J/ψ production and elliptic flow in relativistic heavy-ion collisions Taesoo Song (Texas A&M Univ.,...
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Transcript of J/ψ production and elliptic flow in relativistic heavy-ion collisions Taesoo Song (Texas A&M Univ.,...
J/ψ production and elliptic flow in relativistic heavy-ion
collisions
Taesoo Song(Texas A&M Univ., USA)
Reference : T. Song, C. M. Ko, S. H. Lee and J. Xu, arXiv:1008.2730
Contents
1. Introduction2. Schematic model for fireball
expansion3. Thermal properties of charmonia 4. Charmonia in heavy-ion collisions5. Results6. Summary
1. introduction
QCD phase diagram
• Long time ago, J/ψ suppression was suggested by Matsui and Satz as a signature of QGP formation in heavy-ion collisions. (due to color screening between c and anti-c)
• The suppression was observed at SPS & RHIC.• LQCD suggests the dissociation temperature
of J/ψ higher than Tc.• J/ψ is still one of the promising diagnostic
probes for hot nuclear matter created by heavy-ion collisions.
J/ψ suppression
Phenomenological models
1. Statistical model (P. Braun-Munzinger)Low dissociation temperature of J/ψ Most J/ψ in heavy-on collisions are
regenerated ones.
2. Two-component model (R. Rapp)High dissociation temperature of J/ψ Some of J/ψ come from regeneration, some
of them come from initial production.
NJ/ψ vs. Npart
statistical model two-component model
NJ/ψ vs. Pt
statistical model two-component model
Questions
• How can both models successfully describe experimental data?
• How can both models be discriminated?
2. Schematic model for expanding fireball
• Initial condition• Equation of state (EoS)• modeling
2. 1. Glauber model
function. thickness; ),()(
ondistributiSaxon - Woods; e1
(r) where
),( ),( )(
collisionsbinary ofNumber 2.
)(1 1 )(
)(1 1 )()(
tsparticipan ofNumber 1.
,,
/)r-(r0
2
2
2
0
dxxbbT
zsbzszsdzddbN
sdsTsbTB
sdsbTsTAbN
BABA
C
BAincoll
AinAB
B
inBApart
b
s b-s
2. 2. Initial condition
GeV 200 at 11.0
GeV 130 at 09.0
2)1(
NN
NN
collpart
ppch
BAch
sx
sx
xNN
xd
dN
d
dN
Charged particle multiplicities PRC65, 061901 (2002) dAdNndAdNn
xnn
xV
Ss
collcollpartpart
collpart
00 / ,/ where
,2
)1(3.30
be toassumed is
stage initialin density entropy Local
EoS of QGP• Quasiparticle picture
Strongly interacting massless partons
Noninteracting massive partons to reproduce thermal quantities extracted from LQCD
05.1/ ,170 ,3
, 14.18
18),,(
,),,(ln)211(
48)( where
, 3
)( ,
632
)(
2)/(5.0
2
22
222
222
ccf
c
cTTc
cfc
qfc
g
TMeVTN
T
T
T
eTTF
TTFNNTg
TTgm
NNTTgm
C
P. Levai & U. Heinz PRC 57, 1879
(1998)
