Correlation in Jets Rudolph C. Hwa University of Oregon Workshop on Correlation and Fluctuation in Multiparticle Production Hangzhou, China November 21-24,

Correlation in Jets

Rudolph C. HwaUniversity of Oregon

Workshop on Correlation and Fluctuation in Multiparticle Production

Hangzhou, China

November 21-24, 2006

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Two parts to this title:

Jets and Correlation

Hard scattering is involved.

Jets

pT > 2 GeV/c,

The conventional wisdom is that when

then jets are produced.

But that does not mean that the hard parton fragments. Recombination has been found to be important at intermediate pT, where most correlation data exist.

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shower partons

produced hadrons

correlations between

colliding system

e+e-

Au-Au

jets in

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Correlation of pions in jets in HIC

Two-particle distribution

dNππp1dp1p2dp2

=1

(p1p2)2

dqiqii

∏⎡

⎣ ⎢ ⎤

⎦ ⎥ ∫ F4(q1,q2,q3,q4)R(q1,q3,p1)R(q2,q4,p2)

F4 =(TT+ST+SS)13(TT+ST+SS)24

k

q3

q

1

q4

q2

Non-factorizable terms (ST+SS)13(ST+SS)24

correlated

Factorizable terms:

(TT)13(TT)24

(ST)13(TT)24

(TT)13(ST)24

They do not contribute to C2(1,2)

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C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Hwa & Tan, PRC 72, 024908 (2005)

Pion transverse momenta p1 and p2

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C2(1,2) treats 1 and 2 on equal footing.Experimental data choose particle 1 as trigger, and studies particle 2 as an associated particle. (background subtraction)

STAR, PRL 95, 152301 (2005)

Trigger 4 < pT < 6

GeV/c

Hard for medium modification of fragmentation function to achieve,

but not so hard for recombination involving thermal partons.

Factor of 3 enhancement

7Hwa & Tan, PRC 72, 057902 (2005)

Associated particle distributions in the recombination model

Bielcikova, at Hard Probes (06)

STAR preliminary

Au+Au @ 200 GeVAu+Au @ 200 GeV3GeV/c<p3GeV/c<pTT

triggertrigger<6GeV/c<6GeV/c

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J. Putschke, HP06, QM06

Jet+Ridge on near side

Au+Au 0-10%preliminary

jet

ridge

Jet grows with trigger momentumRidge does not.

J

R≥1

Ridge is understood as enhanced thermal background due to energy loss by hard parton to the medium, and manifests through TT recombination.

Chiu & Hwa, PRC 72 (05).

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STAR preliminary

Jet + Ridge

STAR preliminary

Jet

J. Bielcikova, HP06 --- at lower pt(assoc)

Jet+ridgeJet+ridge Jet onlyJet only

J/R~10-15%J/R~10-15%

trigger even lower!

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J/R ~ 10% for 1<pt(assoc)<2 GeV/c suggests dominance of soft partons that are not part of the ‘jet’ in the numerator.Yet the ridge wouldn’t be there without hard parton, so it is a part of the jet in the broader sense.

Phantom jet: ridge only -- at low pt(assoc)



Bielcikova, QM06

triggered events:

Phantom jet is the only way to understand the problem.

The existence of associated particles falsifies our earlier prediction.

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Since shower s quark is suppressed in hard scattering, is produced by recombination of thermal partons, hence exponential in pT.Normally, thermal partons have no associated particles distinguishable from the background.

But if the s quarks that form the are from the ridge, then can have associated particles above the background, while having exponential pT distribution.

The phantom jet is like a blind boy feeling the leg of an elephant and doesn’t know that it belongs to an elephant. Low pt(trig) and low pt(assoc) suppress the peak above the ridge, and do not show the usual properties of a jet, yet the jet is there, just as the phantom elephant is to a short blind person.

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A. Sickles (PHENIX)

Proton triggered events

M partners: 1.7<pT<2.5 GeV/c

baryon trigger

meson trigger

from the jet

from the ridge

J/R < 0.1?

J/R > 1?

Meson yield in jet is high.

Meson yield in ridge decreases exponentially with pT.

Ridge is developed in very central collisions.

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Forward-backward asymmetry in d+Au collisions

Expects more forward particles at high pT than backward particles

If initial transverse broadening of parton gives more hadrons at high pT, then

• backward has no broadening

• forward has more transverse broadening

F/B > 1

B/F < 1

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Backward-forward ratio at intermediate pT



in d+Au collisions (STAR)B

/F

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B/F asymmetry taking into account TS recombination

(Hwa, Yang, & Fries, PRC 05)

STAR preprint nucl-ex/0609021

There are more thermal partons in B than in F.

