Quarkonium Production in Heavy Ion Collisions
Pengfei Zhuang
(Tsinghua University, Beijing)
● Quarkonium in Vacuum
● Cold and Hot Nuclear Matter Effects
● Transverse Momentum Distributions
● Summary
Wuhan School on High Energy Nuclear Physics,
November, 2011
1
Importance of Quarkonium in Studying QGP
How to probe QGP?
●electro-magnetic signals (leptons and photons)
●jets (fast partons)
●quarkonium
●heavy quarks are produced only in the initial impact, and no extra
production in the later evolution
a clean probe of QGP
●production via pQCD process
rather solid ground
2
Quarkonium in Vacuum
Potential Model in Vacuum
Schroedinger equation for heavy QQ system
 1

2
2





V
r


1
2
 2m
 (r1 , r )  E (r1 , r ),
c




r  r1  r2
radial equation n the rest frame of quarkonium
 1  1 d2

l (l  1) 

r


V
(
r
)



 
nl   Rnl ( r )  0

2
2
r

 mc  r dr

Cornell potential
c
V (r )     r
r
boundary condition
R(0)  , R()  0
three parameters
 c  0.29,   (0.18 GeV) 2 ,
by fitting the quarkonium masses
M 1  M J / ,
solution
M 2  M ' ,
M3
m c  1.84 GeV
M n  2mc   n
binding energy  nl and radial wave function Rnl (r )
r
J /
0.5 fm
4
Debye Screening in QGP
medium effects on QQ potential:
1) string tension  (T ) , in deconfinement phase  (T  Tc )
2) charge rearrangement
Debye screening
the charge density seen by
Coulomb potential 
c
c
becomes small
Yukawa potential 
r
Debye screening length D
Debye screening mass mD

6 1
,

2
g q eq T


D  
1
1
,

T
N
  Nc  f  g 2
  3
6 
0
c
r
e r / D
 1/ mD
Abelian approximation
pQCD with colored gluons
5
Estimation of Quarkonium Dissociation Temperature
2
 c  r / D
p
Hamiltonian of the QQ system at T > Tc: H 
 e
mc r
from uncertainty relation p
2
1/ r 2
 c  r / D
1

e
2
mc r
r
average energy
E
stability condition
dE
 0,
dr
 c (1  r / D )e r / D
2


0
3
2
mc r
r
constraint to the minimum
2
 D (T )
0.84 c mc
dissociation temperature
2
 D (TD )
0.84 c mc
with pQCD calculated D (T )
TD  209 MeV for J/
6
TD in Potential Model
Lattice calculated free energy F for a pair of QQ
slow dissociation
F ,
V
(
r
,
T
)

potential

U  F  TS , rapid dissociation
Schroedinger equation at finite T
average distance r (T )
binding energy  (T )
dissociation temperature:
r (TD )  ,  (TD )  0
for V=U (Satz et al)
T
sequential suppression
7
Cold and Hot Nuclear Matter Effects
Hot Nuclear Matter effects:
1)suppression in QGP and HG
2)regeneration in QGP and HG
Hot Nuclear Matter effects
Cold Nuclear Matter effects
screening only
Cold Nuclear Matter effects:
1)nuclear absorption
2)Cronin effect
3)shadowing effect
screening + regeneration
● initial production controls high pt region
●regeneration becomes important at low pt due to heavy quark energy loss
8
Nuclear Absorption in pA Collisions
Matsui and Satz, 1986:
J/ψ suppression as a probe of QGP in AA collisions
Nuclear Modification Factor:
J /
AA
J /
c pp

