Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State University Ames, USA Brookhaven National Lab, Upton, NY, Jun. 14th 2011

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) 2

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] 3

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 4 ? ?

Picture of Ψ production in Heavy-Ion Coll. 3 stages: 1->2->3 1.Initial production in hard collisions 2.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 - c - c 5

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 N ψ eq : eq. limit of Ψ – Detailed balance is satisfied by sharing common Γ in the loss and gain term – Main microscopic inputs: Γ and N ψ eq 6

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 7 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 8 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c

In-medium Dissociation Mechanisms [Bhanot and Peskin ‘79] [Grandchamp and Rapp ‘01] Gluo-dissociation is not applicable for reduced ε B Ψ <T quasifree diss. becomes dominant suppression mechanism  strong coupling α s ~ 0.3 is a parameter of the approach Dissociation cross section σ iΨ -gluo-dissociation: quasifree dissociation: g+ Ψ →c+g(q)+ Ψ →c+ +g(q) VS. 9 Dissociation rate:

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 10 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c

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] 11

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 12

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 13 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 14 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c

Model Spectral Functions Model spectral function = resonance + continuum At finite temperature: Z(T) reflects medium induced change of resonance strength T diss =2.0T c V=U T diss =1.25T c V=F Z(T diss )=0 In vacuum: Z(T) is constrained from matching lQCD correlator ratio width Γ Ψ threshold 2m c * pole mass m Ψ 15 Regeneration is possible only if T<T diss quasifree diss. rate T diss

Correlators and Spectral Functions Peak structure in spectral function dissolves at T diss Model correlator ratios are compatible with lQCD results weak binding strong binding 16 [Petreczky et al. ‘07]

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 17 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c

Regeneration: Inverse Dissociation For thermal c spectra, N Ψ eq 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] 18 Gain term dictated by detailed balance: Charm relaxation time τ c eq is our second parameter: τ c eq ~ 3/6fm/c

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 19 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c 1.shadowing 2.nuclear absorption 3.Cronin 1.shadowing 2.nuclear absorption 3.Cronin

Kinetic equations lQCD potential diss. & reg. rate: Γ Initial conditions Experimental observables lQCD correlator Link between Lattice QCD and Exp. Data 20 Ψ eq. limit: N Ψ eq εBΨεBΨ m Ψ, m c 1.Coll. energy dep. 2.P t dep. 3.Rapidity dep. 1.Coll. energy dep. 2.P t dep. 3.Rapidity dep. 1.shadowing 2.nuclear absorption 3.Cronin 1.shadowing 2.nuclear absorption 3.Cronin

Compare to data from SPS NA50 weak binding (V=F) strong binding (V=U) incl. J/psi yield Different composition for different scenarios Primordial production dominates in strong binding scenario Significant regeneration in weak binding scenario Large uncertainty on σ cc 21

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/psi yield See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07] 22

J/Ψ yield at LHC (w/o Shadowing) weak binding (V=F) strong binding (V=U) Parameter free prediction – both α s and τ c eq fixed at SPS and RHIC Regeneration component dominates except for peripheral collisions R AA <1 for central collisions (with, ) Comparable total yield for V=F and V=U 23

With Shadowing Included 24 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.

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) 25

High p t Ψ at LHC 26 Negligible regeneration for p t > 6.5 GeV Strong suppression for prompt J/Ψ Significant yield from B feeddown Similar yields and composition between V=U and V=F

P t Dependence at RHIC Mid-Rapidity see also [Y.Liu et al. ‘09] V=U 27 V=U Primordial production dominant at p t >5GeV Regeneration concentrated at low p t due to c quark thermalization Formation time effect and B feeddown increase high p t production [Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88]

R AA (p T ) at RHIC Mid-Rapidity V=F 28 V=F At low p t regeneration component is larger than V=U

J/ψ v 2 (p T ) at RHIC Small v 2 (p T ) for entire p T range -At low p t v 2 from thermal coalescence is small -At high p t regeneration component is gone Even smaller v 2 even in V=F -Small v 2 does not exclude coalescence component strong binding (V=U) 29 weak binding (V=F)

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 R AA than mid-y Larger uncertainty on CNM effects at forward-y incl. J/psi yield See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07] 30

R AA (p T ) at RHIC Forward Rapidity V=U 31 V=U Shadowing pronounced at low p t & fade away at high p t Large uncertainty on CNM effects

