Quarkonia in Medium: From Spectral Functions to Observables

Transcription

1 Quarkonia in Medium: From Spectral Functions to Observables Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA with: D. Cabrera (Madrid), L. Grandchamp, F. Riek + X. Zhao (Texas A&M) Joint CATHIE-INT Mini-Program: Quarkonia in Hot Media: From QCD to Experiment INT Seattle,

2 1.) Introduction: Quarkonia in URHICs Production: - shadowing (nucl. PDF) - p T broadening (Cronin) Pre-Equilibrium: - formation time (Lorentz-dilated) - nuclear absorption - pre-equilibrium medium Equilibrium Matter: - bound-state properties (mass/binding energy) - dissolution temperature (inelastic width formation!) - relation to QGP / hadronic matter: phase transition? order parameter? Expanding Medium: - collectivity (elastic Ψ scattering?) - regeneration c + c Ψ +X open-charm flow

3 Outline 1.) Introduction 2.) Heavy Quarkonia in Medium Potential Models + Spectral Functions T-Matrix Approach and Medium Effects Inelastic Reactions Rates 3.) Phenomenology at SPS + RHIC Rate Equation Approach Suppression vs. Regeneration at SPS + RHIC Momentum, T diss and Rapidity Dependence 4.) Conclusions

4 direct computation of Euclidean Correlation Function 2.1 Quarkonia in Lattice QCD Euclidean correlators weakly T-dependent (zero modes taken out) free/internal energies exhibit significant screening bound states survive? spectral functions?! G α cosh[ ω( τ 1/ 2T )] ( τ,t ) = dω σα( ω,t ) sinh[ ω / 2T ] 0 spectral function [Datta et al., Asakawa et al 03, Umeda et al 04, Iida et al 06, Jakovac et al 07, Aarts et al 07] [Kaczmarek et al., Petreczky et al, ]

5 Lippmann-Schwinger Equation In-Medium - Q-Q T-Matrix: 2.2 Potential Models well established in vacuum (EFT, lattice) Schrödinger equation in medium [Mocsy+Petreczky 06, Alberico et al 06, Wong 07, Laine 07, ] correlators: quark rescattering in continuum [Mannarelli+RR 05,Cabrera+RR 06] T L ( E;q,q' - ) = V L (q,q' ) + dk (q,k ) 2-body potential V L at finite temperature? k 2 V L G QQ ( E,k ) - Q-Q propagator: GQQ ( s ) = 4ω k /[s ( 2ωk + ΣQ + Σ - bound + scattering states (threshold effects!) T Q L ) ( E;k,q' 2 ] )

6 2.2.2 Heavy-Quark Free Energy in Lattice QCD F 1 (r,t) = U 1 (r,t) T S 1 (r,t) V 1 (r,t) X 1 (r,t) X 1 (r=,t) X 1 /2 : in-medium quark-mass correction (?) 2 extreme potential choices: (a) X 1 = F 1 => weak potential, ε B (1.1T c ) ~ 50 MeV small quark-mass correction (b) X 1 =U 1 => strong potential, ε B (1.1T c ) ~ 500 MeV large quark-mass correction approximate compensation in bound-state mass: E ψ = 2m c0 + X 1 ε B [Kaczmarek+Zantow 05]

7 2.2.3 In-Medium Charm-Quark Mass lattice QCD [Kaczmarek +Zantow 05] potential model [Cabrera +RR 07] F susceptibility [Petreczky 08] U : large variation close to T c mass interpretation? remnant of 2.order transition? information from HQ susceptibility G V 00 ~ - T χ(t) finite-width effects (diffusion)?

8 2.2.4 Charmonium Spectral Function + Correlators I: Weak Potential V(r,T) ~ F 1 η c [Mocsy+ Petreczky 07] low threshold (2m c * ~ 2.7GeV), ground state T diss ~ 1.2 T c => early melting scenario ~compatible with lattice QCD

9 2.2.5 Charmonium Spectral Function + Correlators II: Strong Potential V(r,T) = U 1 η c m c =1.7GeV fix, Γ ψ = 40 MeV [Cabrera+RR 06] η c m c* ~ GeV Γ ψ = 40 MeV decreasing 2m c* stabilizes correlator, T diss ~2.5T c

