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Future Measurements to Test Recombination
Rudolph C. HwaUniversity of Oregon
Workshop on Future Prospects in QCD at High
Energy
BNL, July 20, 2006
2
Outline
• Introduction
• Recombination model
• Shower partons
• Hadron production at low pT
• Hadron production at large
• Hadron production at large pT
• Summary
1xF
pT
3
I. Introduction
What are the properties of recombination that we want to know and test?
What partons?
q1,q2
p0 dNπ
dp=
dq1q1∫
dq2q2
Fqq(q1,q2 )Rπ (q1,q2 , p)
Fqq (q1,q2 ) probability of finding partons at
Rπ (q1,q2 , p) probability for recombination to form a pion at pSame partons? What is that
probability?
4
Usual strong evidences for recombination
number of constituent quarks scaling
v2
partons CQ ↔
What about gluons?
Rp /π of order 1 or higher
impossible by fragmentation
Useful to remember in future measurements
5
dNππ
p1dp1p2dp2=
1(p1p2 )
2
dqi
qii∏⎡
⎣⎢
⎤
⎦⎥∫ F4 (q1,q2 ,q3,q4 )R(q1,q3, p1)R(q2 ,q4 , p2 )
Two-particle correlation
q1,q2 ,q3,q4
Where are the partons from? Are they independent? Are they from 1 jet, 2 jets, or thermal medium?
Quantitative questions about recombination eventually always become questions about the nature of partons that are to recombine.
6
Multiparton distributions in terms of the thermal and shower parton distributions
Fqq (q1,q2 )=TT +TS+ SS
Fuud (q1,q2 ,q3)=TTT +TTS+TSS+SSS
F4 (q1,q2 ,q3,q4 )=(TT +TS+SS)13(TT +TS+SS)24
7
II. Recombination ModelRecombination depends on the wave function of the hadron.
Constituent quark model describes the bound-state problem of a static hadron.
What good is it to help us to know about the distribution of partons in a hadron (proton)?
Valons
Valons are to the scattering problem what CQs are to the bound-state problem.
8
Deep inelastic scattering
ee
p
Fq
We need a model to relate to the wave function of the proton
Fq
Valon modelp
U
U
Dvalons
Hwa, PRD 22, 759 (1981)
9
p
U
U
D
Basic assumptions
• valon distribution is independent
of probe
• parton distribution in a valon is independent of the host hadron
xuv (x,Q2 )= dy2GUx
1
∫ (y)KNS(xy,Q2 )
xdv (x,Q2 )= dyGDx
1
∫ (y)KNS(xy,Q2 )
valence quark distr in proton
valon distr in proton, independent of Q
valance quark distribution in valon, whether in proton or in pion
10
Hwa & CB Yang, PRC66(2002) using CTEQ4LQ
11
Recombination function
It is the time-reversed process of the valon distributions
pU
U
D
proton Rp(x1,x2,x3,x) =x1x2x3
x3 GUUDp (
x1
x,x2
x,x3
x)=g(
x1x2
x2 )2.76(x3
x)2.05δ(
x1
x+
x2
x+
x3
x−1)
pion Rπ (x1,x2,x) =x1x2
x2 GUD π (
x1
x,x2
x)=
x1x2
x2 δ(x1
x+
x2
x−1)
From π initiated Drell-Yan process
xqvπ(x) =Ax0.64(1−x)1.11 valon
model Gπ (y1,y2) =δ(y1 +y2 −1)
pU
U
Drecombination function
valon distribution
12
In a pp or AA collision process
U
D_
π+
Is entropy reduced in recombination?
The number of degrees of freedom seems to be reduced.
Soft gluon radiation --- color mutation
without significant change in momentum
The number of degrees of freedom is not reduced.
13
How do gluons hadronize?
In a proton the parton distributions are
Gluons carry ~1/2 momentum of proton but cannot hadronize directly.
