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Spectra of Identified Hadrons
in Pb-Pb collisions at LHC
Lilin Zhu
Sichuan University
Collaborated with
Rudolph C. Hwa
University of Oregon
Outline

Motivation

Physics ideas of the recombination model

Applications to Pb-Pb collisions

Summary & outlook
Lilin Zhu
CPOD2011, Wuhan
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Experimental data
Charged particles
Harder spectrum, flatter p
M.Floris, QM11, arXiv:1108.3257
ALICE, PLB696 (2011) 30-39
Lilin Zhu
CPOD2011, Wuhan
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Transverse momentum spectra
low
intermediate
2
hydro
high
pT
6
no rigorous
theoretical
framework
pQCD
That is where abundant experimental data exist.
At intermediate pT recombination model has been successful.
Lilin Zhu
CPOD2011, Wuhan
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Recombination model

Hadrons are formed by combining quarks.

Gluons are first converted to q and qbar before
hadronization.

Fragmentation is interpreted as a quark recombination
process.

The model is successful in explaining the particle
production at RHIC in central and forward directions.

LHC?
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CPOD2011, Wuhan
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Basic formulas
pT distributions of  and p
Recombination functions
Hwa, Phys. Rev.
D (1980).
Parton distributions
fragmentation
T : thermal parton
S : shower parton
= T T + T S + (SS) 1j + (SS) 2j
=T T T + T T S + T (SS)1j + (SSS)1j + T (SS)2j + ((SS)1jS)2j + (SSS)3j
For Soft
pT < 5 GeV/c,
need partons
to consider 1-jet contribution.
Thermalonly
and shower
components
Lilin Zhu
can also recombine
CPOD2011, Wuhan
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Parton distributions
Thermal partons:
Shower partons:
,
Lilin Zhu
CPOD2011, Wuhan

From k→q: Momentum
degradation in the
medium.

κ-1 is the momentum
fraction of a parton
retained after going
through the medium.
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πproduction in Pb-Pb collisions at 2.76 TeV
Hwa&Yang, PRC70,024905(2004)
Hwa&Zhu, 1109.6300
TT
TS
0-5
0-5
％％
0-5%
RHIC

Our calculation for pions is reliable above pT~1.5 GeV/c.

At LHC minijets are pervasive and their effects dominate the spectra
at the low and intermediate pT range.

TS is found to be more than TT at LHC for pT as low as 0.5, whereas
at RHIC the cross over is between 3 and 4. That is the new finding at
LHC.
Lilin Zhu
CPOD2011, Wuhan
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K/p/Λspectra (0-5% Central)
0-5％
0-5％
Hwa&Zhu, 1109.6300

T=0.38 for thermal partons is
slightly higher than 0.32 at RHIC.

κ=2.6 implies on average
roughly 1-κ-1=60% of the initial
parton energy is lost to the
medium.
Lilin Zhu
CPOD2011, Wuhan
0-5％
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p/π+ ratio
Gentle falloff
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CPOD2011, Wuhan
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Charged particle spectrum

Regard Λ as representative of Σ+.

At pT>5 GeV/c, we maybe have to consider the multi-jet contribution.
Lilin Zhu
CPOD2011, Wuhan
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Summary & outlook

First quantitative study for experimental data on the
spectra of identified hadrons at LHC and shows applicability
of the recombination model at LHC clearly.

Shower partons from minijets play the important role in
hadronization in the intermediate pT region.

Minijets are copiously produced, and are the non-flow
component whose effects cannot be ignored even at low pT.

Examine the centrality dependence in the intermediate
region.

Multi-minijets contribution to hadron spectra at high pT.

Two-particle correlation..
Lilin Zhu
CPOD2011, Wuhan
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Thank you!
Lilin Zhu
CPOD2011, Wuhan
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backup
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CPOD2011, Wuhan
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Shower parton
For all centralities
After averaging over all
creation points
parton distribution at the
surface
Momentum degradation
function
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CPOD2011, Wuhan
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Recombination model for fragmentation
dx1 dx2
xD(x)  
Fqq (x1, x 2 )R(x1 , x2 , x)
x1 x 2
Fragmentation function
known from fitting e+eannihilation data
S

V

G

S
K
G
K
Biennewies, Kniehl, Kramer
Kniehl, Kramer, Pötter
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Recombination function
known in the
recombination model
Hwa, Phys. Rev. D (1980).
Shower parton distributions
j
Si (x1 )
j  u,d,s,u ,d ,s
i  u,d,s,u ,d ,s, g
K, L, G, Ls, Gs
Hwa and Yang, PRC70,024904(2004)
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Parton shower
fragmentation
h
q
recombination
Initiating parton
(hard)
Lilin Zhu
Parton shower
(soft)
CPOD2011, Wuhan
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CPOD2011, Wuhan
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Determining RFs

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


Lilin Zhu
a=b=0
See Phys. Rev. C 66, 025204
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Recombination functions
Given by the valon distribution of the hadrons
R
 , K ,...
R
p , n ,...
( y1 , y2 )  y1 y2GQ1Q2 ( y1 , y2 )
( y1 , y2 , y3 )  y1 y2 y3GQ1Q2Q3 ( y1 , y2 , y3 )
GQ1Q2 ( y1 , y2 )  y y  ( y1  y2  1)
a b
1
2
GQ1Q2Q3 ( y1 , y2 , y3 )  y y y  ( y1  y2  y3  1)
a
b c
1 2 3
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CPOD2011, Wuhan
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Different implementations
 Duke group etc:
 6-dimensional phase space
 using Wigner function from density matrix
 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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CPOD2011, Wuhan
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