EoS of HG
• Resonance gas model 1. all mesons of masses lighter than
1.5 GeV & all baryons of masses lighter than 2.0 GeV are considered in HG phase.
2. They are assumed to have constant masses and to be noninteracting.
Energy density and pressure
0.15 0.20 0.25 0.30 0.350
4
8
12
16
e/T4
p/T4
e/T
4 , p/T
4
T (GeV)
)(
1
1
23
1)(
)(
12
)(
/22
23
/
223
22
22
TBepm
ppdTp
TB
e
pmpdT
Tpm
Tpm
Isothermal lines on transverse plane at τ0=0.6 fm/c
Temperature profiles at various impact parameters
2. 3. fireball expansion
• Radial acceleration in central collision
24.1
2
36.0mass inertia :
~area lcylindrica :
out-freezeat pressure :
)(
part
f
fr
NM
RA
pM
Appa
Parameterized to fit
experimental data <pt> of π, K, p at freeze-out
0 5 10 15 200.1
0.2
0.3
0.4
T (
GeV
)
t (fm/c)
0.2
0.4
0.6
0.8
v T (
c)
Assuming isentropic expansion, s(τ)=s0*v0/V(τ)
• Radial acceleration in non-central collision
3
2
3
22/1
2
2
2
2 sincos)()v( ,
sincos)(
shape, ellipticin expanding Fireball
2.2z , ,1
1
y
y
x
x
yx
xy
xyry
rx
R
v
R
vR
RRR
RR
RRzaa
zaa
Parameter to fit
experimental data v2 of π, K, p at freeze-out
0 2 4 6 8 10 12
4
6
8
10
Ry
Rx
Mixed
HGQGP
Rx,
Ry
(fm
)
(fm/c)
0.2
0.4
0.6
vy
v x, v
y (c
) vx
0.1
0.2
0.3
T (
GeV
)b=9 fm,
Blast wave model
TT
TpT
p
TT
TTT
T
T
TTT
T
pdyddN
pd
pdyddN
pd
v
dydpdN
dp
dydpdN
pdp
p
v
T
mK
T
pIrdrd
m
dydp
dN
22
22
2
22
22
1
1022
2cos
2cos
.tanh where
cosh
sinh
2
formula, Frye-Cooper usingby
0 100 200 300 4000
200
400
600
800
1000
pions kaons protons
<p T
> (
MeV
/c)
Npart
0 1 2 3 4
0
10
20
30
pT (GeV/c)
v 2 (%
)
0
10
20
30
pions kaons protons
baryonfor 3 meson,for 2
14.1 ,/exp
gmultiplyinafter (bottom)1
n
GeVcncpT
3. Thermal properties of charmonia
• Dissociation temperatures • Dissociation cross section in QGP and
in HG
3. 1. wavefunctions & binding energies & radii of charmonia at
finite T
Modified Cornell potentialF. Karsch, M.T. Mehr, H. Satz, Z phys. C. 37, 617 (1988)
σ=0.192 GeV2 : string tension
α=0.471 : Coulomb-like potential constant
μ(T) =√(Nc/3+Nf/6) gT : screening mass in pQCD
In the limit μ(T)→0,
rTrT er
eT
TrV )()(1)(
),(
rrTrV
),(
Ψ’(2S)χc (1P)
GeVGeV
J/ψ (1S)
Screening mass
289 MeV298 MeV306 MeV315 MeV323 MeV332 MeV340 MeV
GeV
Binding energies & radii of charmonia
Screening mass (MeV)
Bin
ding
ene
rgy
(GeV
)
Screening mass (MeV)
Rad
ius
(fm
)
3. 2. dissociation cross section
• Bethe-Salpeter amplitudeDefinition ;
Solution in NR limit ;
Leading Order (LO)
quark-induced Next to Leading Order (qNLO)
gluon-induced Next to Leading Order (gNLO)
Leading Order (LO)
quark-induced Next to Leading Order (qNLO)
gluon-induced Next to Leading Order (gNLO)
In QGP
σdiss= ∑j σ jpQCD
1. partons with thermal mass
2. temperature-dependent wavefunctions from modified Cornell potential are used.
