high p t physics in heavy ion collisions rudolph c. hwa university of oregon ciae, beijing june 13,...
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High pT Physics in Heavy Ion Collisions
Rudolph C. HwaUniversity of Oregon
CIAE, Beijing
June 13, 2005
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Well studied for 20 years ---- pQCD
What was a discovery yesterday
is now used for calibration today.
Instead of being concerned with 5% discrepancy in pp collisions, there are problems involving factors of 10 differences to understand in nuclear collisions.
High pT Physics of Nuclear Collisions at High Energy
particle
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Chunbin Yang (HZNU, Wuhan; UO)
Rainer Fries (Univ. of Minnesota)
Zhiquang Tan (HZNU, Wuhan; UO)
Charles Chiu (Univ. of Texas, Austin)
Work done in separate collaborations with
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Outline
Anomalies at high pT according to the
“standard model of hadronization” --- parton fragmentation
The resolution: parton recombination
• Recombination in fragmentation• Shower partons• Inclusive distributions at all pT• Cronin effect• Hadron correlations in jets
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Conventional approach to hadron production at high pT
D(z)
h
qA A
Hard scattering near the surface because of energy loss in medium --- jet quenching.
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If hard parton fragments in vacuum, then the fragmentation
products should be independent of the medium.
h
q
Particle ratio should depend on the FF D(z) only.
The observed data reveal several anomalies according to that picture.
D(z)
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Anomaly #1 Rp/π
1
Not possible in fragmentation model:
Dp/ q <<Dπ /q
Rp/π
Dp/q
Dπ /q
u
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cm energy cm energy
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Anomaly #2 in pA or dA collisions
kT broadening by multiple
scattering in the initial state.
Unchallenged for ~30 years.
If the medium effect is before fragmentation, then should be independent of h= or p
Cronin Effect Cronin et al, Phys.Rev.D (1975)
p
q
hdNdpT
(pA→ πX)∝ Aα , α >1
A
RCPp >RCP
πSTAR, PHENIX (2003)
Cronin et al, Phys.Rev.D (1975)
p >
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RHIC data from dAu collisions at 200 GeV per NN pair
Ratio of central to peripheral collisions:
RCP
RCPh (pT ) =
dNh
dpT
1NColl
central( )
dNh
dpT
1NColl
peripheral( )
PHENIX and STAR experiments found (2002)
RCPp (pT )>RCP
π (pT )
Can’t be explained by fragmentation.
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RCPp (pT )>RCP
π (pT )Anomaly # 2
STAR
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Anomaly #3 Azimuthal anisotropy
v2(p) > v2() at pT > 2.5
GeV/c
v2: coeff. of 2nd harmonic of distribution
PHENIX, PRL 91 (2003)
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Anomaly #4 Forward-backward asymmetry at intermed. pT
QuickTime™ and aTIFF (LZW) decompressor
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in d+Au collisions (STAR)B
/F
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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 hadrons at high pT, then
• backward has no broadening
• forward has more transverse broadening
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Rapidity dependence of RCP in d+Au
collisions BRAHMS PRL 93, 242303(2004)
RCP < 1 at
=3.2
Central more suppressed than peripheral collisions
Interpreted as possible signature of Color Glass Condensate.
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Anomaly #5 Jet structure
Hard parton jet { (p1) + (p2) + (p3) + ···· }
trigger particle associated particles
The distribution of the associated particles should be independent of the medium if fragmentation takes place in vacuum.
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Anomaly #5 Jet structure for Au+Au collisions is different from that for p+p collisions
pp
Fuqiang Wang (STAR) nucl-ex/0404010
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How can recombination solve all those puzzles?
Parton distribution (log scale)
p
p1+p2p q
(recombine) (fragment)
hadron momentum
higher yield heavy penalty
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The black box of fragmentation
q
A QCD process from quark to pion, not calculable in pQCD
z1
Momentum fraction z < 1
Phenomenological fragmentation function
D/q
z1
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Let’s look inside the black box of fragmentation.
q
fragmentation
z1
gluon radiation
quark pair creation
Although not calculable in pQCD (especially when Q2 gets low), gluon radiation and quark-pair creation and subsequent hadronization nevertheless take place to form pions and other hadrons.
