Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision

Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision

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## Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision

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**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)**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]**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 staticΨ eq. properties into production in the dynamically evolving hot and dense medium ? ?**D**- J/ψ D c - c J/ψ Picture of Ψ production in Heavy-Ion Coll. • 3 stages: 1->2->3 • Initial production in hard collisions • Pre-equilibrium stage (CNM effects) • Thermalized medium • 2 processes in thermal medium: • Dissociation by screening & collision • Regeneration from coalescence • Fireball life is too short for equilibration • Kinetic approach needed for off-equilibrium system**Thermal Rate-Equation**• Thermal rate-equation is employed to describe production in thermal medium (stage 3) • Loss termfor dissociation Gain term for regeneration • Γ: dissociation rate Nψeq: eq. limit of Ψ • Detailed balance is satisfied by sharing common Γ in the loss and gain term • Main microscopic inputs: Γ and Nψeq**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**In-medium Dissociation Mechanisms**• Dissociation rate: • Dissociation cross section σiΨ • gluo-dissociation: VS. quasifreedissociation: g+Ψ→c+ g(q)+Ψ→c+ +g(q) [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**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**Charmonium In-Medium Binding**• Potential model employed to evaluate [Cabrera et al. ’07,Rieket al. ‘10] [Petreczky et al ‘10] • V(r)=U(r) vs. F(r)? (F=U-TS) • 2 “extreme” cases: • V=U: strong binding • V=F: weak binding [Riek et al. ‘10]**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**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**Model Spectral Functions**• Model spectral function = resonance + continuum • In vacuum: • At finite temperature: quasifree diss. rate • Z(T) reflects medium induced change of resonance strength • Z(T) is constrained from matching lQCDcorrelator ratio pole mass mΨ threshold 2mc* Tdiss=2.0Tc V=U Tdiss=1.25Tc V=F widthΓΨ Tdiss Z(Tdiss)=0 • Regeneration is possible • only if T<Tdiss Tdiss**Correlators and Spectral Functions**weak binding strong binding [Petreczky et al. ‘07] • Peak structure in spectral function dissolves at Tdiss • Model correlator ratios are compatible with lQCDresults**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**Regeneration: Inverse Dissociation**• Gain term dictated by detailed balance: • • For thermal c spectra, NΨeqfollows 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 [Braun-Munzinger et al. ’00, Gorenstein et al. ‘01] • Realistic off-kinetic-eq. c spectra lead to weakerregeneration: • Charm relaxation time τceq is our second parameter: τceq~3/6fm/c**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables shadowing nuclear absorption Cronin diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**Link between Lattice QCD and Exp. Data**Initial conditions Kinetic equations Experimental observables Coll. energy dep. Pt dep. Rapidity dep. shadowing nuclear absorption Cronin diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator**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 σcc**J/Ψ yield at RHIC**incl. J/psi yield 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 See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07]**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**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.**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)**High ptΨ 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**Pt Dependence at RHIC Mid-Rapidity**V=U V=U see also [Y.Liu et al. ‘09] • 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]**RAA(pT) at RHIC Mid-Rapidity**V=F V=F • At low pt regeneration component is larger than V=U**J/ψ v2(pT) at RHIC**strong binding(V=U) weak binding(V=F) • Small v2(pT) for entire pT range • At low pt v2 from thermal coalescence is small • At high ptregeneration component is gone • Even smaller v2 even in V=F • Small v2 does not exclude coalescence component**J/ΨYield at RHIC Forward Rapidity**incl. J/psi yield 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 See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07]**RAA(pT) at RHIC Forward Rapidity**V=U V=U • Shadowing pronounced at low pt & fade away at high pt • Large uncertainty on CNM effects**RAA(pT) at RHIC Forward Rapidity**V=F V=F • At low pt reg. component is larger than V=U (similar to mid-y)**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 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, 064905 (2010) X. Zhao and R. Rapp Nucl. Phys. A 859, 114 (2011)**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**J/ψ v2(pT) at RHIC**strong binding(V=U) • Small v2(pT) for entire pT range**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]**3-to-2 to 2-to-2 Reduction**diss. • g(q)+Ψc+c+g(q) reg. dissociation: regeneration: • reduction of transition matrix according to detailed balance**Thermal vs. pQCD Charm Spectra**• regeneration from two types of charm spectra are evaluated: 1) thermal spectra: 2) pQCD spectra: [van Hees ‘05]**Reg. Rates from Different c Spectra**See also, [Greco et al. ’03, Yan et al ‘06] • thermal : pQCD : pQCD+thermal = 1 : 0.28 : 0.47 • strongest reg. from thermal spectra (larger phase space overlap) • introducing c andangular correlation decrease reg. for high ptΨ**ΨRegeneration from Different c Spectra**• strongestregeneration from thermal charm spectra • pQCD spectra lead to larger <pt2> of regenerated Ψ • c angular correlation lead to small reg. and low <pt2> • blastwaveoverestimates <pt2> from thermal charm spectra**V=F V=U**larger fraction for reg.Ψ in weak binding scenario strongbinding tends to reproduce <pt2> data J/Ψ yield and <pt2> at RHIC forward y incl. J/psi yield trans. momentum 42**J/Ψ suppression at forward vs mid-y**comparable hot medium effects stronger suppression at forward rapidity due to CNM effects 43**RAA(pT) at RHIC**V=F V=U • 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 [Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88] [Y.Liu et al. ‘09]**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**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**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**Fireball Evolution**, {vz,at,az} “consistent” with: - final light-hadron flow - hydro-dynamical evolution isentropicalexpansion with constantStot(matched to Nch) and s/nB(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 pt spectra using a locally thermal distribution boosted by medium flow.