RAA 
N
 1, no medium effect

  <1, J / sup pression
>1, J / enhancement

However,
1) suppression is observed in pA collisions where QGP is not expected !
2) J/ψ and ψ’ have the same suppression !
theoretical explanation: nuclear absorption
energy dependence of nuclear absorption:
J/ formation time  f
c
0.5 fm
collision time  c  2 RA / c h yc
SPS
RHIC
LHC
 abs
  abs
  abs
9
Cronin Effect
Cronin effect:
gluons multi scattering with nucleons before they fuse into a cc pair.
transverse momentum broadening !
2
t
p
pA
 p
2
t
pp
2 gN
t
  gN p
0 L
10
Shadowing Effect
parton distribution function (PDF) in a nucleus is different from a
simple superposition (Glauber model) of the PDF in a free nucleon.
shadowing correction factor:
x: momentum fraction,
 F : transverse momentum
S abs
usual PDF
shadowing effect + nuclear absorption
can explain the pA data at RHIC energy.
11
Normal Suppression at SPS
NA38
mechanism: multi-scattering between J/psi and spectator nucleons
R.Vogt, Phys.Rept.310, 197(1999)
C.Gerschel, J.Hufner, Annu.Rev.Nucl.Part.Sci. 49, 225(1999)
 abs  6.5  1.0 mb
conclusion:
nuclear absorption can well explain the J/psi yield in pA and light
nuclear collisions at SPS energy !
12
Anomalous Suppression at SPS (1)
anomalous suppression in heavy ion collisions !
model 1: Debye screening (Matsui & Satz, 1986)
NA38
at T=0
at T≠ 0
charmonium dissociation temperature
(Karsch, Kharzeev, Satz, PLB637, 75(2006)
Asakawa & Hatsuda, 2004
Kaczmarek et al., hep-lat/0312015
13
Anomalous Suppression at SPS (2)
model 2: threshold model (Blaizot, Dinh, Ollitrault, PRL85, 4010(2000)
model 3: comover interaction
(Capella, Feireiro, Kaidalov, PRL85, 2080(2000)
dynamic processes:
J /  meson  D  D
geometric fluctuations
14
J/ψ Puzzles at RHIC
2 puzzles for J/Psi production at RHIC energy:
RAA (|y|<0.35) > RAA (1.2<|y|<2.2)
RAA (RHIC, |y|<0.35) ≈ RAA (SPS)
with the Debye screening theory, the suppression is controlled only by the
temperature, higher T
stronger suppression, it leads to
RAA (|y|<0.35) < RAA (1.2<|y|<2.2)
RAA (RHIC, |y|<0.35) < RAA (SPS)
how to explain the puzzles ?
15
Regeneration at RHIC (1)
there are about 10 pairs of c quarks in a central Au-Au collision at RHIC energy and more
than 100 pairs at LHC energy
very important J/\psi regeneration at high energies:
in QGP
c  c  J /  g
in hadron gas
mesons
the competition between J/\psi suppression and regeneration leads to the question:
J/\psi suppression or enhancement at high energies?
model 1: sudden production
(Andronic, PBM, Redlich, Stachel, NPA789, 334(2007):
J/\psi’s are statistically produced at T=Tc,
no initial production
suppression at RHIC,
no suppression at LHC !
16
Regeneration at RHIC (2)
model 2: continuous production in QGP (Thews, Mangano, PRC73, 014904(2006):
J/\psi’s are continuously produced in the whole QGP region
including anomalous suppression
no initial production
* perturbative calculation with nonrelativistic Coulomb potential (Peskin, Bhanot, NPB156, 365(1979)
* detailed balance
model 3: two-component model
(Grandchamp, Rapp, Brown, PRL92, 212301(2004):
initial production + sudden regeneration
the stronger regeneration at RHIC than
at SPS explains the first J/psi puzzle !
the stronger regeneration at central
rapidity that at forward rapidity explains
the second J/\psi puzzle !
17
Is Regeneration Necessary ?
heavy quark potential (Young, Shuryak, 2008):
V = U,
F=U-TS
Schroedinger equation:
J/psi dissociation temperature Td = 2.7 Tc > maximum T at RHIC.
there is no big difference between SPS and RHIC !
this explains why there is no big difference between the suppressions
at SPS and at RHIC.
regeneration looks not necessary !?
18
62 GeV