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Description of fragmentation by recombination
known from data (e+e-, p, … )
known from recombination model
can be determined
hard partonmeson
fragmentationshower partons recombination
xD(x) =dx1x1
∫dx2
x2Fq,q (x1,x2)Rπ (x1,x2,x)
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Shower parton distributions
Fqq '(i )(x1,x2) =Si
q(x1)Siq ' x2
1−x1
⎛
⎝ ⎜ ⎞
⎠ ⎟
Sij =
K L Ls
L K Ls
L L Ks
G G Gs
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
u
gs
s
d
du
K =KNS+L
Ks =KNS +Ls
Sud,d ,u ,u(sea) =L
valence
sea
L L DSea
KNS L DV
G G DG L
Ls DKSea
G Gs DKG
R
RK
5 SPDs are determined from 5 FFs.
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Shower Parton Distributions
Hwa & CB Yang, PRC 70, 024904 (04)
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BKK fragmentation functions
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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.
The recombination of thermal partons with shower partons becomes conceptually unavoidable.
D(z)
h
qA A
Conventional approach
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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.
The recombination of thermal partons with shower partons becomes conceptually unavoidable.
hNow, a new component
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hard parton (u quark)
d
u
π+
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Inclusive distribution of pions in any direction
r p
pdNπ
dp=
dp1p1
∫dp2
p2Fqq (p1,p2)Rπ (p1, p2,p)
dNπ
pdp=
1p3 dp10
p∫ Fqq (p1,p−p1)
pTPion Distribution
p1p2
pδ(p1 +p2 −p)
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Pion formation: qq distribution
thermal
shower
soft component
soft semi-hard components
usual fragmentation
(by means of recombination)
T
SFqq =TT+TS+SS
Proton formation: uud distribution
Fuud =TTT +TTS +TSS +SSS
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T(p1)=p1dNq
th
dp1=Cp1exp(−p1/T)
Thermal distribution
Fit low-pT data to determine C & T.
Shower distribution in AuAu collisions
S(p2)=ξ∑i ∫dkkfi(k)Sij(p2 /k)
hard parton momentum
distribution of hard parton i in AuAu collisions
SPD of parton j in shower of hard parton i
fraction of hard partons that get out of medium to produce shower
calculable
Contains hydrodynamical properties, not included in our model.
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thermal
fragmentation
soft
hard
TS Pion distribution (log scale)
Transverse momentum
TT
SS
Now, we go to REAL DATA, and real theoretical results.
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production in AuAu central collision at 200 GeV
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Hwa & CB Yang, PRC70, 024905 (2004)
TS
fragmentation
thermal
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Proton production in AuAu collisions
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TTS+TSS
TSS
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Anomaly #1 Proton/pion ratio
resolved
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.All in recombination/ coalescence model
Compilation of Rp/ by R. Seto (UCR)
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d
d
central peripheral
more T more TS
less T less TS
RCPh (pT ) =
dNh
dpT
1NColl
central( )
dNh
dpT
1NColl
peripheral( ) ⇒
more TSless TS
>1
Anomaly #2 d+Au collisions (to study the Cronin Effect)
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d+Au collisions
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Pions
Hwa & CB Yang, PRL 93, 082302 (2004)
No pT broadening by multiple scattering in the initial state.Medium effect is due to thermal (soft)-shower
recombination in the final state.
soft-soft
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Proton
Thermal-shower recombination is negligible.
Hwa & Yang, PRC 70, 037901 (2004)
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Nuclear Modification Factor
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RCPp >RCP
πAnomaly #2
because 3q p, 2q
This is the most important result that validates parton recombination.
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Molnar and Voloshin, PRL 91, 092301 (2003).
Parton coalescence implies that v2(pT)
scales with the number of constituents
STAR data
Anomaly #3 Azimuthal anisotropy
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More interesting behavior found in large pT and large pL region.
It is natural for parton recombination to result in forward-backward asymmetry
Less soft partons in forward (d) direction than backward (Au) direction.
Less TS recombination in forward than in backward direction.
Anomaly #4 Forward-backward asymmetry
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Hwa, Yang, Fries, PRC 71, 024902 (2005)
Forward production in d+Au collisions
Underlying physics for hadron production is not changed from backward to forward rapidity.
BRAHMS data
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Jet Structure
Since TS recombination is more important in Au+Au than in p+p collisions,
we expect jets in Au+Au to be different from those in
p+p.
Consider dihadron correlation in the same jet on the near side.