Sea quark dist. Fq ~ c (1-x)7
Saturated sea quark dist. F’q ~ c’
(1-x)7
Gluon conversion to q-qbarq
q
g
Recombination of with saturated sea gives pion distribution in agreement with data.
x2u(x)
x2g(x)
x [log]
14
III. Shower Partons from Fragmentation Functions
The black box of fragmentation
πq
A QCD process from quark to pion, not calculable in pQCD
z1
Momentum fraction z < 1
15
Description of fragmentation by recombination
known from data (e+e-, p, … )
can be determined
hard partonmeson
fragmentationshower partons recombination
xD(x) =dx1x1
∫dx2
x2Fq,q (x1,x2)Rπ (x1,x2,x)
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xDM (x)=dx1x1∫
dx2x2
Fq,q(x1,x2 )RM (x1,x2 ,x)
xDB (x)=dx1x1∫
dx2x2
dx3x3
Fqqq(x1,x2 ,x3)RB(x1,x2 ,x3,x)
Meson fragmentation function
Baryon fragmentation function
S(xi)
DGp DG
Λand can be calculated in the RM
17
DGM → DG
B Has never been done before in the 30 years of studying FF.
This is done in the RM with gluon conversion shower partons valons hadrons.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & CB Yang, PRC 73, 064904 (2006)
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IV. Hadron production at low pT
EdNπ
dpL
≡H(x) =dx1x1
∫dx2
x2
Fqq (x1,x2)Rπ (x1,x2,x)
.
p p
x
H(x)
First studied in pp collision.
Fu x1( )Fd x2( )Parton distributions at low Q2
Hwa, PRD (1980)
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Hadronic collisions Hwa & CB Yang, PRC 66, 025205
(2002) h + p h’ +X
h h’
p π π π
K+ ππ+ K
+_
Suggested future measurement
Better data at higher energy for p π, K, p, Y
FNAL PL=100 GeV/c (1982)
20
Leading and non-leading D production
π±+ p→ D±(m) + X
Leading (same valence quark)
non-leading (sea quark)
A =σ(leading)−σ(nonleading)σ(leading)+σ(nonleading)
Asymmetry
Hwa, PRD 51, 85
(1995)
Suggested future measurement:xdN
dx(p→ D±)
21
pA collisions
p + A→ h+ Xh bears the effect of momentum degradation --- “baryon stopping”.
NA49 has good data, but never published.
p + Pb→ (p−p) + X p + Pb→ (n−n) + X
(no target fragmentation, only projectile fragmentation)
Hwa & CB Yang, PRC 65, 034905 (2002)
Shape depends on degradation. Normalization not adjustable.Suggested future
measurement:Measure
dN
dx(p + A→ h±+ X)
Need to know well the momentum degradation effect.
for all x at higher energy
22
Transfragmentation Region (TFR)
A + A→ h+ X
Theoretically, can hadrons be produced at xF > 1?It seems to violate momentum conservation, pL > √s/2.
In pB collision the partons that recombine must satisfy
xii∑ <1
p
B
But in AB collision the partons can come from different nucleons
BA
xii∑ >1
(TFR)
In the recombination model the produced p and π can have smooth distributions across the xF = 1 boundary.
23
proton-to-pion ratio is very large. QuickTime™ and a
TIFF (LZW) decompressorare needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
proton
pion
Hwa & Yang, PRC 73,044913 (2006)
: momentum degradation factor
Regeneration of soft parton has not been considered.
Suggested future measurement
Determine the xF distribution in the TFR
Particles at xF>1 can be produced only by recombination.
24
V. Large BRAHMS data show that in d+Au collisions there is suppression at larger . QuickTime™ and a
TIFF (LZW) decompressorare needed to see this picture.
BRAHMS, PRL 93, 242303 (2004)
Hwa, Yang, Fries, PRC 71, 024902 (2005).
