recombination in nuclear collisions
DESCRIPTION
Recombination in Nuclear Collisions. Rudolph C. Hwa University of Oregon. Critical Examination of RHIC Paradigms University of Texas at Austin April 14-17, 2010. Outline. 1. Introduction Earlier evidences for recombination Recent development A. Azimuthal dependence --- ridges - PowerPoint PPT PresentationTRANSCRIPT
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Recombination in Nuclear Collisions
Rudolph C. HwaUniversity of Oregon
Critical Examination of RHIC Paradigms
University of Texas at Austin
April 14-17, 2010
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Outline
1. Introduction
2. Earlier evidences for recombination
3. Recent development
A. Azimuthal dependence --- ridges
B. High pT jets --- scaling behavior
4. Future possibilities and common ground
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1. Introduction
pQCDReCoHydro
Fragmentation
kT > pT
Hadronization
Cooper-Frye
k1+k2=pT
lower ki higher density
TT TS SS
low highintermediate
2 6
Usual domains in pT
pT
GeV/c
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Regions in time
(fm/c)
1 8
hadronization
0.6rapid thermalization
hydro
Cronin effect: --- initial-state transverse broadening
What about Cronin effect for proton, larger than for ?
Early-time physics: CGC, P violation, …
Pay nearly no attention to hadronization at late times.
In ReCo: Final-state effect, not hard-scattering+Frag, not hydro.
What about semihard scattering (kT<3GeV/c) at <0.6 fm/c?
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2. Earlier evidences for Recombination
A. pT distribution at mid-rapidity
Recombination function
R (k1,k2 , pT ) =k1k2
pT2
δ(k1 +k2
pT
−1)
q and qbar momenta, k1, k2, add to give pion pT
It doesn’t work with transverse rapidity yt
TT F(ki ) =Cki exp(−ki /T )dN
pTdpT
=C2
6exp(−pT /T )
TTTdN p
pT dpT
=NppT
2
mT
exp(−pT /T ) same T for partons, , p
empirical evidence
At low pT
phase space factor in RF for proton formation
Pion at y=0 p0 dN
dpT
=dk1
k1∫
dk2
k2
Fqq(k1,k2 )R (k1,k2 , pT )
Proton at y=0
p0 dN p
dpT
=dk1
k1∫
dk2
k2
dk3
k3
Fuud(k1,k2 ,k3)Rp(k1,k2 ,k3, pT )
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PHENIX, PRC 69, 034909 (04)
went on to mT plot
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Hwa-Zhu (preliminary)
dN p
pT dpT
=NppT
2
mT
exp(−pT /T )
Proton production from reco
Same T for , K, p --- a direct consequence of ReCo.
Slight dependence on centrality --- to revisit later
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B. p/ ratio
At higher pT shower partons enter the problem; TS recombination enters first for pion, and lowers the ratio.
It is hard to get large p/ ratio from fragmentation of hard partons.
Rp / (pT ) =dNp / pTdpT
dN / pTdpT
dominated by thermal partons at low pT
= pT2
mT (pT )
ReCo
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C. Revisit very early formulation of recombination
[at the suggestion of organizers: Hwa, PRD22,1593(1980)]
The notion of valon needs to be introduced.
q
q
For p+pp+X we need
Rp (x1, x2 , x3, x)uud
p
Consider the time-reversed processu
ud
p puu
d
p+p+X Feynman x distribution at low pT
xdN
dx=
dx1
x1∫
dx2
x2
Fqq(x1,x2 )R (x1,x2 ,x)
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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
A valence quark carries its own cloud of gluons and sea quarks --- valon
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p
U
U
D
Basic assumptions
• valon distribution is independent
of probe
• parton distribution in a valon is independent of the 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
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Rp (x1, x2 , x3, x) =g(x1x2
x2 )2.76 (x3
x)2.05δ(
x1
x+
x2
x+
x3
x−1)
R (x1,x2 ,x) =x1x2
x2 δ(x1
x+
x2
x−1) initiated
DY process
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p + p h + X in multiparticle production at low pT
p
U
U
Dvalon distribution collisio
n process
partons
chiral-symmetry breaking quarks gain masses momenta persist
U
D
RF
+
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No adjustable parameters
1979 data (Fermilab E118)
Not sure whether anyone has done any better
Feynman’s original parton model PRL(69)
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D. Shower partons in AA collisions
At higher pT Hard scattering calculable in pQCD Hadronization by fragmentation
In between hard scattering and fragmentation is jet quenching.