Anomaly #5 Jet structure in Au+Au different from that in p+p
collisions
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Correlations
1. Correlation in jets: trigger, associated particle, background subtraction, etc.
2. Two-particle correlation with the two particles treated on equal footing.
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Correlation function
C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
ρ2(1,2)=dNπ1π2
p1dp1p2dp2
ρ1(1) =dNπ1
p1dp1
Normalized correlation function
K2(1,2) =C2(1,2)
ρ1(1)ρ1(2)=r2(1,2)−1 r2(1,2) =
ρ2(1,2)ρ1(1)ρ1(2)
In-between correlation function
G2(1,2)=C2(1,2)
ρ1(1)ρ1(2)[ ]1/ 2
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Correlation of partons in jets
A. Two shower partons in a jet in vacuum
Fixed hard parton momentum k (as in e+e- annihilation)
k
x1
x2
ρ1(1) =Sij(x1)
ρ2(1,2)= Sij(x1),Si
j'(x2
1−x1
)⎧ ⎨ ⎩
⎫ ⎬ ⎭
=12
Sij(x1)Si
j'(x2
1−x1
) +Sij (
x1
1−x2
)Sij'(x2)
⎧ ⎨ ⎩
⎫ ⎬ ⎭
r2(1,2) =ρ2(1,2)
ρ1(1)ρ1(2)
x1 +x2 ≤1
The two shower partons are correlated.
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no correlation
Hwa & Tan, nucl-th/0503052
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B. Two shower partons in a jet in HIC
Hard parton momentum k is not fixed.
ρ1(1) =Sj(q1) =ξ dkkfi∫
i∑ (k)Si
j(q/ k)
ρ2(1,2)=(SS)jj'(q1,q2) =ξ dkkfi∫
i∑ (k) Si
j(q1
k),Si
j'(q2
k−q1
)⎧ ⎨ ⎩
⎫ ⎬ ⎭
r2(1,2) =ρ2(1,2)
ρ1(1)ρ1(2)fi(k)
fi(k) fi(k)
fi(k) is small for 0-10%, smaller for 80-92%
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QuickTime™ and aTIFF (LZW) decompressor
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QuickTime™ and aTIFF (LZW) decompressor
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Hwa & Tan, nucl-th/0503052
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Correlation of pions in jets
Two-particle distribution
dNππ
p1dp1p2dp2=
1(p1p2)
2
dqi
qii∏
⎡
⎣ ⎢ ⎤
⎦ ⎥ ∫ 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
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Correlation function of produced pions in HIC
C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
ρ2(1,2)=dNπ1π2
p1dp1p2dp2
ρ1(1) =dNπ1
p1dp1
F4 =(TT+ST+SS)13(TT+ST+SS)24
Factorizable terms: (TT)13(TT)24 (ST)13(TT)24 (TT)13(ST)24
Do not contribute to C2(1,2)
Non-factorizable terms (ST+SS)13(ST+SS)24
correlated
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C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
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Hwa & Tan, nucl-th/0503052
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G2(1,2)=C2(1,2)
ρ1(1)ρ1(2)[ ]1/ 2
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along the diagonal
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa and Tan, nucl-th/0503052
RCPG2 (1,2) =
G2(0−10%)(1,2)
G2(80−92%)(1,2)
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Trigger at 4 < pT < 6 GeV/c
p+p: mainly SS fragmentation Au+Au: mainly TS
Associated particle
p1 (trigger)
p2 (associated)
kq1
q2
q3
q4
ξ∑i ∫dkkfi(k)S(q1)T(q3)R(q1,q3,p1) trigger
S(q2)T(q4)R(q2,q4,p2) associated
Correlation studied with triggers
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Correlation of pions in jets
Two-particle distribution
dNππ
p1dp1p2dp2=
1(p1p2)
2
dqi
qii∏
⎡
⎣ ⎢ ⎤
⎦ ⎥ ∫ F4(q1,q2,q3,q4)R(q1,q3,p1)R(q2,q4, p2)
F4 =(TT+ST+SS)13(TT+ST+SS)24
backgroundassociated particle
2<p2<4 GeV/c
must also involve S
trigger
4<p1<6 GeV/c
must involve S
q4
q2
k
q3
q
1
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STAR has measured: nucl-ex/0501016
Associated charged hadron distribution in pT
Background subtracted and distributions
Trigger 4 < pT < 6
GeV/c
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and distributions
P1
P2
pedestal
subtraction point no pedestal
short-range correlation?
long-range correlation?