10 2.2.6 Free vs. Internal Energy as Potential Qualitative Considerations tot QQ F (r,t ) = F (r,t ) F (T ) no obvious minimization constraint QQ internal energy thermal expect. value of (static) 2-body Hamiltonian: [ ] FQQ FQ Q(r,T ) = T 2 ln dγ exp Η QQ / T, UQQ (r,t ) = T = Η T QQ perturbation theory: F T S U tot QQ QQ QQ (inherent) time scales: Landau-Zener transitions F U gauge-dependence problem (r,t ) (r,t ) (r,t ) = = = αs mdr 4 e 4α m 3 r 3 s 4 mdr αsmd( 1 e ) 3 mdr 4αse ( 1 + m ) 3 r D D

11 2.3 Quarkonium Widths in QGP sensitive to binding energy (color screening) J/ψ Dissociation Cross Section [Bhanot+Peskin 79, Kharzeev+Satz] q q [Grandchamp+RR 01, Park et al 07] J/ψ Dissociation Width shrinking phase space for gluo-dissociation Γ Ψ = 100 MeV ~60% J/ψ destroyed in Δτ=2fm/c

12 2.3.2 Relation of Quarkonium Widths to EFT Singlet-octet transition Landau damping q q

13 2.3.3 Width Effects on Euclidean Correlators c-quark width in cc- propagator: G cc ( s ) = ω k /[s / 4 ( ω 1 k + Γc ) 2 2 ] η c [Cabrera+RR 06] width Γ Ψ = MeV few-% enhancement further stabilization with increasing T

14 2.3.4 Momentum Dependence of Inelastic Width dashed lines: gluo-dissociation solid lines: quasifree dissociation q q [Zhao+RR 07] similar to full NLO calculation [Park et al 07]

15 3.) Quarkonium Production in URHICs 3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG S tot = exp[-σ nuc ρ L] exp[-γ QGP τ QGP ] exp[-γ HG τ HG ] Regeneration in QGP + HG: - backward reaction (detailed balance!) if J/ψ survives J/ψ + g c + c + X dn ψ dτ = Γ - ψ ( N reaction rate equilibrium limit (ψ -width) dn / dp,m,m ) ψ N eq ψ ( c T ψ c (links to lattice QCD) ) [PBM et al 00, Gorenstein et al 02, Thews et al 01, Grandchamp+RR 01, Ko et al 02, Cassing et al 03, Zhu et al 05, ] J/ψ solve rate equation in hydro/fireball/transport background c - c D - D J/ψ

16 fixed charm-quark number ~ N coll (b) Equilibrium Limit N cc = 1V 2 FB γ c n equil. charmonium eq 2 d q = 3 ψ α Nψ VFB γc f (m α = ψ,t ) Ncc, number ( 2π ) sensitive to open-charm spectrum! op (m 3 c,d I ;T ) I 1 0 ( γcv ( γ V c corr corr n n op op ) ) + ψ N eq ψ [Grandchamp et al 03] m J/ψ = 2 m c ε B = const

17 3.2 Charmonium at CERN-SPS σ abs (J/ψ,ψ )= 4.4,7.9 mb, T 0 = MeV (MB-central) suppression controlled by α s ~ 0.25 in quasifree dissociation rate Centrality Dependence Momentum Dependence gauge anomalous J/ψ suppression (mostly in QGP) p t dependence Cronin effect (p-a) (quasifree rate suppresses p t2 ) [Zhao+RR 07]

18 3.3 Charmonium at RHIC: Centrality Dependence fireball with T 0 = MeV (MB-central) schematic relax. for c-quark equilibration N ψ eq (τ)~ N ψ therm (τ) [1-exp(-τ/τ c eq )] [Grandchamp+RR 03, Zhao+RR 07] ~50% regeneration in central Au-Au sensitivity to c-quark equilibration, T diss?

19 3.3.2 Momentum Spectra Au-Au 200AGeV regeneration part blast-wave at T c regeneration at low p T high p T : formation time ( ), bottom feeddown, [Karsch+Petronzio 87, Blaizot+Ollitrault 87] [Zhao+RR 07, 08]

20 3.3.3 Rapidity Dependence at RHIC problematic in dynamic approaches modified cold-nuclear-matter effects at forward y?! [Kharzeev et al. 07, Ferreiro et al. 08]

21 4.) Conclusions Interplay of color-screening and heavy-quark mass (+ width) essential to understand quarkonia in QGP Small binding + small quark mass (V QQ ~ F 1 ) or large binding/quark-mass (V QQ ~ U 1 ) compatible with lat-qcd Charmonium in heavy-ion collision: - suppression prevalent at SPS (dissociation width) - significant regeneration at RHIC (p t spectra) Intimate relations to charm diffusion Bottomonium: - suppression sensitive to color screening (width!)

