QGP Formation Signals and
Quark Recombination
Model
Chunbin Yang
Central China Normal
University Wuhan
Outline
Heavy ion collisions and QGP formation
 Anomalies at RHIC
 Physics ideas in the recombination model
 Fragmentation in the recombination model
 Applications to Au+Au collisions

NCQ scaling of flow v2
 Violation of the scaling

Particle species dependence of Cronin effect
 Discussions

C.B. Yang
Recombination Model
2
time
CYM & LGT
Initial conditions
and interactions
Hot and Dense
P C M & c lu s t. h a d ro n iza tio n
Cooling down
freezing out
NFD
N F D & h a d ro n ic T M
s trin g & h a d ro n ic T M
P C M & h a d ro n ic T M
C.B. Yang
Recombination Model
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QGP formation signals
Strangeness enhancement
 Suppression of J/Ψ
 Dilepton enhancement
Parton degree of QGP?
 Direct photon
QGP signal from the bulk?
…

Experimental probes:
1) Penetrating probes: “jets” energy loss
2) Bulk probes :Elliptic flow, radial flow
…
C.B. Yang
Recombination Model
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Evidence for the formation of QGP
Dihadron
Single hadron
Jet quenching
Energy loss of
jets in medium
Yang
NoC.B.suppression
for p spectrum
Recombination Model
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Hadron production mechanisms

Partons are produced in high energy
collisions like e++e-, e+p, p+p, p+A,A+A

Partons in the final stage of evolution are
converted into hadrons
HOW?
C.B. Yang
Recombination Model
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Traditional models
 String
formation and break for low p T
 Fragmentation for high p T
The string model may not be applicable
to heavy ion collisions
Fragmentation failed for central Au+Au
collisions
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Recombination Model
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Anomalies at intermediate pT
• B/M
p/ ≈1
• v2(pT)
v2(baryons) > v2(mesons)
•Jet structure
not the same as in pp
• Cronin effect
RCPp > RCP
Hard to be understood in traditional models
C.B. Yang
Recombination Model
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Hadronization by recombination
The colliding system generates quarks
and gluons in the phase space
 The quarks get dressed
 The dressed quarks recombine into
hadrons to the detector

C.B. Yang
Recombination Model
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Why Recombination?
meson momentum
Parton
distribution
(log scale)
p
p1+p2
p
q
(recombine) (fragment)
higher yield heavy penalty
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Recombination Model
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Features
 quark momenta add, higher yield for high
produced pT hadrons
soft parton density depends on medium
 more quarks for baryons than for mesons
 enhanced dependence on centrality for
baryons when thermal partons are involved
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Recombination Model
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No anomalies in recombination
 At intermediate pT, aplenty soft quarks are more
important for proton production than for pionsp/1
 For baryons, three quarks contribute to the flow,
while only two quarks for mesons  v2(baryons) >
v2(mesons), quark number scaling
 Soft and semi-soft recombination  Cronin effect
 Process dependence of soft partons different jet
structure in dA and AA
C.B. Yang
Recombination Model
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Recombination models
• Use just the lowest Fock state
i.e. valence quarks

qqqB
q qbarM
• Gluons converted to quarks first
• The probability for two (three) quarks to form
a meson (baryon) is given by a process
independent recombination function R
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Recombination Model
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Different implementations

Duke group etc:
 6-dimensional
phase space
 using Wigner function from density matrix

Oregon group:
 one-dimensional
momentum space
 using phenomenological recombination function
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Recombination Model
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Duke approach
E
dN M
3
d P
E
dN B
3
d P
  d

  d

P u
(2 )
3
P u
(2 )
w ( , p)  g e
3


 ,


 ,  ,
 p v ( ) / T

2

 dxw ( R, xP )w( R, x P )w( R, (1  x  x ) P ) |  B ( x, x ) |
 / 2 
2
e

 dxw ( R, xP )w( R, (1  x) P ) |  M ( x) |
2
'
'
'
f (  , )
Low
pT recombination
high pT fragmentation
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Recombination Model
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2
Texas/Ohio approach
Texas A&M/Budapest (Ko, Greco, Levai,
Chen)
Monte Carlo implementation (with spatial
overlap)
 Soft and hard partons
 Soft-hard coalescence allowed

Ohio State (Lin, Molnar)

ReCo as a solution to the opacity puzzle
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Recombination Model
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Basic formulas in Oregon approach
x
dN
p ,  ,...
dx
C.B. Yang


dx1 dx 2 dx 3
x1
x2
x3
F ( x1 , x 2 , x 3 ) R
p ,  ,...
x1 x 2 x 3
( ,
, )
x x x
Recombination Model
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Recombination functions
Given by the valon distribution of the hadrons
R
R
 , K ,...
p , n ,...
( y1 , y 2 )  y1 y 2 G Q1Q 2 ( y1 , y 2 )
( y1 , y 2 , y 3 )  y1 y 2 y 3 G Q1Q 2 Q3 ( y1 , y 2 , y 3 )
G Q1Q 2 ( y1 , y 2 )  y 1 y 2  ( y1  y 2  1)
a
b
G Q1Q 2 Q3 ( y1 , y 2 , y 3 )  y1 y 2 y 3  ( y1  y 2  y 3  1)
a
C.B. Yang
b
c
Recombination Model
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Determining R

