in the intermediate pT region.

Large Baryon/Meson ratio in the inclusive distributions

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P. Fachini, arXiv:0808.3110

B/M~1.7 up to pT~11 GeV/c!How is it to be explained by fragmentation?

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2. Ridges

Single-particles inclusive distribution can reveal only limited information about the nature of jet-medium interaction.

For more information we need to consider two-particle correlation.

Ridges are the response of the medium to the passage of semihard partons, detected in di-hadron correlation.

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Primary correlation variables: , η

ηη

TriggerTrigger

Correlation on the near side

, η are the variables of the associated particle relative to the trigger particle.

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Putschke, Quark Matter 2006

STAR

Ridge

R

J

η

J+R

ridge R Jet J

Jet: medium effect on hard parton

Ridge: effect of hard parton on medium

Structure of particles associated with a trigger

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R yield increases with Npart medium effect

1. Centrality dependence

Jet+Ridge ()

Jet ()

Jet(η)

Putschke, QM06 pt,assoc. > 2 GeVSTAR preliminary

2. pT,trig dependence

Strongly correlated to jet production, even for trigger momentum < 4 GeV/c.

Four features about Ridges

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3. Dependence on pT,assoc

Putschke, QM06

Ridge is exponential in pT,assoc slope independent of pT,trig

4. Baryon/meson ratio

Suarez QM08

B/M in ridge even higher than in inclusive distr.

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Trigger: 3 < pT < 4 GeV/c

Associated: 1.5 < pT < 2 GeV/c

Not hard enough for pQCD to be reliable, too hard for hydrodynamics.

We have no reliable theoretical framework in which to calculate all those subprocesses.

Physical processes involve:

• semihard parton propagating through dense medium

• energy loss due to soft emission induced by medium

• enhancement of thermal partons

• hydro flow and hadronization

• ridge formation above background

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associated particles

These wings are useful to identify the Ridge

SS

trigger

TT ridge (R)ST

peak (J)

Partonic basis for ridge formation

Mesons:Baryons: TTT in the ridge

Suarez QM08

B/M in ridge even higher than in inclusive distr. It can only be explained by Recombination.

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3. Dependence of ridge yield on the trigger azimuthal angle

ηηTrigger

Trigger

restrict |η|<0.7

What is the direction of the trigger T?

irrelevant

very relevant

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Quark Matter 2008 -- A. Feng (STAR)

Dependence on trigger azimuthal angle

1

43

2

56

in-plane

out-of-plane

φs = φT − Ψ RP

top 5%

20-60%

in-plane S=0 out-of-plane S=90o

• In 20-60%, away-side evolves from single-peak (φS =0) to double-peak (φS =90o).• In top 5%, double peak show up at a smaller φS.• At large φS, little difference between two centrality bins.

STAR Preliminary

STAR Preliminary

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STAR Preliminary

in-plane S=0 out-of-plane S=90o

Rid

ge

Jet

3<pTtrig<4, 1.5<pT

trig<2.0 GeV/c

20-60%

assoc

Ridge and Jet components are separated.

In-plane

Out

-of-

plan

e

1

43

2

56

Ridge shapes in are similar.Study the area, which is the yield.

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Jet and Ridge Yield

20-60% top 5%jet part, near-side

ridge part, near-side

jet part, near-side

ridge part, near-side

Ridge: seem to decrease with φs . More significant in 20-60% than top 5%.

Jet: seem to slightly increase with φs .

Strong near-side jet-medium interaction in reaction plane, generating sizable ridge?

Minimal near-side jet-medium interaction perpendicular to reaction plane?

STAR Preliminary3<pT

trig<4, 1.5<pTassoc<2.0 GeV/c

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The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow.

If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened.

Correlation between s and

C(x, y,φs) =exp −(φs− (x,y))

2

2λ⎡

⎣⎢

⎤

⎦⎥

Semihard parton directed at s , loses energy along the way, and enhances thermal partons in the vicinity of the path.

s

But parton direction s and flow direction are not necessarily the same.

s

Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction .

Flow direction normal to the surface

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3<pTtrig<4, 1.5<pT

assoc<2.0 GeV/c

Data: Feng QM08

λ=0.09

~20o

Chiu-Hwa -- PRC 79, 034901 (2009)

Correlated emission model (CEM)

Strong ridge is developed when the trigger direction is aligned with the flow direction.

