Transcript INT06 - University of Oregon

Correlation in Jets at RHIC
Rudolph C. Hwa
University of Oregon
Institute of Nuclear Theory
University of Washington
December 5, 2006
Outline
• General comments on hadron production at high pT
• d-Au collisions
• Au-Au collisions
• centrality dependence of correlation
• ridge under the jet peak
• Omega puzzle and its resolution
• proton trigger and meson partners
• Transfragmentation region
• Mid-F/B rapidity correlation
• Away-side correlation
• 2-jet recombination -- LHC
2
Regions of transverse momentum
Traditional classification in terms of scattering
0
2
soft
4
6
8
10
pT
hard
pQCD + FF
3
Regions of transverse momentum
Traditional classification in terms of scattering
0
2
4
6
soft
8
pT
10
hard
pQCD + FF
A different classification in terms of hadronization
0
2
(low)
thermal-thermal
4
6
8
pT
10
(intermediate)
thermal-shower
Terminology used in recombination
(high)
shower-shower
4
soft
TT
thermal
TS
hard
fragmentation
SS
Transverse momentum
Phenomenological successes of this picture
5
 production in AuAu central collision at 200 GeV
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fragmentation
thermal
TT
TS
SS
Hwa & CB Yang, PRC70, 024905 (2004)
6
Basic equation for meson production by recombination
dN
dq1 dq2
p

Fjj' (q1 ,q2 )R (q1 ,q2 , p)
dp
q1 q2
R (q1,q2, p) 
q1q2
 (q1  q2  p)
p
Shower parton distributions are determined from
Fragmentation
dx1 dx2  j
x2 

j'
xDi (x)  
) R (x1 , x2 , x)
Si (x1 ),Si (
function
x1 x2 
1 x1 
Basic
assumption:
Dynamically independent,
kinematically constrained.
7
Proton production by recombination
p
dN p
dp

dq1 dq2 dq3
 q1 q2 q3 Fuud (q1,q2 ,q3 )Rp (q1,q2 ,q3 p)
Proton recombination
function determined in
the valon model
e
e
u
u
p
p
d
u
u
d
p
p
U
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U
D
TTS+TSS
Rp (x1 , x2 , x3 , x)  g(
x1 x2 2.76 x3 2.05 x1 x2 x3
) ( )  (    1)
x2
x
x
x
x
8
Rp /  : 1
for pT ~ 3 GeV/c in Au-Au collision at 200 GeV.
recombination/
coalescence
Commonly regarded as “baryon anomaly”.
There is no “baryon anomaly”, if fragmentation is not
regarded as the standard hadronization process.
9
Conventional thinking:
Jets  fragmentation of hard partons
That’s true in e+e- annihilation, and pp collision,
but false in heavy-ion collisions at moderate pT
(even with modified fragmentation function).
Since
Dq p
Dq
 0.1 , the p/ ratio
Rp / : 0.1
is characteristic of fragmentation.
May still be valid for pT>8 GeV/c
10
correlations between
colliding
system
shower partons
produced hadrons
e+ejets
in
Au-Au
 q1  j '  q2 
S

 k  i  k  q1 
 i  dk fi (k)Sij 
2 (1, 2)
r2 (1, 2) 
1 (1)1 (2)    dk f (k)S
i
i
i
j
 q1 
j  q2 

dk
f
(k)
S



x

   11
i
i 
 
i

k
k
no correlation
C2 (1, 2)  [r2 (1, 2)  1]1 (1)1 (2)
0
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Hwa & Tan, PRC 72, 024908 (2005)
x1
x2
12
2 (1,2)
r2 (1,2) 
 1 (1) 1 (2)
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fi(k)
fi(k) fi(k)
fi(k) is small for 0-10%, but smaller for 80-92%
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13
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
14
negative
correlation
C2(1,2)  2 (1,2)  1(1) 1(2)
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Pion transverse
momenta p1
and p2
Hwa & Tan, PRC 72, 024908 (2005)
15
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.
16
Associated particle distributions
in the recombination model
Au+Au @ 200 GeV
3GeV/c<pTtrigger<6GeV/c
STAR preliminary
Hwa & Tan, PRC 72, 057902 (2005)
17
Bielcikova, at Hard Probes (06)
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
18
Backward-forward ratio at intermediate pT
in d+Au collisions (STAR)
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19
B/F asymmetry calculated in
the Recombination Model
(Hwa, Yang, & Fries, PRC 05)
STAR preprint
nucl-ex/0609021
20
BRAHMS, PRL 93, 242303 (2004)
Large 
BRAHMS data show that in
d+Au collisions there is
suppression at larger .
Hwa, Yang, Fries, PRC 71,
024902 (2005).
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No change in physics
from =0 to 3.2
Soft parton density decreases, as  is increased
(faster for more central collisions).
TS recombination diminishes at higher .
More suppressed in central than
in peripheral collisions.
21
Correlation with triggers
 and  distributions
STAR, PRL 95, 152301 (2005)
P1
Pedestal
Why?
P2
22
Longitudinal
Transverse
t=0
later
23
Thermal partons
Events without jets
T(q)  Cqe q / T
Events with jets
Thermal medium enhanced due
to energy loss of hard parton
T' (q)  Cqe
new parameter
 q/ T '
in the vicinity of the jet
T’- T = T > 0
24
For STST recombination
F4'    dkkfi (k)T' (q3 ){S(q1 ),S(q2 )}T'(q4 )G( , q2 / k)
i
enhanced thermal
trigger
associated particle
Sample with trigger particles and with
background subtracted
F4tr bg   L (ST') 13 (T'T'  TT) 24  ( ST') 13 ( ST') 24 G
Pedestal
peak in 
& 
25
dN tri gbg
d1  min dp2 p2  dp1 p1