R p was determined from CTEQ
 From


the parton distributions in proton
a=b=1.755, c=1.05 at Q2=1GeV2
R  was determined from Drell-Yan
processes
 a=b=0
 See
C.B. Yang
Phys. Rev. C 66, 025204
Recombination Model
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Fragmentation? Recombination?
Answer: NO FRAGMENTATION
only RECOMBINATION
Fragmentation is not a description of the
hadronization process.
It uses phenomenological functions D(z) that
give the probability of momentum fraction z of
a hadron in a parton jet
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Recombination Model
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Fragmentation
D(z)
A
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q
A
Recombination Model
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Parton shower
fragmentation
q
Initiating parton
(hard)
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h
recombination
Parton shower
(semi-hard)
Recombination Model
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Recombination for fragmentation
Recombination function
known in the
recombination model
Fragmentation function
known from fitting e+eannihilation data
S
V
G
S
G



K
K
BKK
KKP etc
C.B. Yang
Hwa, Phys. Rev. D (1980).
Shower parton distributions
j
S i ( x1 )
j  u, d, s ,u , d , s
i  u , d , s, u , d , s , g
K, L, G, Ls, Gs
Recombination Model
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Fitted results
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Recombination Model
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Shower parton distributions
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Recombination Model
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Application to Au+Au collisions
Thermalized low pT (soft) partons
 Hard partons (semi-hard) shower partons
 Three types of recombination for mesons

 thermal
parton & thermal parton
 thermal parton & shower parton
 shower parton & shower parton

Joint parton distribution is not factorizable
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Recombination Model
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Parton sources
Thermal parton distribution is assumed
dpT C exp(  pT / T )
Hard parton distributions fi(k) can
be calculated from
 pQCD
 nuclear shadowing
 nuclear geometry
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Recombination Model
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Parton sources
Single shower parton distribution is
 dkkf i ( k )
dp
p
j
Si ( p / k )
Joint two (three) shower parton distribution
can also be written down
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Recombination Model
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 Spectrum (0-10%)
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Recombination Model
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Nuclear modification RAA
dN
AA
p T dp T dyd 
R AA 
NC
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dN
pp
p T dp T dyd 
Recombination Model
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p spectrum
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Recombination Model
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p/
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Recombination Model
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Centrality dependence
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Recombination Model
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New physics
Thermal-thermal recombination makes p/
increase from very small value to about 1
at pT3GeV/c
 Thermal-shower recombination plays an
important role
 This recombination can be equivalently
regarded as modification of the
fragmentation functions

C.B. Yang
Recombination Model
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NCQ scaling
AMPT
model
results: by
For hadron
formation
Scaling
partonicpartons
dof
coalescenc
e ofincov2-:moving
dominant;
meson
quark
v2
( pT )  2  v 2
( pT 2 )
No scaling in quark
v2 : hadronic
baryon
v 2 dominant
( pT )  3  v 2
( pT 3)
dof
=>
A tool to search for the
possible phase boundary!
The
C.B. Yang
beam energy
dependence of the partonic
cross sections will not affect
the v2 scaling argument.
=>
Important for Beam Energy
Scan
program.Model 35
Recombination
NCQ scaling violation
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Recombination Model
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Why NCQ scaling ?
φdependence
joint distribution
collinear
Assumptions:
F(p1,p2)=F(p1)F(p2)
Validity of the assumptions?
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Recombination Model
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Why NCQ scaling violates?
Because of quark interactions, joint
distributions are not products of quark
distributions
 Recombined quarks not necessarily have
the same momentum
 Fluctuations: large n=1,3 terms appears in
quarks distributions. They contribute to v2
 NCQ at RHIC may be coincident

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Recombination Model
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Application to d+Au collisions
Basic formulas the same as for Au+Au
collisions
 Soft parton distribution the same form, T
not temperature but inverse slope
 No jet quenching
 Nuclear shadowing a little different from
that in Au+Au case

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Recombination Model
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Pion spectrum
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Centrality dependence
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Cronin effect
Enhancement of hadron spectrum in pA
collisions at high pT
Traditional explanation: initial interactions
Many soft collisions before the last hard
one, each gives a kT kick
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Recombination Model
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Cronin effect
(
RCP 
(
dN
)
C en tra l
N C pT d pT d y
dN
N C pT d pT d y
)
P erip h era l
Shadowing effect is cancelled partially
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Recombination Model
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Puzzles
If Cronin effect is really due to initial
interactions, dilepton spectrum should
show similar effect.
 Experimentally, the effect for dilepton is
very small, no definite conclusion
 Species dependence of the Cronin effect

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Recombination Model
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From recombination
Medium density depends on centrality
Medium effects are different in meson
and baryon production
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Recombination Model
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Proton spectrum
T different
for different
centralities
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Recombination Model
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RCP for proton
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Recombination Model
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RCP for p & 
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Discussions
QGP signal can be found from the bulk
 Hadronization of partons can be described
by ReCo for d+Au and Au+Au collisions
 ReCo naturally explains species
dependence, such as baryon enhancement,
v2 scaling...
 Cronin effect can be interpreted as from final
state interactions

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Discussions
Combination with other models, such as
hydrodynamics etc, is needed and under
development
 Recombination formulism from pQCD
How to calculate the joint distributions?

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