39 GeV

SQM2011 experimental summary by K.Safarik:
overall suppression of J/ψ is nearly identical
between SPS, RHIC & LHC !
Transverse Momentum Distribution
the transverse momentum distribution which depends more
directly on the production mechanism must contain additional
information about the nature of the medium and J/\psi and may
help to distinguish between different scenarios.
SPS
RHIC
LHC (model)
A Full Transport Approach for Quarkonia in HIC
Tsinghua Group, 2005-2011
● QGP hydrodynamics
+ equation of state (ideal gas or
strongly coupled matter from lattice)
●quarkonium transport equations (  J / ,  ', c )
α: suppression β: regeneration
● analytic solution
●initial production
f ( p, x , t0 ) , including CNM.
Dissociation Cross Section
J / ()  g  Q  Q
● gluon dissociation cross section described by OPE (Bhanot, Peskin,1999):
 ( p , pg )
● at finite temperature, we use the classical relation
 ( p , pg , T )
r 2 (T )
2
r (0)
 ( p , pg )
r 2 (T ) is calculated through the
Schroedinger equation
● dissociation rate of  at a fixed medium velocity v=0.5 and for V=U:
1)T-dependence of the
differential cross section is still
an open problem;
2) we did not consider quasifree processes which may play
an important role at high T<Td.
● regeneration rate is determined by the detailed balance
Transverse Momentum at SPS
J.Hufner and PZ, PLB2002,2003
no regeneration at SPS
very important leakage effect !
23
J/ψ RAA ( pt ) at RHIC
Y.Liu, Z.Qu, N.Xu, PZ, PLB2009
the competition between initial production and regeneration
leads to a minimum, a signature for the coexistence of both
production mechanisms.
 0  0.6 fm, T0  344 MeV ,
 ppJ /  0.74b,
 ccpp  0.12nb (PHENIX pp data) at mid rapidity
J/ψ Rapidity Dependence at RHIC
Y.Liu, N.Xu, PZ, JPG2010
less regeneration in forward rapidity explains the two puzzles naturally.
J /
 pp
 0.42b,
 ccpp  0.04nb at forward rapidity
J/ψ RAA ( Np ) at high pt at RHIC
STAR data, QM2011
high pt particles can survive in hot medium.
centrality dependence of J/ψ RAA ( pt ) at RHIC
STAR data, QM2011
more suppression in central collisions
J/ψ RAA ( Np ) at LHC
ALICE
PHENIX
more regeneration at LHC  RAA  RAA
 0  0.6 fm,
T0  430 MeV (Hirano, Heinz),
 ppJ /  2.33b (arXiv:1107.0137),
 ccpp  3.45nb (total, QM2011 talk by Dainese)
J/ψ RAA ( Np ) at high pt at LHC
ALICE
CMS
more regeneration at low pt  RAA  RAA
 0  0.6 fm,
T0  484 MeV (Hirano, Heinz),
J /
d pp
/ dy  3.5 b (arXiv:1107.0137)
Averaged Transverse Momentum
SPS:
Cronin effect
RHIC:
competition
between the two
sources
LHC:
dominant
regeneration
J/psi elliptic flow at RHIC
our prediction:
L.Yan, N.Xu, PZ, PRL2006
impact parameter b=7.8 fm
STAR data, QM2011
almost no J/psi V2 at RHIC !
J/psi elliptic flow at LHC
K.Zhou, N.Xu, PZ, NPA2010
our prediction at \sqrt s = 5.5 TeV and b=7.8 fm :
remarkable v2 at LHC !
Υ, a Cleaner Probe at RHIC
J/ψ :
the production and suppression mechanisms are
complicated: there are primordial production and
nuclear absorption in the initial state and regeneration
and anomalous suppression during the evolution of
the hot medium.
Υ:
1) the regeneration can be safely neglected;
2) there is almost no feed-down forΥ ;
3) weaker CNM effect
Υat RHIC: RAA( Np )
Y.Liu, B.Chen, N.Xu, PZ,PLB2011
for minimum bias events:
PHENIX dada: RAA<0.64 (NPA2009)
our result: RAA = 0.63 for V=U
RAA= 0.53 for V=F
●from the comparison with data, V is close to U.
Υat LHC: RAA( Np )