In hadronic matterFactorization formula:
σdiss(p)= ∑ j ∫dx σ ipQCD (xp)Dj i(x)
Dj i(x) is PDF of parton i in hadron j interacting with charmonia
1. Massless partons
mass factorization, loop diagrams and renormalization remove collinear, infrared and UV divergence respectively
2. Coulomb wavefunctions are used.
4. Charmonia in heavy-ion collisions
• Cronin effect• Nuclear absorption (nuclear
destruction)• Thermal decay and leakage effect• Regeneration
Two-component model
Initial production of J/ψ through binary N-N collisions
Thermalization (QGP formation)≈ 0.6 fm/c
HadronizationT≈ 170 MeV
Regenerated J/ψ Thermal decay
in hadronic matter
Thermal decay in QGP
Nuclear absorption
detector
Kinetic freeze-outT≈ 120 MeV
Thermal decay in hadronic matter
Cronin effect
Beforecc production
4. 1. Cronin effect
1. Charmonia are produced mainly through g+g fusion
2. Different from in p+p collision, gluon in A+B collision can get additional Pt through g+N collision
3. It broadens Pt distribution of gluons
4. Subsequently, it broadens Pt distribution of J/ ψ in A+B collision, compared with in p+p collision
ABggN
gN
tpp
Jt
AB
Jt LP
PP
2
/
2
/
2
Primordial J/ψ is produced
Nucleus A
Nucleus B
4. 2. Nuclear destruction
'
2
),()1(exp
),()1(exp
)',(),(')(
1),(
z
nucBBB
z
nucAAA
BAAB
nucnuc
zsbdzB
zsdzA
zsbzsdzsdzdbT
bS
Primordial J/ψ is produced
Nucleus A
Nucleus B
Nuclear destruction cross
section is obtained from pA
collisionσdiss=1.5mb
4. 3. Thermal decay
J/ψ
QGP phase
Mixed phase(Assuming 1st order phase transition)
HG phase
J/ψ
J/ψ
Thermal decay widths in QGP & HG
phaseHG in )()(
phase mixedin )(*)1()(*)(
phase QGPin )()(
J/ ofsection crosson dissociati :
J/ and jbetween velocity relative :
J/ ngdissociatihardon or parton ofdensity :
)()(),()2( 3
3
HG
HGQGP
QGP
diss
rel
j
dissreljj
j
ff
v
n
TTvTnkd
g
Ψ’(2S)χc (1P)
J/ψ (1S)
The leakage effect
Thermal decay width =0
Thermal decay width ≠0
Thermal decay width : Γ→Γ*θ[R(τ)-r(τ)]
Considering feed-down from χc , Ψ’ to J/ψ, '/ 08.025.067.0
HGQGPHGQGPJ
HGQGPHGQGP SSSS c
')'(exp0
dS HGQGP
Survival probability from thermal decay
4. 4. Regeneration
• From Glauber model (dσccNN/dy=63.7(μb) from
pQCD),
• From Statistical model,
• Discrepancy between them is corrected with fugacity
• GCE is converted to CE because of small # of pairs
),(),()( 2BBBAAA
NNcc
ABcc zsbdzzsdzsdABbN
VnnN ChiddenopenABcc C
2
1
VnVnN ChiddenCopenABcc 2
2
1
VnVnI
VnIVnN hidden
open
openopen
ABcc C
2
C 0
C 1C ) (
) (
2
1
Canonical suppression
Relaxation factor for kinetic equilibrium
ionhadronizatat time the:
iparton by
charm-charm/anti ofsection cross scattering elastic :
iparton ofdensity number :
)/(1 timerelaxation where,
exp10 .