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New issues to consider:
• Angular distribution (1D -> 3D)
shower partons in jet cone
• Thermal distribution enhanced due to
energy loss of hard parton
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Longitudinal
Transverse
t=0 later
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z
1
p1
trigger
Assoc p2kq2
z
hard parton
shower parton
ψ =θ −θ1
η−η1 =Δη
tanψ2
=g(η,η1)=e−η −e−η1
1+e−η−η1
=e−η1e−Δη −1
1+e−Δη−2η1
⎡
⎣ ⎢ ⎤
⎦ ⎥
Expt’l cut on trigger: -0.7 < 1 < +0.7k
jet cone exp[−ψ 2 /2σ 2(x)]
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Events without jets T(q) =Cqe−q/T
Thermal medium enhanced due to energy loss of hard parton
Events with jets
T'(q) =Cqe−q/T 'in the vicinity of the jet
T’- T = T > 0new parameter
Thermal partons
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For STST recombination
enhanced thermal
trigger associated particle
Sample with trigger particles and with background subtracted
Pedestal peak in &
F4
' =ξ dkkfi∫i
∑ (k)T'(q3){S(q1),S(q2)}T'(q4)e−ψ 2 /2σ 2 (q2 / k) |ψ =2tan−1 g(η,η1)
F4tr−bg =∑∫L (ST')13 (T'T' −TT)24 +(ST')13 (ST')24
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Pedestal in
P1,2 = dp2pmin(1,2)
4
∫dN(T'T'−TT)
dp2|trig
0.15 < p2 < 4 GeV/c, P1 = 0.4
2 < p2 < 4 GeV/c, P2 = 0.04
more reliable
P1
P2
less reliableparton dist
T'(q) =Cqe−q/T '
found T ’= 0.332 GeV/c
cf. T = 0.317 GeV/c
T ’ adjusted to fit pedestal
T = 15 MeV/c
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67Chiu & Hwa, nucl-th/0505014
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Chiu & Hwa, nucl-th/0505014
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We have not put in any (short- or long-range) correlation by hand.
The pedestal arises from the enhanced thermal medium.
The peaks in & arise from the recombination of enhanced thermal partons with the shower partons in jets with angular spread.
Correlation exists among the shower partons, since they belong to the same jet.
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Summary
Traditional classification by scattering
pT0 2 4 6 8 10
hardsoft
pQCD + FF
More meaningful classification by hadronization
pT0 2 4 6 8 10
hardsoft semi-hard
(low) (intermediate)
thermal-thermal thermal-shower
(high)shower-shower
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All anomalies at intermediate pT can be understood in terms of recombination of
thermal and shower partons
Recombination is the hadronization process ---- at all pT.
Parton recombination provides a framework to interpret the data on jet correlations.
There seems to be no evidence for any exotic correlation outside of shower-shower correlation in a jet.
Conclusion
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dNtrig−bg
p1dp1p2dp2=
ξ(p1p2)
3 dkkfi∫i∑ (k) dq1 dq2 ⋅∫∫
×
T'(p1 −q1)Sq1
k⎛ ⎝
⎞ ⎠
T'(q2)T'(p2 −q2)−T(q2)T(p2 −q2)[ ]
+T'(p1 −q1){Sq1
k⎛ ⎝
⎞ ⎠ ,S
q2
k−q1
⎛
⎝ ⎜ ⎞
⎠ ⎟ }T'(p2 −q2)J (ψ ,q2 / k)
⎧
⎨ ⎪
⎩ ⎪
⎫
⎬ ⎪
⎭ ⎪
1Ntrig
dNdΔη
=dη1 dp2p2 dp1p1
dNtrig−bg
p1dp1p2dp24
6
∫passocmin
4
∫−0.7
0.7
∫
dη1−0.7
0.7
∫ dp1p1dNtrig
p1dp14
6
∫
dNtrig
p1dp1=
ξp1
3 dkkfi∫i∑ (k) dq1∫ T'(p1 −q1)S
q1
k⎛ ⎝
⎞ ⎠
next slide
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kq2
z
hard parton
shower partonShower parton
angular distribution in jet cone
J (ψ ,q2 /k)=exp−(2tan−1g(η1 +Δη,η1))
2
2σ 2(q2 /k)
⎡
⎣ ⎢ ⎤
⎦ ⎥
Cone width
σ(x) =σ 0(1−x)
another parameter ~ 0.22
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Correlation without triggers
Correlation function
C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
ρ2(1,2)=dNπ1π2
p1dp1p2dp2
ρ1(1) =dNπ1
p1dp1
Normalized correlation function
G2(1,2)=C2(1,2)
ρ1(1)ρ1(2)[ ]1/ 2
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Physical reasons for the big dip:
(a) central: (ST)(ST) dominates
S-S correlation weakened by separate recombination with uncorrelated (T)(T)
(b) peripheral: (SS)(SS) dominates
SS correlation strengthened by double fragmentation
The dip occurs at low pT because at higher
pT power-law suppression of 1(1) 1(2)
results in C2(1,2) ~ 2(1,2) > 0
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Porter & Trainor, ISMD2004, APPB36, 353 (2005)
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( pp collisions )
G2
STAR
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QuickTime™ and aTIFF (LZW) decompressor
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