 pp
 14b,
 bb
pp  43nb
●again, V is close to U.
History
theory
1986,Matsui and Satz:
J/ψ suppression as a probe of QGP
experiment
1989, pA and light nuclear collisions at SPS:
J/ψ normal suppression
2 puzzles: suppression already in pA, and the
same suppression for J/ψ and ψ’.
nuclear absorption
1996, Pb-Pb at Elab=200 A GeV at SPS:
J/ψ anomalous suppression
Debye screening in QGP,
hadrom gas model,
cold nuclear matter effect, ……
2006, Au-Au at s  200 A GeV at RHIC
2 puzzles: RAA (|y|<0.35) > RAA (1.2<|y|<2.2)
regeneration
RAA (RHIC, |y|<0.35) ≈ RAA (SPS)
2010, Pb-Pb at LHC
RHIC! RHIC! and LHC! LHC! LHC!
New data mean new surprises !
36
many other open questions
● medium effect on charm quark and charmonium
strongly coupled QGP, chiral symmetry restoration, critical behavior,
mass, width, binding energy,......
● charm quark potential
between free energy F=U-TS and internal energy
different dissociation temperature (from Schroedinger equation)
● cold nuclear matter effect (parton distribution)
● charm quark production in QGP
● ......
37
Dependence on EoS
J/Psi Pt distribution at LHC where EoS plays an essential role!
wQGP
sQGP
Only Cold Nuclear Matter Effect ?
Υat RHIC: RAA( pt )
Liu, Chen, Xu, Zhuang: arXiv:1009.2585,PLB2011
central Au+Au at √s=200 GeV
● strong Cronin effect
Υat RHIC:
pt2 ( N p )
relation between ϒ at RHIC and J/ψ at SPS:
● no ϒ regeneration at RHIC and no J/ψ regeneration at SPS
no ϒ(1s) suppression at RHIC
TD (1s )  4Tc  TRHIC
●
no J/ψ suppression at SPS
TDJ /  2Tc  TSPS
both are controlled by the Cronin effect !
 pt2  pt2
2 RHIC
t 
 p

AA
 pt2
RHIC
agN
RAu
a
SPS
gN
RPb
pp
 agN L
2 SPS
t J /
 p
2 SPS
t J /
 2.4 p
Au+Au at √s=200 GeV
Liu, Chen, Xu, Zhuang: arXiv:1009.2585,PLB2011
Measuring RHIC Temperature by Excited ϒ States
initial temperature dependence of RAA
central Au+Au at √s=200 GeV
Liu, Chen, Xu, Zhuang: arXiv:1009.2585,PLB2011
suppression of excited ϒ states is sensitive to the fireball temperature !
Υat LHC: RAA( pt )
high pt is controlled by initial production !
Conclusions:
● pt dependence is more sensitive to the production and
suppression mechanism.
● regeneration is important at RHIC and LHC.
● competition between initial production and regeneration
can explain systematically the data from SPS to LHC.
● Upsilon production at RHIC and LHC supports V=U.
Uncertainty analysis:
pp collision, shadowing effect, EoS, time scales, ……
Suggestions:
● measure D-Dbar correlation at LHC (Zhu, Bleicher, Huang,
Schweda, Stoecker, Xu, Zhuang, PLB2007, Zhu, Xu, Zhuang, PRL2008)
● measure J/psi-D correlation at LHC (since both are from the
same source )
● measure quarkonium v2 at LHC (which is very sensitive to the
production and suppression mechanisms ).
45
Charmonium in pp Collisions
pp ' X
 


B
(

'


 )
observation: J / , '    ,
1.5%
pp J / X
 

 B( J /    )
difficult to observe ψ’ !
Ψ’ and χc decay into J/ψ:


P (  c  J /   ) 30%
Ψ’
χc
P ( '  J /  2 ) 10%
direct production
J/ψ
mechanisms for quarkonium production in pp:
60%
it is difficult to describe quarkonium formation due to confinement problem
1) color evaporation model:
color evaporation
gg  colored cc  
 J /
2) color-singlet model:
gg  cc J /  g
3) color-octet model:
  gg  cc 
n
X

n
n: quantum numbers of color, angular momentum and spin
46
near side
DD correlation at LHC
Zhu, Xu, Zhuang, PRL100, 152301(2008)
* c quark motion in QGP:
for strongly interacting quark-gluon plasma:
we take drag coefficient to
be a parameter charactering
the coupling strength
* QGP evolution:
ideal hydrodynamics
● at RHIC, the back-to-back correlation is washed out.
● at LHC, c quarks are fast thermalized, the strong
flow push the D and Dbar to the near side!
large drag parameter is confirmed by R_AA and v_2 of
non-photonic electrons (PHENEX, 2007; Moore and Teaney,
2005; Horowitz, Gyulassy, 2007).
ATHIC III at Wuhan,
October, 2010
47