Fine, at very high pT (> 6GeV/c), but not reliable at intermediate pT
pT
qD
i (
pT
q)
T(q1)S(q2/q)R(q1,q2,pT)
Fragmentation: D(z) => SS recombination, but there can also be TS
recombination at lower pT
dNTS+SS
pTdpT
=1pT
2
dqq
Fi∫ (q)[TS∂i∑ (q, pT ) + SS∂ (q, pT )]pio
n
proton [TTS∑ +TSS∑ + SSS∑ ]
We need shower parton distribution.
∫dk k fi(k) G(k,q)
k
q
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Description of fragmentation
known from data (e+e-, p, … )
known from recombination model
can be determined
recombination
xD(x) =dx1x1
∫dx2
x2Fq,q (x1,x2)Rπ (x1,x2,x)
shower partons
hard partonmeson
fragmentation
by recombination
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Shower parton distributionsFqq '
(i )(x1,x2) =Siq(x1)Si
q ' x2
1−x1
⎛
⎝ ⎜ ⎞
⎠ ⎟
Sij =
K L Ls
L K Ls
L L Ks
G G Gs
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
u
gs
s
d
du
L L DSea
KNS L DV
GG DG
L Ls DKSea
G Gs DKG
5 SPDs are determined from 5 FFs.
assume factorizable, but constrained kinematically.
Hwa & CB Yang, PRC 70, 024904 (04)
BKK FF(mesons)Using SSS we can calculate baryon FF
DM ⇔ DB
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Hwa-Yang, PRC 73, 064904 (06)
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Other topics:
1. Constituent quarks, valons, chiral-symmetry breaking, f
2. Collinear recombination
3. Entropy
4. Hadronization of gluons
5. Dominance of TS over TT at pT>3 GeV/c
6. Single-particle distributions
7. RCPp(pT)> RCP
(pT)
8. Forward-backward asymmetry in dAu collisions
9. Large p/ ratio at large
10. v2 (pT) Quark-number scaling
11. Ridges
12. Correlations
earlier
later
recent
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3. Recent developmentAzimuthal dependence
PHENIX 0903.4886
85<<90
30<<45
0<<15
pT
Npart
A. pT < 2 GeV/c
B. pT > 2 GeV/c
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A. pT<2 GeV/c
Region where hydro claims relevance --- requires rapid thermalization
0 = 0.6 fm/c
Something else happens even more rapidly
Semi-hard scattering 1<kT<3 GeV/c
Copiously produced, but not reliably calculated in pQCD t < 0.1 fm/c
1. If they occur deep in the interior, they get absorbed and become a part of the bulk.
2. If they occur near the surface, they can get out. --- and they are pervasive.
[Tom Trainor’s minijets (?)]
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On the way out of the medium, energy loss enhances the thermal partons --- but only locally.
Recombination of enhanced thermal partons ridge particles
ρ1(pT ,φ,b) = B(pT ,b) + R(pT ,φ,b)
Base, independent of , not hydro bulk
Ridge, dependent on , hadrons formed by TT reco
• Ridge can be associated with a hard parton, which can give a high pT trigger.• But a ridge can also be associated with a semihard parton, and a trigger is not necessary; then, the ridge can be a major component of
ρ1(pT ,φ,b)
Correlated part of two-particle distribution on the near side
ρ2corr (1,2) = ρ2
J (1,2) + ρ2R (1,2)
Putschketrigger
assoc part
JET RIDGE
How are these two ridges related?
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BOOM
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Hard parton
Ridge
without trigger
but that is a rare occurrence
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Semihard partons, lots of them in each event
Ridges without triggers --- contribute significantly to single-particle distribution
ratatatatatata
We need an analogy
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1
2
1
2
Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2
R(φ2 ) ∝ dφ1∫ ρ2R(φ1,φ2 )
Ridge is present whether or not 1 leads to a trigger.
Semihard partons drive the azimuthal asymmetry with a dependence that can be calculated from geometry. Hwa-Zhu, 0909.1542, PRC (2010)
If events are selected by trigger (e.g. Putschke QM06, Feng
QM08), the ridge yield is integrated over all associated particles 2.
Y R (φ1) ∝ dφ2∫ ρ2R(φ1,φ2 )
Enhanced thermal partons on average move mainly in the direction normal to the surface
~|2-1|<~0.33 Correlated emission model
(CEM) Chiu-Hwa, PRC 79 (09)
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Geometrical consideration in Ridgeology
For every hadron normal to the surface there is a limited line segment on the surface around 2
through which the semihard parton 1 can be emitted.