0.7
p ass oc
4
1 dN
p1 dp1 p2 dp2

tri g
0.7
6
dN
Ntri g d
0.7 d1 4 dp1 p1 p1dp1
0.7
4
6
dN


dkkfi (k) dq1  dq2 
3 
p1dp1 p2 dp2 ( p1 p2 ) i
trigbg

q

T' (p1  q1 )S 1 T' (q2 )T' ( p2  q2 )  T(q2 )T(p2  q2 )
 k 


 


q1   q2 

}T' (p2  q2 )G( , q2 / k ) 
T' ( p1  q1 ){S
,S
 k  k  q1 


dN tri g

q1 
 3   dkkfi (k) dq1T' ( p1  q1 )S 
p1 dp1 p1 i
k
26
Pedestal in 
dN(T' T' TT)
P1,2  p (1,2) dp2
|tri g
min
dp2
4
0.15 < p2 < 4 GeV/c,
2 < p2 < 4 GeV/c,
P1
parton distribution
less reliable
P1 = 0.4
P2 = 0.04
T' (q)  Cqe
q / T '
find T ’= 0.332 GeV/c
cf. T = 0.317 GeV/c
P2
more reliable
T ’ adjusted to fit pedestal
T = 15 MeV/c
27
pedestal
T=15 MeV
Chiu & Hwa, PRC 72, 034903 (2005)
28
Associated particle distribution in 
Chiu & Hwa, PRC 72, 034903 (2005)
29
 and  production at intermediate pT
pT distribution of  by recombination
For 
Strange quark shower is very suppressed.
30
Hwa & CB Yang, nucl-th/0602024
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recombination
s
s
0
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hard parton
scattering
recombination
s
s
s

s
fragmentation
If it is hard scattering followed by
fragmentation, one expects jets of particles.
Thermal-parton recombination
There are other
particles
associated with
 and 
31
A prediction that can be checked now!
Since shower partons make insignificant
contribution to  production for pT<8
GeV/c, no jets are involved.
Select events with  or  in the 3<pT<6 region,
and treat them as trigger particles.
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Predict: no associated particles giving rise
to peaks in , near-side or away-side.
Thermal partons are uncorrelated,
so all associated particles are in the background.
STAR did the analysis to check our prediction,
and reported their result at QM06.
32
STAR
Ruan (Tuesday, plenary)
Barranikova (Wed, plena.)
Bielcikova (Sunday, 3.1)
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At face value the data
falsify the prediction and
discredits RM.
I now explain why the prediction was wrong
and how the data above can be understood.
Recombination still works, but we need a deeper
understanding of what is going on.
Phantom jet
33
The core issue is the (seemingly) contradictory phenomena:
(1)  spectrum is exponential
up to 6 GeV/c.
(2)  triggered events have
associated particles.
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(1) means that there is no
contribution from hard scattering,
which is power-law behaved;
hence, there is no jet.
(2) means that there is jet structure.
The resolution is to recognize
that it is a phantom jet.
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34
yield,)
Calderon showed on Tuesday
Jet+Ridge ()
Jet ()
Jet)
3<pt,trigger<4 GeV
Au+Au 0-10%
preliminary
pt,assoc.>2 GeV
preliminary
Npart
But p/ ratio depends on centrality.

Jet yield is independent of centrality.