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s>0

In CEM we found an asymmetry in the distribution

trigger pt=3-4 GeV/c

Jet

Ridge

s|

CEM model

STAR Preliminary

Ridge: assoc pt=1-1.5 GeV/cRidge: assoc pt=1.5-2 GeV/cJet: assoc pt=1.5-2 GeV/c

Netrakanti

QM09

R only

s<0

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What we have discussed is about RIDGE ---

the effect of jet on the medium.

4. Hadron correlation in back-to-back jets

Now we discuss the effect of medium on jets ---

correlation of hadrons in di-jets. Hwa-Yang - 0812.2205 [PRC (09)]

24c=0 (0%) most central

c=0.5 (50%) mid-central

Near-side jet p

TT TS SS

Fi (q)=1βL

dkkfiq

qeβL

∫ (k)

L: path length in medium

In reality, L cannot be fixed. Experiment can only specify centrality c.

Single-particle distribution

dN

pdp=

C2

6e−p/T +

1p2

dqq∫i

∑ Fi (q)[TS(q, p) +pq

Di (p / q)]

k q

q =ke−βt

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QuickTime™ and aTIFF (Uncompressed) decompressor

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QuickTime™ and aTIFF (Uncompressed) decompressor

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QuickTime™ and aTIFF (Uncompressed) decompressor

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c=0.05

c=0.86

Inclusive spectra fitted by one parameter for each centrality βL = ξ (c)

Fit by the average of ξ (c)

P(ξ,c) =Nξ(ξ0 −ξ)αc

2 parameters: ξ0, α; data >100 pts.

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Associated particle on near-side jet

dN

ptdptpadpa

=1

(ptpa)2

dqq∫i

∑ Fi (q)H(q→ pt, pa)

[TS+SS]

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QuickTime™ and aTIFF (Uncompressed) decompressor

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nearly independent of c

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Suppression factorΓnear (pT ) =

q

k pT

Fraction of energy loss

1−Γnear (pT )

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~ 15%

Near-side jets originate from the rim to minimize energy loss

Trigger bias

Insensitive to centrality

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Back-to-back jets

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dN

ptdptpbdpb

=1

(ptpb)2

dqq

dq'q'∫

i∑ Fi '(q,q')H(q→ pt)H(q'→ pb)

QuickTime™ and aTIFF (Uncompressed) decompressor

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Yield is insensitive to pt

Yaway =O(10−1)Y

near

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Suppression factorΓaway (pt , pb ) =

q '

k ' pt , pb

Fraction of energy loss1−Γaway(pt, pb)

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ξ (0.05) = 2.9

~ 0.7

much larger than on near side ~ 0.15

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.Away-side hard parton travels a longer distance in the medium, losing more momentum.

<k’> much larger than <k>

Anti-trigger bias

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Symmetric dijets

Let pt =pb =p

pt

pt

pb

pb

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away

Same degree of quenching on both sides.

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near

knows nothing about the away side.

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The only way that can be true is that all symmetric dijets are tangential jets at any c.

Suppressions on both sides are similar, independent of c.

Surface-to-volume ratio is Npart

2/3.

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Au+Au vs d+Au comparison

T1A1_T2

T2A1_T1

-1-2 0 1 2 3 4 5

2

0 1

_d

N_

Ntr

ig d

(

)

STAR Preliminary

200 GeV Au+Au, 12% central

• Di-jets are suppressed.• Once select di-jets, away-side associated particles NOT suppressed.• Shapes of near- and away-sides similar.• Central Au+Au ~ d+Au.

No energy loss for triggered di-jets!Tangential di-jets (or punch-through without interactions).

T1: pT>5 GeV/c, T2: pT>4 GeV/c, A: pT>1.5 GeV/c

Au+Au

d+Au

-1-2 0 1 2 3 4 5

1

0

1

_d

N_

Ntr

ig d

(

)

STAR Preliminary

2

3

200 GeV Au+Au & d+Au

Barannikova (STAR) QM08

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Surface effect

T1: pT>5GeV/c

T2: pT>4GeV/c

• If the triggers have tangential bias:

expect a term related to the surface: ~ R2 ~ Npart2/3

STAR Preliminary

T1= 5 GeV/c

1000 200 300 Npart

0

N

trig__

Nev

t Np

art

2/3

0.4

d+Au

x10 -3

STAR Preliminary

#T1T2 pairs / #Single triggers

#Di-Jets / #Single triggers

1000 200 300

0.015

0.05

0.01

Npart

Barannikova (STAR) QM08

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Conclusion

We have discussed jet-medium interaction at intermediate pT.

