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![Page 1: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/1.jpg)
Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision
Xingbo Zhaowith Ralf Rapp
Department of Physics and Astronomy
Iowa State University Ames, USA
Brookhaven National Lab, Upton, NY, Jun. 14th 2011
![Page 2: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/2.jpg)
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Outline
Thermal rate-equation approach• Dissociation rate in quasi-free approximation• Regeneration rate from detailed balance• Connection with lattice QCD
Numerical results compared to exp. data• Collision energy dependence (SPS->RHIC->LHC)• Transverse momentum dependence (RHIC)• Rapidity dependence (RHIC)
![Page 3: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/3.jpg)
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Motivation: Probe for Deconfinement• Charmonium (Ψ): a probe for deconfinement– Color-Debye screening reduces binding energy -> Ψ dissolve
• Reduced yield expected in AA collisions relative to superposition of individual NN collisions
• Other factors may also suppress Ψ yield in AA collision- Quantitative calculation is needed
[Matsui and Satz. ‘86]
![Page 4: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/4.jpg)
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Motivation: Eq. Properties Heavy-Ion Coll.
• Equilibrium properties obtained from lattice QCD– free energy between two static quarks ( heavy quark
potential)– Ψ current-current correlator ( spectral function)
• Kinetic approach needed to translate static Ψ eq. properties into production in the dynamically evolving hot and dense medium
?
?
![Page 5: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/5.jpg)
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Picture of Ψ production in Heavy-Ion Coll.
• 3 stages: 1->2->31. Initial production in hard collisions2. Pre-equilibrium stage (CNM effects)3. Thermalized medium
• 2 processes in thermal medium:1. Dissociation by screening & collision 2. Regeneration from coalescence
• Fireball life is too short for equilibration - Kinetic approach needed for off-equilibrium system
J/ψ D
D-
J/ψc-c
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Thermal Rate-Equation• Thermal rate-equation is employed to describe
production in thermal medium (stage 3)
– Loss term for dissociation Gain term for regeneration– Γ: dissociation rate Nψ
eq: eq. limit of Ψ– Detailed balance is satisfied by sharing common Γ in the
loss and gain term– Main microscopic inputs: Γ and Nψ
eq
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
![Page 8: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/8.jpg)
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
![Page 9: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/9.jpg)
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In-medium Dissociation Mechanisms
[Bhanot and Peskin ‘79][Grandchamp and Rapp ‘01]
• Gluo-dissociation is not applicable for reduced εBΨ<T
quasifree diss. becomes dominant suppression mechanism
- strong coupling αs~ 0.3 is a parameter of the approach
• Dissociation cross section σiΨ
- gluo-dissociation: quasifree dissociation:
g+Ψ→c+ g(q)+Ψ→c+ +g(q)
VS.
• Dissociation rate:
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
![Page 11: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/11.jpg)
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Charmonium In-Medium Binding•
• Potential model employed to evaluate
• V(r)=U(r) vs. F(r)? (F=U-TS)
• 2 “extreme” cases:
• V=U: strong binding
• V=F: weak binding
[Cabrera et al. ’07, Riek et al. ‘10]
[Riek et al. ‘10]
[Petreczky et al ‘10]
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T and p Dependence of Quasifree Rate
• Gluo-dissociation is inefficient even in the strong binding scenario (V=U)• Quasifree rate increases with both temperature and ψ momentum• Dependence on both is more pronounced in the strong binding scenario
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
![Page 14: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/14.jpg)
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
![Page 15: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/15.jpg)
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Model Spectral Functions• Model spectral function = resonance + continuum
• At finite temperature:
• Z(T) reflects medium induced change of resonance strength
Tdiss=2.0Tc V=U
Tdiss=1.25Tc V=FZ(Tdiss)=0
• In vacuum:
• Z(T) is constrained from matching lQCD correlator ratio
width ΓΨ
threshold 2mc*
pole mass mΨ
• Regeneration is possible only if T<Tdiss
quasifree diss. rate
TdissTdiss
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Correlators and Spectral Functions
• Peak structure in spectral function dissolves at Tdiss • Model correlator ratios are compatible with lQCD results
weak binding strong binding
[Petreczky et al. ‘07]
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
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Regeneration: Inverse Dissociation
• For thermal c spectra, NΨeq follows from statistical model
- charm quarks distributed over open charm and Ψ states according to their mass and degeneracy
- masses for open charm and Ψ are from potential model
• Realistic off-kinetic-eq. c spectra lead to weaker regeneration:
[Braun-Munzinger et al. ’00, Gorenstein et al. ‘01]
• Gain term dictated by detailed balance:
• Charm relaxation time τceq is our second parameter: τc
eq~3/6fm/c
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
1. shadowing2. nuclear
absorption3. Cronin
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Kinetic equations
lQCD potential
diss. & reg. rate: Γ
Initial conditions Experimental observables
lQCD correlator
Link between Lattice QCD and Exp. Data
Ψ eq. limit: NΨeq
εBΨ mΨ, mc
1. Coll. energy dep.2. Pt dep.3. Rapidity dep.
1. shadowing2. nuclear
absorption3. Cronin
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Compare to data from SPS NA50 weak binding (V=F) strong binding (V=U)
incl
. J/p
si y
ield
• Different composition for different scenarios
• Primordial production dominates in strong binding scenario
• Significant regeneration in weak binding scenario
• Large uncertainty on σcc
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J/Ψ yield at RHIC weak binding (V=F) strong binding (V=U)
• Larger primordial (regeneration) component in V=U (V=F)
• Compared to SPS regeneration takes larger fraction in both scenarios
• Formation time effect and B meson feeddown are included
incl
. J/p
si y
ield
See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07]
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J/Ψ yield at LHC (w/o Shadowing) weak binding (V=F) strong binding (V=U)
• Parameter free prediction – both αs and τceq fixed at SPS and RHIC
• Regeneration component dominates except for peripheral collisions
• RAA<1 for central collisions (with , )
• Comparable total yield for V=F and V=U
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With Shadowing Included
• Shadowing suppresses both primordial production and regeneration• Regeneration dominant in central collisions even with shadowing• Nearly flat centrality dep. due to interplay between prim. and reg.
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Compare to Statistical Model weak binding (V=F) strong binding (V=U)
• Regeneration is lower than statistical limit:- statistical limit in QGP phase is more relevant for ψ regeneration
- statistical limit in QGP is smaller than in hadronic phase
- charm quark kinetic off-eq. reduces ψ regeneration
- J/ψ is chemically off-equilibrium with cc (small reaction rate)
![Page 26: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/26.jpg)
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High pt Ψ at LHC
• Negligible regeneration for pt > 6.5 GeV• Strong suppression for prompt J/Ψ• Significant yield from B feeddown• Similar yields and composition between V=U and V=F
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Pt Dependence at RHIC Mid-Rapidity
see also [Y.Liu et al. ‘09]
V=UV=U
• Primordial production dominant at pt>5GeV• Regeneration concentrated at low pt due to c quark thermalization• Formation time effect and B feeddown increase high pt production [Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88]
![Page 28: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/28.jpg)
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RAA(pT) at RHIC Mid-RapidityV=FV=F
• At low pt regeneration component is larger than V=U
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J/ψ v2(pT) at RHIC
• Small v2(pT) for entire pT range
- At low pt v2 from thermal coalescence is small
- At high pt regeneration component is gone
• Even smaller v2 even in V=F
- Small v2 does not exclude coalescence component
strong binding (V=U) weak binding (V=F)
![Page 30: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/30.jpg)
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J/Ψ Yield at RHIC Forward Rapidity weak binding (V=F) strong binding (V=U)
• Hot medium induced suppression and reg. comparable to mid-y
• Stronger CNM induced suppression leads to smaller RAA than mid-y
• Larger uncertainty on CNM effects at forward-y
incl
. J/p
si y
ield
See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07]
![Page 31: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/31.jpg)
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RAA(pT) at RHIC Forward RapidityV=UV=U
• Shadowing pronounced at low pt & fade away at high pt
• Large uncertainty on CNM effects
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RAA(pT) at RHIC Forward RapidityV=FV=F
• At low pt reg. component is larger than V=U (similar to mid-y)
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Summary and Outlook• A thermal rate-equation approach is employed to describe
charmonium production in heavy-ion collisions• Dissociation and regeneration rates are compatible with lattice QCD
results • J/ψ inclusive yield consistent with experimental data from collision
energy over more than two orders of magnitude• Primordial production (regenration) dominant at SPS (LHC)• RAA<1 at LHC (despite dominance of regeneration) due to incomplete
thermalization (unless the charm cross section is really large)
• Calculate Ψ regeneration from realistic time-dependent charm phase space distribution from e.g., Langevin simulations
![Page 34: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/34.jpg)
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Thank you!