R AA (p T ) at RHIC Forward Rapidity V=F 32 V=F At low p t reg. component is larger than V=U (similar to mid-y)

33 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) R AA <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 33

Thank you! based on X. Zhao and R. Rapp Phys. Lett. B 664, 253 (2008) X. Zhao and R. Rapp Phys. Rev. C 82, (2010) X. Zhao and R. Rapp Nucl. Phys. A 859, 114 (2011) 34

Compare to data from SPS NA50 weak binding (V=F) strong binding (V=U) incl. J/psi yield trans. momentum primordial production dominates in strong binding scenario 35

J/ψ v 2 (p T ) at RHIC Small v 2 (p T ) for entire p T range strong binding (V=U) 36

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] 37

3-to-2 to 2-to-2 Reduction reduction of transition matrix according to detailed balance dissociation:regeneration: g(q)+ Ψ c+c+g(q) diss. reg. 38

Thermal vs. pQCD Charm Spectra regeneration from two types of charm spectra are evaluated: 1) thermal spectra: 2) pQCD spectra: [van Hees ‘05] 39

Reg. Rates from Different c Spectra thermal : pQCD : pQCD+thermal = 1 : 0.28 : 0.47 introducing c and angular correlation decrease reg. for high p t Ψ strongest reg. from thermal spectra (larger phase space overlap) See also, [Greco et al. ’03, Yan et al ‘06] 40

Ψ Regeneration from Different c Spectra strongest regeneration from thermal charm spectra c angular correlation lead to small reg. and low pQCD spectra lead to larger of regenerated Ψ blastwave overestimates from thermal charm spectra 41

42 V=F V=U larger fraction for reg.Ψ in weak binding scenario strong binding tends to reproduce data J/Ψ yield and at RHIC forward y incl. J/ psi yield trans. momentum 42

43 J/Ψ suppression at forward vs mid-y comparable hot medium effects stronger suppression at forward rapidity due to CNM effects 43

R AA (p T ) at RHIC Primordial component dominates at high p t (>5GeV) Significant regeneration component at low p t Formation time effect and B-feeddown enhance high p t J/ Ψ See also [Y.Liu et al. ‘09] V=FV=U [Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88] 44

45 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 45

46 J/Ψ Abundance vs. Time at LHC V=F V=U regeneration is below statistical equilibrium limit 46

Ψ Reg. in Canonical Ensemble Integer charm pair produced in each event c and anti-c simultaneously produced in each event, c and anti-c correlation volume effect further increases local c (anti-c) density 47

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 48

49 Fireball Evolution, {v z,a t, a z } “consistent” with: - final light-hadron flow - hydro-dynamical evolution isentropical expansion with constant S tot (matched to N ch ) and s/n B (inferred from hadro-chemistry) EoS: ideal massive parton gas in QGP, resonance gas in HG [X.Zhao+R.Rapp ‘08] 49

Primordial and Regeneration Components Linearity of Boltzmann Eq. allows for decomposition of primordial and regeneration components For primordial component we directly solve homogeneous Boltzmann Eq. For regeneration component we solve a Rate Eq. for inclusive yield and estimate its p t spectra using a locally thermal distribution boosted by medium flow. 50

Rate-Equation for Reg. Component For thermal c spectra, N eq follows from charm conservation: Non-thermal c spectra lead to less regeneration: (Integrate over Ψ phase space) typical [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] 51

follows from Ψ spectra in pp collisions with Cronin effect applied Initial Condition and R AA is obtained from Ψ primordial production follows from Glauber model with shadowing and nuclear absorption parameterized with an effective σ abs assuming nuclear modification factor: N coll : Number of binary nucleon-nucleon collisions in AA collisions R AA =1, if without either cold nuclear matter (shadowing, nuclear absorption, Cronin) or hot medium effects 52

Correlators and Spectral Functions pole mass m Ψ (T), width  Ψ (T) threshold 2m c *(T), two-point charmonium current correlation function: charmonium spectral function: lattice QCD suggests correlator ratio ~1 up to 2-3 T c : [Aarts et al. ’07, Datta te al ’04, Jakovac et al ‘07] 53

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 σ abs from p(d)-A data 54

Kinetic equations lQCD potential diss. & reg. rates Initial conditions Experimental observables lQCD correlator (Binding energy) Link between Lattice QCD and Exp. Data 55