• Effect of jets on medium:

Semi-hard parton -> energy loss to medium -> Ridge. Our interpretation is that the ridge is formed by the recombination of thermal partons enhanced by jet. The prediction on asymmetry has been verified by data.

• Effect of medium on dijets:

Energy loss to medium -> strong correlation between jets.It is hard to probe the medium interior by dijets because of dominance by tangential jets --- also verified by data on 2jet+1 correlation.

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Will the problem be clarified at LHC?

Physics at LHC is not likely to be simply the extrapolation from RHIC.

Di-hadron correlation will be far more complicated.

Many people predict that p/ ratio ~0.5 for 10<pT<20 GeV/c in single particle distribution (by fragmentation).

We (RH & CBYang) predicted 5< p/ <20 due to jet-jet recombination.

I doubt it.

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Thank you.

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backup

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There is severe damping on the away side, but no damping on the near side.

to detector

undamped

absorbed

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A more revealing way to see the properties of jet-medium interaction is to examine the azimuthal dependence of jet production

φtrigger

associated particle

Dihadron correlations

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1. Centrality dependence

STAR preliminary

Jet

SS TS

STAR preliminary

Jet + Ridge

TT

For pT,trig as low as 3 GeV/c, the semihard parton is created not far from the surface because of absorption by the medium.

Enhanced thermal partons are strongly dependent on medium

Ridge is formed by recombination of enhanced thermal partons due to energy loss of a semihard parton created near the surface as it traverses the medium.

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What partons?Putschke, QM06

Ridge is exponential in pT,assoc

3. Dependence on pT,assoc

Thermal partons correlated to jetsInverse slope:

T’ (for R) > T (for inc.) T~40-50 MeV/cquark ~ exp(-qT/T’)

hadron ~ exp(-pT/T’)

RF ~ (pT-i qiT)

T’ same for quarks and hadrons

2.-3. Ridge is formed by enhanced thermal partons

pt,assoc. > 2 GeVSTAR preliminary

2. pT,trig dependence

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Geometry

x

y

h

w

Ellipse:x

w⎛⎝⎜

⎞⎠⎟

2

+yh

⎛⎝⎜

⎞⎠⎟

2

=u

grad u(x,y) => normal to the ellipse

(x, y) = tan−1 w2y

h2x

⎛

⎝⎜⎞

⎠⎟

x0, y0

x1, y1t s t = distance from creation

point to surface along s

Survivability function:

S(t)= 1+ expt−t0

t1

⎛

⎝⎜⎞

⎠⎟⎡

⎣⎢

⎤

⎦⎥

−1

Density: D(x, y) depends on TA,B(s) -- a la Glauber

t’

Fluctuation:

Γ(x, y,φ) = exp −(φ −ψ (x, y))2

2γ t '

⎡

⎣⎢

⎤

⎦⎥

Fluctuation of ridge hadron at from local flow direction

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ξ0 1

Ridge particle distribution

R(φ,φs,x0 ,y0 ) =NS(t)t dξD(xξ0

1

∫ ,yξ )C(xξ ,yξ ,φs)Γ(xξ ,yξ ,φ)

Observable ridge distribution per trigger

R(φ,φs) =dx0dy0R(φ,φs,x0 ,y0 )∫dx0dy0S(t(x0 ,y0 ))∫

III

III IV

0 <φs < / 2

III

III IV

− / 2 < φs < 0

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Yield per trigger

Y (φs) = dφφs−1

φs+1

∫ R(φ,φs)

R(φ,φs,x0 ,y0 ) =NS(t)t dξD(xξ0

1

∫ ,yξ )C(xξ ,yξ ,φs)Γ(xξ ,yξ ,φ)

a constantλ

t0

t1 ~ 0.1 t0

Adjust N to fit overall normalization for top 5%; relative normalization for 20-60% not adjustable.

N encapsules all uncalculable effects of the soft processes involved in the ridge formation, and is not essential to the study of the s dependence.

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QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

CEM

s