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:

Contents 1.Introduction 2.Schematic model for fireball expansion 3.Thermal properties of charmonia 4.Charmonia in heavy-ion collisions 5.Results 6.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.

N J/ψ vs. N part statistical model two-component model

N J/ψ vs. P t 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 b s b-s

2. 2. Initial condition Charged particle multiplicities PRC65, (2002)

EoS of QGP Quasiparticle picture Strongly interacting massless partons Noninteracting massive partons to reproduce thermal quantities extracted from LQCD 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

Isothermal lines on transverse plane at τ 0 = 0.6 fm/c

Temperature profiles at various impact parameters

2. 3. fireball expansion Radial acceleration in central collision Parameterized to fit experimental data of π, K, p at freeze-out

Assuming isentropic expansion, s(τ)=s 0 *v 0 /V(τ)

Radial acceleration in non-central collision Parameter to fit experimental data v 2 of π, K, p at freeze-out

b=9 fm,

Blast wave model

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 potential F. Karsch, M.T. Mehr, H. Satz, Z phys. C. 37, 617 (1988) σ=0.192 GeV 2 : string tension α=0.471 : Coulomb-like potential constant μ(T) =√(N c /3+N f /6) gT : screening mass in pQCD In the limit μ(T)→0,

Ψ’(2S) χ c (1P) GeV J/ψ (1S) Screening mass 289 MeV 298 MeV 306 MeV 315 MeV 323 MeV 332 MeV 340 MeV GeV

Binding energies & radii of charmonia Screening mass (MeV) Binding energy (GeV) Screening mass (MeV) Radius (fm)

3. 2. dissociation cross section Bethe-Salpeter amplitude Definition ; 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 σ diss = ∑ j σ j pQCD 1. partons with thermal mass 2. temperature-dependent wavefunctions from modified Cornell potential are used. In hadronic matter Factorization formula: σ diss (p)= ∑ j ∫dx σ i pQCD (xp)D j i (x) D j 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 Hadronization T≈ 170 MeV Regenerated J/ψ Thermal decay in hadronic matter Thermal decay in QGP Nuclear absorption detector Kinetic freeze-out T≈ 120 MeV Thermal decay in hadronic matter Cronin effect Before cc 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

Primordial J/ψ is produced Nucleus A Nucleus B

4. 2. Nuclear destruction Primordial J/ψ is produced Nucleus A Nucleus B Nuclear destruction cross section is obtained from pA collision σ diss =1.5mb

4. 3. Thermal decay J/ψ QGP phase Mixed phase (Assuming 1 st order phase transition) HG phase J/ψ

Thermal decay widths in QGP & HG

Ψ’(2S) χ c (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 χ c, Ψ’ to J/ψ, Survival probability from thermal decay

4. 4. Regeneration From Glauber model ( dσ cc NN /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 Canonical suppression

Relaxation factor for kinetic equilibrium

the number of regenerated J/ψ N J/ψ rec = VRγ 2 {n J/ψ S J/ψ HG +Br(χ c )*n χc *S χc HG + Br(ψ’) *n ψ’ * S ψ’ HG } n J/ψ, n χc, n ψ’ : number densities of charmonia S J/ψ HG, S χc HG, S ψ’ HG : survival rate of charmonia in HG Br(χ c ), Br(ψ’) : branching ratios of χ c, ψ’ to J/ψ R : relaxation factor γ : fugacity

5. Results R AA vs. N part R AA vs. p T V 2 Higher-order corrections in pQCD

5. 1. R AA of J/ψ From RHIC near midrapidty at √s NN =200 GeV

R AA of J/ψ as a function of N part (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) T J/ψ =386 MeV, T χc =199 MeV, T Ψ’ =185 MeV with g= ‘g’ determines the thermal widths of charmonia (Г ∼ g 2 in LO, and Г ∼ g 4 in NLO) 3. ‘g’ determines the relaxation factor of charm quarks

W/O initial dissociation of J/ψ without

R AA of J/ψ as a Function of p t (For J/ψ, T f =160 MeV)

of J/ψ

v 2 of J/ψ (b=9 fm) 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.

R AA of J/ψ as a function of N part (near midrapidity in Cu+Cu collision at √s=200 GeV) Regeneration

Applying to Pb+Pb collision at √s NN =5.5 TeV (LHC) with the modified parameters by extrapolation, Entropy dS/dη= 30.3{(1-x)N part /2+xN coll } to 78.5{(1-x)N part /2+xN coll }, where x=0.11 J/ψ production cross section per rapidity in p+p collision dσ J/ψ pp /dy= μb to 6.4 μb from pQCD, cc production cross section per rapidity in p+p collision dσ cc pp /dy= 63.7 μb to 639 μb Ref. is NPA 789, 334 (2007) 7.36 μb at 7 TeV (Nov. 2010)

R AA of J/ψ as a function of N part (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)

R AA of J/ψ as a function of N part (near midrapidity in Au+Au collision at √s=200 GeV)

R AA of J/ψ as a Function of p t

of J/ψ

v 2 of J/ψ (b=9 fm)

5. Summary

Summary of nuclear modification of charmonia in heavy-ion collision Before production ; Cronin effect (p t ↑) After production ; nuclear destruction (N J/ψ ↓) ; initial dissociation (N J/ψ ↓) After thermalization ; thermal decay (N J/ψ ↓) ; leakage effect (N J/ψ ↑, p t ↑) ; regeneration (N J/ψ ↑) ; flow effect (p t ↑)

Summary of results We reproduced successfully R AA of J/ψ in Au+Au and Cu+Cu collisions at RHIC and estimated R AA in Pb+Pb collision at LHC by using 2-component model. There seems to be a kink in R AA vs. N part curve in Au+Au collision. → initial temperature begins to be over T J/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. p t of J/ψ : In 2-component model, Cronin effect mainly enhances p t while in the statistical model, flow effect mainly enhances. → both models successfully describe R AA and p t of J/ψ in RHIC. Only v 2 of J/ψ seems to be able to discriminate two models. → Precise measurement of v 2 of J/ψ will reveal the fraction of regenerated J/ψ