Transcript Correlation in Jets Rudolph C. Hwa University of Oregon

Correlation in Jets
Rudolph C. Hwa
University of Oregon
Workshop on Correlation and Fluctuation in
Multiparticle Production
Hangzhou, China
November 21-24, 2006
Two parts to this title:
Jets
Jets
Correlation
and
The conventional wisdom is that when
pT > 2 GeV/c,
then jets are produced.
Hard scattering is involved.
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.
2
correlations between
colliding
system
shower partons
produced hadrons
e+ejets
in
Au-Au
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Correlation of pions in jets in HIC
Two-particle distribution
 dqi 
dN
1

F4 (q1 ,q2 ,q3 , q4 )R(q1 ,q3 , p1 )R(q2 ,q4 , p2 )
2  

p1dp1 p2 dp2 ( p1 p2 )  i qi 
F4  (TT + ST + SS)13 (TT + ST + SS) 24
Factorizable terms:
(TT)13 (TT)24
(ST)13(TT)24
(TT)13(ST)24
k
q1
q3
Non-factorizable terms
q2
q4
They do not
contribute to
C2(1,2)
(ST + SS)13(ST + SS)24
correlated
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C2(1,2)  2 (1,2)  1(1) 1(2)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Pion transverse
momenta p1
and p2
Hwa & Tan, PRC 72, 024908 (2005)
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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
Factor of 3
enhancement
Hard for medium modification of
fragmentation function to achieve,
but not so hard for recombination
involving thermal partons.
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Associated particle distributions
in the recombination model
Au+Au @ 200 GeV
3GeV/c<pTtrigger<6GeV/c
STAR preliminary
Hwa & Tan, PRC 72, 057902 (2005)
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Bielcikova, at Hard Probes (06)
Jet+Ridge on near side
Au+Au 0-10%
jet
preliminary
J. Putschke, HP06, QM06
ridge
Jet grows with trigger momentum
Ridge does not.
J
1
R
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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J. Bielcikova, HP06 --- at lower pt(assoc)
Jet + Ridge
STAR preliminary
Jet
STAR preliminary
J/R~10-15%
 trigger
even lower!
Jet+ridge
Jet only
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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)
 triggered events:
The existence of
associated particles
falsifies our earlier
prediction.
Phantom jet is the only
way to understand the
problem.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Bielcikova, QM06
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Since shower s quark is
suppressed in hard scattering,
 is produced by recombination
of thermal partons, hence
exponential in pT.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
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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Proton triggered events
A. Sickles (PHENIX)
meson trigger
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
from the jet
J/R > 1?
baryon trigger
from the ridge
M partners: 1.7<pT<2.5 GeV/c
Meson yield in jet is high.
Meson yield in ridge decreases
exponentially with pT.
J/R < 0.1?
Ridge is developed in very
central collisions.
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Forward-backward asymmetry in d+Au collisions
If initial transverse broadening of parton
gives more hadrons at high pT, then
• forward has more
transverse broadening
• backward has no
broadening
Expects more
forward particles at
high pT than
backward particles
F/B > 1
B/F < 1
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Backward-forward ratio at intermediate pT
in d+Au collisions (STAR)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
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B/F asymmetry taking into
account TS recombination
(Hwa, Yang, & Fries, PRC 05)
There are more thermal partons
in B than in F.
STAR preprint
nucl-ex/0609021
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Associated particles on the away side
Collective response of the medium: Mach cone, etc.
Markovian parton scattering (MPS) Chiu & Hwa (06)
Non-perturbative process
Trajectories can bend
Divide into many segments:
Scattering angle  at each step
retains no memory of the past.
2.5<pT(trig)<4 GeV/c
Markovian
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Model input
• Cone width
 i  i / Ei
• Step size
i  Ei e i
• Energy loss
Ei 1  Ei 1   es  i

simulated result
Transport coefficient

2
  0.17
q̂
dE
  s q̂E
dx
2
Our
 
q̂     q̂  0.36 GeV2/fm
 s 
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.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
(a) Exit tracks: short,
bend side-ways,
large 
(b) Absorbed tracks:
longer, straighter,
stay in the medium
until Ei<0.3 GeV.
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Data from PHENIX (Jia)
1<pT(assoc)<2.5 GeV/c
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.

Chiu & Hwa, nucl-th/0609038
Exit tracks hadronized
by recombination,
added above pedestal
Energy lost during
last step is
thermalized and
converted to
pedestal distribution
PRC (to be published)
One deflected jet per trigger at most,
unlike two jets simultaneously, as in Mach
cone, etc.
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Extension to higher trigger momentum pT(trig)>8 GeV/c,
keeping model parameters fixed.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
(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
d-Au collision
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)
 distributions of both (B) and (F) peak at ,
but the normalizations are very different.
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STAR (F.Wang, Hard Probes 06)
Correlation shapes are the
same, yields differ by x2.
d
associated yield
in this case Au
x=0.05
x=0.7
is larger than
associated yield
in that case
Au
d
x=0.7
x=0.05
Degrading of the d valence q?
Don’t forget the soft partons.
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higher yield
lower yield
Recombination of thermal and shower partons
B/F ~ 2
3.9    2.7
2.7    3.9
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Backward-forward ratio at intermediate pT
Inclusive single-particle distributions
in d+Au collisions (STAR)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
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Au+Au centrality variation
dN/d
|trig|<1, 2.7<|assoc|<3.9
3<pTtrig<10 GeV/c, 0.2<pTassoc< 2 GeV/c
Near side
consistent with
zero.
Away-side broad
correlation in
central collisions.
Broader in more
central collisions

Normalization fixed at |±1|<0.2. Systematic uncertainty plotted for 10-0% data. 25
Au-Au collisions
No difference
in F or B recoil
More path length,
more deflection
At 2.7<||<3.9, the recoil
parton is moving almost as
fast as the cylinder front.
What is the Mach cone effect?
Width of  distribution
broadens with centrality
Less path length,
less deflection
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Two-jet recombination at LHC
Hwa & Yang, PRL 97, 042301 (2006)
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
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10  pT  20 GeV/c
The particle detected has some associated partners.
But they are part of the background of an ocean of
hadrons from other jets.
There should be no observable jet structure
distinguishable from the background.
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.
(a very conservative view)
Beyond what is known about jet quenching, not much has been learned
so far about the dense medium from studies of correlation in jets.
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.
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