based on X. Zhao and R. Rapp Phys. Lett. B 664, 253 (2008)
X. Zhao and R. Rapp Phys. Rev. C 82, 064905 (2010)
X. Zhao and R. Rapp Nucl. Phys. A 859, 114 (2011)
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Compare to data from SPS NA50 weak binding (V=F) strong binding (V=U)
incl
. J/p
si y
ield
tran
s. m
omen
tum
• primordial production dominates in strong binding scenario
![Page 36: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/36.jpg)
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J/ψ v2(pT) at RHIC
• Small v2(pT) for entire pT range
strong binding (V=U)
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Explicit Calculation of Regeneration Rate
• in previous treatment, regeneration rate was evaluated using detailed balance
• was evaluated using statistical model assuming thermal charm quark distribution
• thermal charm quark distribution is not realistic even at RHIC ( )
• need to calculate regeneration rate explicitly from non-thermal charm distribution
[van Hees et al. ’08, Riek et al. ‘10]
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3-to-2 to 2-to-2 Reduction
• reduction of transition matrix according to detailed balance
2 2
gcc g gc gcM M ( )2c
pp
dissociation: regeneration:
• g(q)+Ψ c+c+g(q)diss.
reg.
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Thermal vs. pQCD Charm Spectra
• regeneration from two types of charm spectra are evaluated:
1) thermal spectra: 2 2( ) exp /c cf p m p T
2) pQCD spectra:
22
( )1 /
c
p Af p
p B
[van Hees ‘05]
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Reg. Rates from Different c Spectra
• thermal : pQCD : pQCD+thermal = 1 : 0.28 : 0.47
• introducing c and angular correlation decrease reg. for high pt Ψ
• strongest reg. from thermal spectra (larger phase space overlap)
See also, [Greco et al. ’03, Yan et al ‘06]
![Page 41: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/41.jpg)
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Ψ Regeneration from Different c Spectra
• strongest regeneration from thermal charm spectra
• c angular correlation lead to small reg. and low <pt2>
• pQCD spectra lead to larger <pt2> of regenerated Ψ
• blastwave overestimates <pt2> from thermal charm spectra
![Page 42: Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State.](https://reader035.fdocuments.in/reader035/viewer/2022070400/56649f125503460f94c253c0/html5/thumbnails/42.jpg)
4242
V=F V=U
• larger fraction for reg.Ψ in weak binding scenario• strong binding tends to reproduce <pt
2> data
J/Ψ yield and <pt2> at RHIC forward y
incl
. J/p
si y
ield
tran
s. m
omen
tum
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4343
J/Ψ suppression at forward vs mid-y
• comparable hot medium effects• stronger suppression at forward rapidity due to CNM effects
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RAA(pT) at RHIC
• Primordial component dominates at high pt (>5GeV)
• Significant regeneration component at low pt
• Formation time effect and B-feeddown enhance high pt J/Ψ
• See also [Y.Liu et al. ‘09]
V=F V=U
[Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88]
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4545
J/Ψ Abundance vs. Time at RHIC V=F V=U
• Dissoc. and Reg. mostly occur at QGP and mix phase
• “Dip” structure for the weak binding scenario
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4646
J/Ψ Abundance vs. Time at LHC V=F V=U
• regeneration is below statistical equilibrium limit
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Ψ Reg. in Canonical Ensemble
• Integer charm pair produced in each event