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b normalized to RA
Ridge due to enhanced thermal partons near the surface
R(pT,,b) S(,b)nuclear density
S(,b) 2
Base
ρ1(pT ,φ,b) = B(pT ,b) + R(pT ,φ,b)
Ridge
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base
ridge
inclusive
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ridge
inclusive
RH-L.Zhu (preliminary)
ρ1 (pT ,φ,b) = B(pT ,b) + R(pT ,φ,b) = N(pT ,b)[e− pT /T0 + e− pT /T1 (b)aD(b)S(φ,b)]
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Single-particle distribution at low pT without elliptic flow, but with Ridge
T0 for base
T1(b) for ridge
a can be determined from v2, since S(,b) is the only place that has dependence.
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ridge bas
e
Azimuthal dependence of ρ1(pT,,b) comes entirely from Ridge ---
In hydro, anisotropic pressure gradient drives the asymmetry
x
y
requiring no rapid thermalization, no pressure gradients.
Since there more semihard partons emerging at ~0 than at ~/2, we get in ReCo anisotropic R(pT,,b),
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∝ S(φ1,b)
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Hwa-Zhu, PRC (10)
Y R (φ1) ∝ dφ2∫ ρ2R(φ1,φ2 )
Ridge yield’s dependence on trigger
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Feng QM08
φs ⇒ φ1
Normalization adjusted to fit, since yield depends on exp’tal cuts
Normalization is not readjusted.
s dependence is calculated
S(,b) correctly describes the dependence of correlation
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Nuclear modification factor
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art
Summary
dependencies in
Ridge R(pT,,b) v2(pT,b)=<cos 2 > yield YR() RAA(pT,,b)
are all inter-related --- for pT<2 GeV/c
Hwa-Zhu, 0909.1542 PRC (2010)
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B. pT>2 GeV/cPHENIX 0903.4886
Need some organizational simplification. and b are obviously related by geometry.
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Scaling behavior in --- a dynamical path length
5 centralities and 6 azimuthal angles () in one universal curve for each pTLines are results of calculation in Reco.
Hwa-Yang, PRC 81, 024908 (2010)
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Complications to take into account:
• details in geometry
• dynamical effect of medium
• hadronization
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Nuclear medium that hard parton traverses
x0,y0
k
Dynamical path length
=γl (x0 , y0 ,φ,b) γ to be determined
Geometrical path length
l (x0 , y0 ,φ,b) = dtD[x(t),y(t)]
0
t1 (x0 ,y0 ,φ,b)
∫D(x(t),y(t))
Geometrical considerations
Average dynamical path length
(φ,b) = γ dx0dy0∫ l (x0 , y0 ,φ,b)Q(x0 , y0 ,b)
Q(x0 , y0 ,b) =TA(x0 ,y0 ,−b / 2)TB(x0 ,y0 ,b / 2)
d2rsTA(rs+
rb / 2)TB(
rs−
rb / 2)∫
Probability of hard parton creation at x0,y0
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Define
P(,φ,b) = dx0 dy0Q(x0 ,y0∫ ,b)δ[ −γl (x0 ,y0 ,b)] (φ,b) = dξξP(∫ ξ ,φ,b)
KNO scaling
P(,φ,b) =ψ (z) (φ,b)
z = / dzψ (z) =1∫dzzψ (z) =1∫
For every pair of and c:
• we can calculate
• PHENIX data gives
(φ,c)
RAA (φ,c)
We can plot the exp’tal data
RAA ( )
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There exist a scaling behavior in the data when plotted in terms of
(φ,c)
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Theoretical calculation in the recombination model Hwa-Yang, PRC 81, 024908 (2010) ( γ = 0.11 )
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ρ1
TS +SS (pT ,φ,b) =dq
q∫ Fii
∑ (q,φ,b)H i (q, pT )
b
q
TS+SS recombination
G(k,q,) =qδ(q−ke− )
degradation
hadronization
dNihard
kdkdyy=0
= fi (k)
Fi (q,) = dkkfi∫ (k)G(k,q,)
k probability of hard parton creation with momentum k
geometrical factors due to medium
dNTS
pTdpT
=1pT
2
dqq∫
i∑ Fi (q)TS∂ (q, pT )
TS∂ (q, pT ) =
dq2
q2∫ Si
j (q2
q) dq1∫ Ce−q1 /T R (q1,q2 , pT )
dNSS
pTdpT
=1pT
2
dqq∫
i∑ Fi (q)SS∂ (q, pT )
xDi (x) =
dx1
x1∫
dx2
x2
Sij (x1),Si
j '(x2
1−x1
)⎧⎨⎩
⎫⎬⎭R (x1,x2 ,x)
x =pT / q
Nuclear modification factor
RAA (pT ,φ,c) =
dNAA / dpTdφ
NcolldNpp / dpT
only adjustable parameter γ = 0.11
=γl (x0 , y0 ,φ,b)
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4. Future Possibilities
At kT not too large, adjacent jets can be so close that shower partons from two parallel jets can recombine.