No change in physics from =0 to 3.2
In the RM the soft parton density decreases, as is increased (faster for more central coll).
Suggested future measurement
dN
dpTdpTfor π and p
25
BRAHMS, nucl-ex/0602018
AuAu collisions
26
TT
TS
TTT
xF = 0.9
xF = 0.8 TFR
xF = 1.0
?
27
No jet => no associated particles
pT distribution fitted well by recombination of thermal partons
Suggested future measurement
• Focus on xF>1 region.• Determine p/π ratio.• Look for associated particles
QuickTime™ and aTIFF (LZW) decompressor
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QuickTime™ and aTIFF (LZW) decompressor
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Hwa & Yang (2006)
28
VI. Hadron production at large pT, small pL
A. Cronin Effect
Cronin et al, Phys.Rev.D (1975)
α >1dN
dpT(pA→ hX) ∝ Aα , for h= both π and p
This is an exp’tal phenomenon. Not synonymous to initial-
state kT broadening.In the RM we have shown that final-state recombination alone (without initial-state broadening) is enough to account for CE.
We obtained it for both π and p -- impossible by fragmentation. Hwa & Yang, PRL 93, 082302 (2004); PRC 70, 037901 (2004).
Suggested future measurement
Measure and ratios in d+Au collisions at all , both backward and forward.
Λ / Kp /π
29
Backward-forward Asymmetry
If hadrons at high pT are due to initial transverse broadening of parton, then
• backward has no broadening
• forward has more transverse broadening
RM has B/F>1, since dN/d of soft partons decrease as increases.
Suggested future measurement
Measure p and π separately at larger range of , and for different centralities.
Expects more forward particles at high pT than backward particles
QuickTime™ and aTIFF (LZW) decompressor
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B
F
30
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)
Soft partons -- less in forward, more in backward
RM => less particles produced forward, more backward
31
B. p/π Ratio
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.All in recombination/ coalescence model
Success of the recombination model
Measure the ratio to higher pT
If it disagrees with prediction, it is not a breakdown of the RM. On the contrary the RM can be used to learn about the distributions of partons that recombine.
32
C. Strange particles
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642
Hwa & CB Yang, nucl-th/0602024
Data from STAR nucl-ex/0601042
This is not a breakdown of the RM. We have not taken into account the different hyperon channels in competition for the s quark in the shower.
40% lower
30% higher
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production
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130 GeV
production
smallmore suppressed
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We need to do more work to understand the upbending of .
It is significant to note that thermal partons can account for the ratio up to pT=4 GeV/c.
QGP: s quarks enhanced & are thermalized.
We have assumed RFs for & that may have to be modified.
35
If and are produced mainly by the recombination of thermal s quarks, then no jets are involved.
Select events with or in the 3<pT<5 region, and treat them as trigger particles. Look for associated particles in the 1<pT<3 region.
Predict: no associated particles giving rise to peaks in , near-side or away-side.
Suggested future measurement
Verify or falsify that prediction
36
2. Correlation of pions in jetsTwo-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
q1
q4
q2
C2(1,2)=ρ2(1,2)−ρ1(1)ρ1(2)
ρ2(1,2)=dNπ1π2
p1dp1p2dp2
ρ1(1) =dNπ1
p1dp1
QuickTime™ and aTIFF (LZW) decompressor
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This can be measured.
G2(1,2)=C2(1,2)
ρ1(1)ρ1(2)[ ]1/ 2
Hwa & Tan, PRC 72, 024908 (2005)
D. Jet Correlations1. Correlation of partons in jets is negative
but not directly measurable
37
3. D(zT)Trigger-normalized fragmentation
functionTrigger-normalized momentum fraction
zT =pT (assoc)pT (trig)
X.-N. Wang, Phys. Lett. B 595, 165 (2004) J. Adams et al., nucl-ex/0604018
STAR claims universal behavior in D(zT)
fragmentation
Focus on this region
violation of universal behavior due to medium effect ---- thermal-shower recombination
38
Suggested future measurement
Study zT ~ 0.5 with pT(trigger) ~ 8-10
GeV/c pT(assoc) ~ 4-5 GeV/c Measure p/π ratio of associated particles.
