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
5
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
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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
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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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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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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)
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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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CEM
s