H ii '(q,q ', pT ) =1pT
2
dq1
q1∫
dq2
q2
Sij (
q1
q)Si '
j '(q2
q')R
Γ (q1,q2 , pT )
≅ΓRπ (q1,q2 , pT )
Γ - probability for overlap of two shower partons
ρAA2 j ∝ Ncoll
2
RAA2 j (pT ,φ,c) =
ρAA2 j (pT ,φ,c)
Ncollρpp1 j (pT ,c)
At LHC, the densities of hard partons is high.
A. Two-jet recombination at LHC
Two hard partons
dNAA2 j
pT dpT dφ=
dqq∫
dq'q'
Fi (qii '∑ ,φ,b)Fi '(q',φ,b)Hii '(q,q', pT )
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Scaling
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Scaling badly broken
Hwa-Yang, PRC 81, 024908 (2010)
2jet
Pion production at LHC
Observation of large RAA at pT~10 GeV/c will be a clear signature of 2-jet recombination.
>1 !
Proton production due to qqq reco is even higher.
Hwa-Yang, PRL 97 (06)
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B. Back-to-back dijets
C. Forward production of p and
D. Large correlation
E. Auto-correlation
F. P violation: hadronization of chirality-flipped quarks
G. CGC: hadronization problem
Common ground with the 2-component model of UW-UTA alliance
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B. Two-component model
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T.Trainor, 0710.4504, IJMPE17,1499(08)
Hwa-Yang, PRC70,024905(04)
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Similar to our Base, B ~ exp(-pT/T0), T0 independent of b
minijets
Strong enhancement of hard component at small yt
Similar to our Ridge, R ~ exp(-pT/T1), T1 depends on b
ρAA
npart / 2= SNN (yt ) + ν H AA (yt ,ν )
SNN(yt) is independent of
Ridge due to semihard partons --- minijets?
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Comparison
Recombination 2-component
semihard partons minijets
recombination of enhanced fragmentation thermal partons
Ridges --- TT reco effect of jet on medium low-yt enhancement
Jets --- TS+SS effect of medium on jet high-yt suppressionρ1 = B + R + J ρ1 = S + H
no dependence on depend on b and
B+R accounts for v2 at pT<2GeV/c some quadrupole component without hydro without hydro ρ(η Δ ,φΔ )
ρ ref
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In Recombination
averaged over B(pT) R(pT,b)ρ
1
h (pT ,b) = N h (pT ,b)[e− pT /T0 + A(b)e− pT /T1 ]
QuickTime™ and a decompressor
are needed to see this picture.
In 2D autocorrelation
UW-UTA alliance
dependence
ρ(η Δ ,φΔ )
ρ ref
R(pT ,φ,b)=N(pT ,b)e−pT /T1 (b)aD(b)S(φ,b)
![Page 39: Recombination in Nuclear Collisions](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b88550346895d8fa651/html5/thumbnails/39.jpg)
QuickTime™ and a decompressor
are needed to see this picture.QuickTime™ and a
decompressorare needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
Scaling in variable that depends on initial-state collision parameters only
ρρref
=Δρnf
ρ ref
(η Δ ,φΔ ) + 2Δρ[m]
ρ refm=1
2
∑ cos(mφΔ )
No hydro
Trainor, Kettler, Ray, Daugherity
minijet contribution
φΔ ηΔ
from the hard comp 2<yt<4
I would like to know how it depends on at each b
QuickTime™ and a decompressor
are needed to see this picture.
cf. our ridge component
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Conclusion
We should seek common grounds as well as recognize differences.
• Has common ground with minijets.
At pT<2GeV/c, ridges due to semihard scattering and TT reco account for various aspects of the data.At pT>2GeV/c, hard scattering and TS+SS reco account for the scaling behavior observed.
• Recombination can accommodate fragmentation.
• Has thermal distribution at late times, though not thermalization and hydro expansion at early times.