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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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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)
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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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QuickTime™ and aTIFF (LZW) decompressor
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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
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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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QuickTime™ and aTIFF (LZW) decompressor
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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.
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(a) 4<pT(assoc)<6 GeV/c(b) pT(assoc)>6 GeV/c
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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
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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)