H
i
i
reli
iirelax
relax
n
vn
dR
H
the number of regenerated J/ψ
NJ/ψrec=
VRγ2 {nJ/ψSJ/ψHG +Br(χc)*nχc *Sχc
HG + Br(ψ’) *nψ’* Sψ’HG }
• nJ/ψ, nχc , nψ’ : number densities of charmonia
• SJ/ψHG, Sχc
HG , Sψ’HG : survival rate of charmonia in HG
• Br(χc), Br(ψ’) : branching ratios of χc, ψ’ to J/ψ• R : relaxation factor• γ : fugacity
5. Results
• RAA vs. Npart
• RAA vs. pT
• <pT>
• V2
• Higher-order corrections in pQCD
5. 1. RAA of J/ψ
enhenced. is J/ 1, R
.suppressed is J/ 1, R
1
factoron modificatiNuclear
AA
AA
/
//
Jnn
JAA
coll
JAA N
N
NR
From RHIC near midrapidty at √sNN=200
GeV
RAA of J/ψ as a function of Npart
(near midrapidity in Au+Au collision at √s=200
GeV)
Regeneration
The role of coupling constant g in our model
1. ‘g’ determines dissociation temperatures of charmonia
(screening mass μ=√(Nc/3+Nf/6) gT) TJ/ψ=386 MeV, Tχc =199 MeV, TΨ’=185 MeV with
g=1.5
2. ‘g’ determines the thermal widths of charmonia (Г∼g2 in LO, and Г∼g4 in NLO)
3. ‘g’ determines the relaxation factor of charm quarks
W/O initial dissociation of J/ψ
without
RAA of J/ψ as a Function of pt
(For J/ψ, Tf=160 MeV)
<Pt2> of J/ψ
v2 of J/ψ (b=9 fm)
<Assumption>1. Elastic cross section
of J/ψ(color singlet) in QGP is much smaller than that of charm quark.
2. For J/ψ, inelastic collision is more effective than elastic collision in QGP because of its small binding energy and large radius at high T.
RAA of J/ψ as a function of Npart
(near midrapidity in Cu+Cu collision at √s=200 GeV)
Regeneration
Applying to Pb+Pb collision at √sNN=5.5 TeV (LHC) with the modified
parameters• by extrapolation,
Entropy dS/dη= 30.3{(1-x)Npart/2+xNcoll}
to 78.5{(1-x)Npart/2+xNcoll}, where x=0.11
J/ψ production cross section per rapidity in p+p collision
dσJ/ψpp/dy= 0.774 μb to 6.4 μb
• from pQCD,
cc production cross section per rapidity in p+p collision
dσccpp/dy= 63.7 μb to 639 μb
Ref. is NPA 789, 334 (2007)
7.36 μb at 7 TeV (Nov. 2010)
RAA of J/ψ as a function of Npart
(near midrapidity in Pb+Pb collision at √s=5.5 TeV)
Regeneration
5. 2. Higher-order corrections
• Dissociation cross section of charmonia σ [J/ψ+q(g)→c+c+q(g)] *A ; enhances decay of charmonia
• Elastic cross section of charm quarks σ [c+q(g)→c+q(g)] *B ; enhances regeneration of charmonia
Fractions of regenerated J/ψ
=(A,B)
RAA of J/ψ as a function of Npart
(near midrapidity in Au+Au collision at √s=200
GeV)
RAA of J/ψ as a Function of pt
<Pt2> of J/ψ
v2 of J/ψ (b=9 fm)
5. Summary
Summary of nuclear modification of charmonia in heavy-ion collision
• Before production; Cronin effect (pt↑)• After production; nuclear destruction (NJ/ψ↓) ; initial dissociation (NJ/ψ↓)• After thermalization; thermal decay (NJ/ψ↓); leakage effect (NJ/ψ↑, pt↑); regeneration (NJ/ψ↑); flow effect (pt↑)
Summary of results
• We reproduced successfully RAA of J/ψ in Au+Au and Cu+Cu collisions at RHIC and estimated RAA in Pb+Pb collision at LHC by using 2-component model.
• There seems to be a kink in RAA vs. Npart curve in Au+Au collision. → initial temperature begins to be over TJ/ψ?
• 2-component model vs. statistical model The number of J/ψ : the excessive number of J/ψ in 2-component
model is reduced by multiplying relaxation factor to regenerated J/ψ.
pt of J/ψ : In 2-component model, Cronin effect mainly enhances pt while in the statistical model, flow effect mainly enhances.
→ both models successfully describe RAA and pt of J/ψ in RHIC.
• Only v2 of J/ψ seems to be able to discriminate two models. → Precise measurement of v2 of J/ψ will reveal the fraction of
regenerated J/ψ