22 X.) Example for Comprehensive Analysis: NA60 Dileptons Charmonium Production Charmonium Flow thermal medium radiating from around T c with melted ρ, well-bound J/ψ with large collectivity

23 2.3.2 Bottomonium Dissociation Rates in QGP color-screening accelerates dissociation significance at RHIC: τ Y 50 5 fm/c [Grandchamp et al. 05]

24 solve kinetic rate-equation: (evolve over fireball) Time Evolution J/ψ in Central Au-Au at RHIC dnψ eq = Γψ ( Nψ Nψ ) dτ N eq ψ (τ)~ N therm ψ (τ) [1-exp(-τ/τ eq c )] Equilibration close to T c?!

25 3.5 Charmonium Observables at SPS Pb(158AGeV)-Pb In(158AGeV) In Satz, Digal, Fortunato Rapp, Grandchamp, Brown Capella, Ferreiro Percolation Plasma Comovers NA60 preliminary QGP-suppression prevalent jumps / plateaus in centrality? [Grandchamp etal 03]

26 3.4 Upsilon at RHIC No Color-Debye Screening With Color-Debye Screening [Grandchamp et al. 05] ϒ(1S,2S) suppression unambiguous QGP signature?! NB: 50% feed-down on ϒ(1S)

27 3.3.3 Dissociation Temperature Suppression only (Hydro) Including Regeneration T diss = 2.0 T c 1.2 T c threshold melting finite width [Zhao+RR 08] finite width and regeneration wash out step structure [Gunji et al. 07]

28 2.2.1 Color Screening + Quarkonium Binding in QGP e.g. screened Cornell pot.: Charmonium V QQ (r, μ(t )) = ( e μ(t σ 1 ) μ(t )r ) Bottomonium 4α s e 3r μ(t )r ~T c ~T c μ ~ gt [GeV] μ ~ gt [GeV] [Matsui+Satz 86, Karsch,Mehr+Satz 88, Wong 04, ] quarkonium binding substantially reduced above T c

29 3.2.3 Charm-Quark Selfenergy + Transport = Selfenergy L,a Qq ΣQ ( p) d k f ( ω )T ( p+ k ) L,a 3 q k Friction Coefficient γ p = d k F T( k, p ) k 3 2 charm quark widths Γ c = -2 ImΣ c ~ 250MeV close to T c friction coefficients increase(!) with decreasing T T c!

30 3.4 Single-Electron Spectra at RHIC heavy-quark hadronization: coalescence at T c [Greco et al. 04] + fragmentation hadronic correlations at T c quark coalescence! charm bottom crossing at p Te ~ 5GeV in d-au (~3.5GeV in Au-Au) ~25% uncertainty due to differences in U 1 potential suppression early, v 2 late

31 3.3 Heavy-Quark Spectra at RHIC relativistic Langevin simulation in elliptic expanding fireball background Nuclear Modification Factor Elliptic Flow p T [GeV] p T [GeV] T-matrix approach effective resonance model similar to coll. dissoc. [Adil+Vitev 07]; radiative E-loss? (2 3),

32 3.2.2 Charm-Light T-Matrix with lqcd-based Potential Temperature Evolution + Channel Decomposition [van Hees, Mannarelli, Greco+RR 07] meson and diquark S-wave resonances up to T c P-waves and (repulsive) color-6, -8 channels suppressed

33 3.2 Potential Scattering in sqgp T-matrix for Q-q scatt. in QGP T a L = V a L + dk V a L G 0 Qq T a L [Mannarelli+RR 05] Casimir scaling for color chan. a in-medium heavy-quark selfenergy: Determination _ of potential fit lattice Q-Q free energy currently significant uncertainty when using F 1 pqcd! F QQ = UQQ TS, VQQ ( r ) = UQQ ( r ) UQ Q [Wong 05] [Shuryak+ Zahed 04]