Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with...

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

2

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)

3

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]

4

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

?

?

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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

7

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

8

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

9

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

11

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

14

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

15

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

20

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]

23

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)

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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]

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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)

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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]

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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)

3333

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

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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

36

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]

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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

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

4343

J/Ψ suppression at forward vs mid-y

• comparable hot medium effects• stronger suppression at forward rapidity due to CNM effects

44

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]

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

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

4949

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

55

Kinetic equations

lQCD potential

diss. & reg. rates

Initial conditions

Experimental observables

lQCD correlator

(Binding energy)

Link between Lattice QCD and Exp. Data