A lot of action is going on in
the ridge!
35

Jet+Ridge on near side
J. Putschke, QM-1.3
Unidentified
charged hadron
J
1
R
J. Bielcikova (HP06, QM06) at lower pt(assoc)
J/R~10-15%
 trigger
even lower!
Jet+ridge
Jet only
J
 0.1
R 36
Thus we have a ridge without any significant peak on top.
The ridge would not be there without a hard scattering,
but it is not a usual jet, because it contain no shower
partons, only thermal partons.
Phantom Jet
When pT(trig) is low, and the trigger is , it is not in the
jet, since s quark is suppressed in the shower partons.
The s quarks in the ridge form the .
One can see the usual peak when pT(assoc) is increased,
and the ridge height will decrease.
37
The ridge has been interpreted as the recombination of
enhanced thermal partons due to the energy loss to the
medium by the passage of hard parton.
Longitudinal
expansion results
in broad  ridge
Radial expansion
does not broaden
the ridge under the
peak in 
Chiu & Hwa, PRC 72, 034903 (2005)
38
Resolution of the  puzzle
The ridge contains thermalized partons: u, d, s
Hence, sss recombine to form the trigger .
Other partons can form the associated
particles.
(1) The pT distribution of  is exponential.
(2) There are associated particles.
The  looks like a peak, but it is all ridge.
Our earlier prediction that there is no jet
is still right, if ‘jet’ is meant to be the
usual jet.
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But we were wrong to conclude that there would be no
associated particles, because a phantom jet is associated with
the  and it is the ridge that sits above the background. 39
Since  is among the particles in the ridge and
is formed by TTT recombination, everything
calculated previously remains valid.
Predictions for  triggered events:
The ridge should be found in .
The ridge has abundant u, d, s. So the
associated particles should have the
characteristic feature of recombination, i.e.,
large p/ and /K ratios, ~O(1).
Since the ridge arises out of enhanced
thermal partons, the associated particles
should have exponential pT distribution.
40
Baryon vs meson triggered events (PHENIX)
meson trigger
from the jet
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J/R > 1?
baryon trigger
from the ridge
J/R < 0.1?
Meson yield in jet is high.
Meson yield in ridge decreases
exponentially with pT.
Ridge is developed in very
central collisions.
41
Forward production of hadrons
PHOBOS, nucl-ex/0509034
Back et al, PRL 91, 052303 (2003)
Without knowing pT,
it is not possible to
determine xF
42
BRAHMS, nucl-ex/0602018
43
xF = 0.9
xF = 0.8
TFR
44
Theoretically, can hadrons be produced at xF > 1? (TFR)
It seems to violate momentum conservation, pL > √s/2.
In pB collision the partons that recombine must satisfy
x
i
1
i
x
p
i
1
i
B
A
B
But in AB collision the partons can come from different nucleons
In the recombination model the produced p and  can
have smooth distributions across the xF = 1 boundary.
45
proton
: momentum
degradation factor
proton-to-pion ratio
is very large.
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pion
Hwa & Yang, PRC 73,044913 (2006)
Regeneration of soft
parton has not been
considered.
Particles at xF>1 can
be produced only by
recombination.
46
xF = 0.9
xF = 1.0
xF = 0.8
TS
TFR
?
TTT
TT
47
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Hwa & Yang, nucl-th/0605037
48
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Hwa & Yang, nucl-th/0605037 (to be revised)
49
Hwa & Yang, nucl-th/0605037
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Thermal distribution fits well
 no shower partons involved
 no jets involved
 no jet structure
 no associated particles
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High Rp/ is already known
from 200 GeV data, not
62.4 GeV yet.
This is not a ridge effect, since
jets are suppressed at large50.
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.
51
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.
52
higher yield
lower yield
Recombination of thermal and shower partons
B/F ~ 2
3.9    2.7
2.7    3.9
53
Backward-forward ratio at intermediate pT
Inclusive single-particle distributions
in d+Au collisions (STAR)
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54
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. 55
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
56
F. Wang, Ponta Delgada, 2006
Even though the Mach cone effect is weaker, its presence
implies collective medium response to the passage of a parton.
What is the speed of sound? It seems to be too low.
What is the nature of the “shock wave” at forward rapidity?
The dominant effect seems to be due to deflected jets -at midrapidity and forward region.
57
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
58
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
59
Individual tracks may not
be realistic, but (like
Feynman’s path integral)
the average over all
tracks may represent
physical deflected jets.
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(a) Exit tracks: short,
bend side-ways,
large 
(b) Absorbed tracks:
longer, straighter,
stay in the medium
until Ei<0.3 GeV.
60
Data from PHENIX (Jia)
1<pT(assoc)<2.5 GeV/c
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
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.
61
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
Physics not changed from low
to high trigger momentum.
62
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
63
dN h
 H h(1) ( pT )  ( pT )H h(2) ( pT )
pT dpT
overlap
probability
H h(2) ( pT )   2   dkdk ' kfi (k)k ' fi ' (k ')
i,i '

dpl 
   p  Fii ' (k, k '; p1, p2 ,[ p3 ])Rh ( p1, p2 ,[ p3 ]; pT )
l
pion
l
 p1  j '  p2 
Si   Si '  
 k   k' 
j
p1  p2  pT
Given pT , k and k’ can be smaller, thus enhancing fi(k)fi’(k’).
Effect is even more pronounced for proton formation.
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QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
( pT ) : pT7
( pT )  0
Does not approach
limiting dist. for 1-jet
Limiting distribution for
1-jet fragmentation
Fragmentation of a parton to a
proton has very low probability,
but recombination of shower
partons from two jets increases
the yield.
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Proton-to-pion ratio at LHC
 -- probability
of overlap of 2
jet cones
If (pT)~pT-7,
then we get
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
single jet
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Hwa & Yang,
PRL (to appear),
nuclth/0603053
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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.
That is very different from a super-high pT jet.
A jet at 30-40 GeV/c would have lots of
observable associated particles.
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We predict for 10<pT<20 Gev/c at LHC
• Large p/ ratio
• NO associated particles
above 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.
(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.
For example, nothing learned about critical behavior from recoil
parton traversing the dense medium undergoing phase transition.
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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Backup slides
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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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