• c and anti-c simultaneously produced in each event,c c c cf f f f
• c and anti-c correlation volume effect further increases local c (anti-c) density
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Ψ Reg. in Canonical Ensemble
• Larger regeneration in canonical ensemble
• Canonical ensemble effect is more pronounced for non-central collisions
• Correlation volume effect further increases Ψ regeneration
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Fireball Evolution• , {vz,at,az} “consistent” with: - final light-hadron flow - hydro-dynamical evolution
• isentropical expansion with constant Stot (matched to Nch) and
s/nB (inferred from hadro-chemistry)• EoS: ideal massive parton gas in QGP, resonance gas in HG
2 2 20 0
1 1( ) ( ) ( )
2 2FB z zV z v a r a
[X.Zhao+R.Rapp ‘08]
( )( )tot
FB
Ss T
V
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Primordial and Regeneration Components • Linearity of Boltzmann Eq. allows for decomposition of primordial and
regeneration components
;tot prim regf f f
/ ;prim prim primf t v f f
/ ;reg reg regf t v f f
00regf
0 0
prim totf f
• For primordial component we directly solve homogeneous Boltzmann Eq.
• For regeneration component we solve a Rate Eq. for inclusive yield and estimate its pt spectra using a locally thermal distribution boosted by medium flow.
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Rate-Equation for Reg. Component
/eqN G
/reg reg regf v f f •
3 3,p G d pd x
/reg regdN d N G
/reg reg eqdN d N N
• For thermal c spectra, Neq follows from charm conservation: 21 1
=2 2
tot eqcc oc c oc FB c FBN N +N n V n V
• Non-thermal c spectra lead to less regeneration:
[1 exp( / )]eq eq eq eqcN R N N
(Integrate over Ψ phase space)
typical 3 10 fm/eqc c
[van Hees et al. ’08, Riek et al. ‘10]
[Braun-Munzinger et al. ’00, Gorenstein et al. ‘01]
[Grandchamp, Rapp ‘04]
[Greco et al. ’03]
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• follows from Ψ spectra in pp collisions with Cronin effect applied
Initial Condition and RAA
• is obtained from Ψ primordial production0( , , )f x p t
0 0 0( , , ) ( , ) ( , )f x p t f x t f p t
• follows from Glauber model with shadowing and nuclear absorption parameterized with an effective σabs
0( , )f x t
assuming
0( , )f p t
• nuclear modification factor:AAΨ
AA ppcoll Ψ
NR
N N
Ncoll: Number of binary nucleon-nucleon collisions in AA collisions
RAA=1, if without either cold nuclear matter (shadowing, nuclear absorption, Cronin) or hot medium effects
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Correlators and Spectral Functions
†( , ) ( , ) (0,0) ,G r j r j
pole mass mΨ(T), width Ψ(T)
threshold 2mc*(T),
• two-point charmonium current correlation function:
• charmonium spectral function: 0
cosh[ ( 1/ 2 )]( , ) ( , )
sinh[ / 2 ]
TG T d T
T
• lattice QCD suggests correlator ratio ~1 up to 2-3 Tc:
( , )
( , )Grec
G TR
G T
[Aarts et al. ’07, Datta te al ’04, Jakovac et al ‘07]
5, 1, , ...j q q
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Initial Conditions• cold nuclear matter effects included in initial conditions• nuclear shadowing: • nuclear absorption:• Cronin effect:
• implementation for cold nuclear matter effects:• nuclear shadowing• nuclear absorption• Cronin effect Gaussian smearing with smearing width
guided by p(d)-A data
Glauber model with σabs from p(d)-A data
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Kinetic equations
lQCD potential
diss. & reg. rates
Initial conditions
Experimental observables
lQCD correlator
(Binding energy)
Link between Lattice QCD and Exp. Data