162.5<pT(trig)<4 GeV/c

Associated particles on the away side

Collective response of the medium: Mach cone, etc.Markovian parton scattering (MPS) Chiu & Hwa (06)

Non-perturbative processTrajectories can bend

Markovian

Divide into many segments:

Scattering angle at each step retains no memory of the past.

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• Cone width σ i ∝ ρ i / Ei

• Step size Δi ∝ Ei e−ρ i

• Energy loss Ei+1 =Ei 1−κeρs −ρi( )2

simulated result

κ =0.17

Model input

Transport coefficient

q̂

dE

dx=− s q̂E

Our

q̂ ∝κs

⎛

⎝⎜⎞

⎠⎟

2

⇒ q̂=0.36 GeV2/fm Comparable to Vitev’s value

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Individual tracks may not be realistic, but (like Feynman’s path integral) the average over all tracks may represent physical deflected jets.

(a) Exit tracks: short, bend side-ways, large Δ

(b) Absorbed tracks: longer, straighter,

stay in the medium until Ei<0.3 GeV.

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Δ

Energy lost during last step is thermalized and converted to pedestal distribution

Exit tracks hadronized by recombination, added above pedestal

Data from PHENIX (Jia)

1<pT(assoc)<2.5 GeV/c

One deflected jet per trigger at most, unlike two jets simultaneously, as in

Mach cone, etc.

Chiu & Hwa, nucl-th/0609038PRC (to be

published)

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Extension to higher trigger momentum pT(trig)>8 GeV/c, keeping model parameters fixed.



(a) 4<pT(assoc)<6 GeV/c(b) pT(assoc)>6 GeV/c



Physics not changed from low to high trigger momentum.

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Mid- and forward/backward-rapidity correlation

Trigger: 3<pT(trig)<10 GeV/c, |(trig)|<1 (mid-rapidity)Associated: 0.2<pT(assoc)<2 GeV/c,

(B) -3.9<(assoc)<-2.7 (backward) (F) 2.7<(assoc)<3.9 (forward)

Δ distributions of both (B) and (F) peak at ,but the normalizations are very

different.

d-Au collision

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is larger than

Aud

associated yield in this case

x=0.7x=0.05

Correlation shapes are the same, yields differ by x2.

Aud

x=0.05x=0.7

associated yieldin that case

Degrading of the d valence q?

STAR (F.Wang, Hard Probes 06)

Don’t forget the soft partons.

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Recombination of thermal and shower partons

higher yield

lower yield

B/F ~ 2−3.9 < η < −2.7 2.7 < < 3.9

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Backward-forward ratio at intermediate pT



in d+Au collisions (STAR)B

/FInclusive single-particle distributions

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Au+Au centrality variation|trig|<1, 2.7<|assoc|<3.9

3<pTtrig<10 GeV/c, 0.2<pT

assoc< 2 GeV/c

Normalization fixed at |Δ±1|<0.2. Systematic uncertainty plotted for 10-0% data.

dN

/dΔ

Δ

Near side

consistent with

zero.

Away-side broad

correlation in

central collisions.

Broader in more central collisions

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Au-Au collisions

No difference in F or B recoil

More path length, more deflection

Less path length, less deflection

Width of Δ distribution broadens with centrality

At 2.7<||<3.9, the recoil parton is moving almost as fast as the cylinder front. What is the Mach cone effect?

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Two-jet recombination at LHC

New feature at LHC: density of hard partons is high.

High pT jets may be so dense that neighboring jet cones may overlap.

If so, then the shower partons in two nearby jets may recombine.

2 hard partons

1 shower parton from each

p

Hwa & Yang, PRL 97, 042301 (2006)

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The particle detected has some associated partners.

There should be no observable jet structure distinguishable from the

background.

10 < pT < 20 GeV/c

But they are part of the background of an ocean of hadrons from other jets.

If this prediction is verified, one has to go to pT(assoc)>>20 GeV/c to do jet tomography.

What happens to Mach cone, etc?

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Conclusion

Many correlation phenomena related to associated particles observed at moderate pT can be understood in terms of recombination.

However, there remains a lot to be explained.

More dramatic phenomena may show up at LHC, but then the medium produced may be sufficiently different to require sharper probes.

We have learned a lot from experiments at SPS, RHIC, and soon from LHC.

At each stage the definition of a jet has changed from >2 to >8 to >20 GeV/c.

What kind of correlation is interesting will also change accordingly.

Beyond what is known about jet quenching, not much has been learned so far about the dense medium from studies of correlation in jets.

(a very conservative view)

Documents

Correlation in Jets Rudolph C. Hwa University of Oregon Workshop on Correlation and Fluctuation in Multiparticle Production Hangzhou, China November 21-24,