My guess: R(p/π) >> 0.1
if so, it can only be explained by recombination.
Do this for both near and away sides.
39
4. Three-particle correlation
Conical Flow vs Deflected Jets
Mediumaway
near
deflected jets
away
near
Medium
mach cone
Medium
away
near
di-jets
0
0π
π
Ulery’s talk at Hard Probes 06
40
Signal Strengths
Au+Au Central 0-12% Triggered
Δ1
Δ2
d+Au
Δ1
Δ2
• Evaluate signals by calculating average signals in the boxes.• Near Side, Away Side, Cone, and Deflected.
41
• What is the multiplicity distribution (above background) on the away side?
• If n=2 is much lower than n=1 events (on away side), then the Mach-cone type of events is not the
dominant feature on the away side.
• What is the p/π ratio (above background) on the away side?
• Evolution with higher trigger momentum should settle the question whether cone events are realistic.
• Whatever the mechanism is, hadronization would be by recombination for pT<6 GeV/c.
More studies are needed.
42
5. Using Factorial Moments to suppress statistical background event by event.
Factorial moment for 1 event
fq =1M
njj=1
M
∑ (nj −1)⋅⋅⋅(nj −q+1)
Normalized factorial moment
Fq = fq / f1q
Event averaged NFM Fq
(a) background only (b) bg + 1jet
(c) bg + 2jets
Try it out, but it is not a way to test recombination.
Chiu & Hwa, nucl-th/0605054
43
VII. Two-jet Recombinationπ and p production at high pT at LHCNew 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
π p
44
QuickTime™ and aTIFF (LZW) decompressor
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Proton-to-pion ratio at LHC -- probability of overlap of 2 jet cones
Hwa & Yang, PRL (to appear),
nucl-th/0603053
single jet
If (pT)~pT-7,
then we get
45
The particle detected has some associated partners.
There should be no observable jet structure distinguishable from the
background.
10 < pT < 20 GeV/c
That is very different from a super-high pT jet.
But they are part of the background of an ocean of hadrons from other jets.
A jet at 30-40 GeV/c would have lots of observable associated
particles.
46
We predict for 10<pT<20 Gev/c at LHC• Large p/π ratio
• NO associated particles above the
background
Suggested future measurement
Verify or falsify these two predictions
47
Summary
In general, all hadrons produced with pT<6 GeV/c are by recombination.
Specifically, many measurements have been suggested.
Good signatures: large Rp/π
in some regions no particles associated with high pT trigger.
After recombination is firmly established,the hadron spectra can be used to probe the
distributions of partons that recombine.
48
Backup slides
49
Let’s look inside the black box of fragmentation.
πq
fragmentation
z1
gluon radiation
quark pair creation
50
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 DπSea
KNS L DπV
G G DπG L
Ls DKSea
G Gs DKG
Rπ
RK
5 SPDs are determined from 5 FFs.
assume factorizable, but constrained kinematically.
No gluon column
51
Shower Parton Distributions
Hwa & CB Yang, PRC 70, 024904 (04)
52
D. Jet Correlations
1. 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)
r2(1,2) =ρ2(1,2)
ρ1(1)ρ1(2)x1 +x2 ≤1
ρ2 (1,2) = Sij (x1),Si
j '(x2
1− x1
)⎧⎨⎩
⎫⎬⎭
0
The two shower partons are correlated.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
C2 (1,2)=[r2 (1,2)−1]ρ1(1)ρ1(2)
no correlation
Hwa & Tan, PRC 72, 024908 (2005)
No way to measure this directly.
53
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%
QuickTime™ and aTIFF (LZW) decompressor
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Also, cannot be measured directly.