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Quarkonia in Medium
and their Fate at Future RHIC
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
Workshop on “Future Perspectives in QCD at High Energy”Brookhaven National Laboratory, 19.07.06
1.) Introduction: Quarkonia Probing the QGP• immerse -pair into the QGP
Vacuum properties change:
• color screening (reduced binding)• dissociation reactions (and reverse!)• heavy-quark mass (→ mass and decay rates, threshold)
Experiment:• no direct access (?) to spectral shape (unlike → e+e-): J/ decay outside medium with 1:200 (: 5:1)
• number of J/, ’, Y, … and their pT-spectra, v2(pT)
Challenges: - in-Medium -spectral functions - infer confinement of QGP! order parameter?!
1.) Introduction
2.) Medium Effects on Quarkonia 2.1 Color Screening 2.2 Dissociation Reactions 2.3 Heavy-Quark Masses in QGP 2.4 Spectral Functions and Correlators ↔ Lattice QCD
3.) Phenomenology in URHICs 3.1 Suppression and Regeneration 3.2 The Role of Open Charm 3.3 Observables
4.) Summary and Outlook
Outline
2.1 Onia in QGP: Color Screening and Binding
[Shuryak etal ’04, Wong ’04, Alberico etal ’05, Mocsy etal ‘05, …]
• small binding energies above Tc (~ screened Cornell pot.)
• even smaller(!) for V1 = (1-U1 + F1
• solve Schrödinger-Eq. with lattice-QCD U1(r) as potential
BottomoniumCharmonium
[Wong ’06]
(i) Gluo- Dissociation
• diss() peaked at ≈1.4B
• ok for free J/Bvac=640MeV
• not for screening, ’, c
2.2.1 Charmonia in QGP: Dissociation Reactions
[Bhanot+Peskin ‘84]
Cross Sections
(ii) “Quasifree” Dissociation
• neglects bound-state structure• appropriate for small binding• also involves (anti-) quarks
[Grandchamp+RR ‘01] _
Dissociation Times
2.2.2 Bottomonium Lifetimes in QGP
[Grandchamp etal ’05]
• appreciable sensitivity to color screening!• significance at RHIC: Y ≈ 50 → 5 fm/c
~ gT [GeV]
~Tc[Karsch,Mehr +Satz ‘88]
“Quasifree” Suppression Bottomonium Screening
2.3 Heavy-Quark Masses in the QGP
[Kaczmarek +Zantow ‘05]
• in-/decreasing heavy-quark mass ?!
• close to Tc: entropy contribution?
• quarkonium mass: m= 2mc* - B
• asymptotic energies F∞ = U∞ - TS∞
U∞
F∞
2.4 Spectral Functions and Euclidean Correlators
• Vacuum Spectral Function ~ Bound State + Continuum:
() = F2 (-m) + 2 -thrf
thr
• In-Medium Bound-State / Resonance
() ~ Im D:122 ]/im[)(D B
*c
- real part (pole ) ↔ screening, in-medium quark-mass - imaginary part (width) ↔ dissociation
e.g. = ‹ np diss vrel › ≈ 10 fm-3 1mb ½ ≈ 100 MeV (T≈250MeV) for QGP=2fm/c: S= exp[-QGP] ≈ 0.37
“stable” J/ at RHIC unlikely
2
J/’
cont.
• In-Medium Continuum: Ethr(T) , nonperturbative Q-Q rescattering
_
2.4.2 Euclidean Correlation Functions (or R = G / Grecon )
• accurate “data” from lattice QCD, integral over spectral function
)(~)T,(G,]T/[
)]T/([)T,(d)T,(G
vacrecon
sinhcosh
221
0
• S-wave charmonia little changed to ~2Tc, P-wave signal enhanced(!)
c
c
[Datta etal ‘04]
2.4.3 Euclidean Correlator -- Potential Model
• Spectral Function: ( = F2 (- m) + 2 -thrf
thr
- Bound State: Schrödinger eq. with screened Cornell, or lQCD U1
- Continuum: pQCD with Ethr(T) = 2mc+V∞
• opposite trend as on lattice• compatible with lattice• increase due to reduced Ethr(T)!
[Mocsy+Petreczky ‘05]
2.4.4 Eucl. Correlator -- Model II: T-Matrix Approach
• use potential to solve Lippmann-Schwinger-Eq. for Q-Q T-Matrix: -
)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T LQQLLL02
[Mannarelli+RR ’05, Cabrera+RR in prep] 000
QQLQQQQL GTGG)E(GCorrelator:
[Cabrera+RR in prep]
• comprehensive treatment of bound and scattering states
• nonperturbative threshold effects large
• finite-width effects
2.4.4 Eucl. Correlators from T-Matrix Approach• lattice U1-potential, mc=1.7GeV fix, Grecon(Ethr=2mD)
[Cabrera+RR in prep]
c c
• trends roughly as on lattice, except magn. + T-dep. of c; threshold?!
[Dattaetal ’04]
2.4.4 Eucl. Correlators from T-Matrix Approach• lattice U1-potential, mc=1.7GeV fix, Grecon= G(T=1.1Tc)
[Cabrera+RR in prep]
• sensitive to Grecon !
• ~ insensitive to width effects!
c
3.) Phenomenology in URHICs
3.1 Suppression + Regeneration
3.2 The Role of Open Charm
3.3 Observables
• 3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG
Stot = exp[-nuc L] exp[-QGP QGP ] exp[-HGHG ]
• Regeneration in QGP + HG: - microscopically: backward reaction (detailed balance!)
key ingredients: reaction rate equilibrium limit ( -width) )m,m,N( ccc
(links to lattice QCD)
)NN(d
dN eq
3.1 Suppression and Regeneration in URHICs
[PBM etal ’01, Gorenstein etal ’02,Thews etal ’01,Grandchamp+RR ’01, Ko etal ’02, Cassing etal ‘03] J/ + g c + c + X←→ -
- for thermal c-quarks and gluons:
- nuc(SPS) ≈ 4.5mb → used for RHIC predictions; - but: RHIC d-Au data → nuc≈1.5mb
• softer c-quarks → more formation ↔ c-quark diffusion: ceq = mcT/D
3.2 The Role of Open Charm and Regeneration
[van Hees etal ‘05]
e± Spectra
• need more detailed studies! (e.g. transport, Langevin)
[Greco etal ‘05]
pQCD scatt.
nonpert. scatt.
• yields differ by factor 3 • importance of Cronin [Thews+ Mangano’05]
[Ko etal ’02, Cassing etal ‘03 Gossiaux etal ’06, Zhang ’06, …]
J/ Coalescence at Tc
• nuc=4.4mb, ceq ~ 2.5fm/c (schem.)
• QGP-regeneration dominant• sensitive to: mc* , (Ncc )2
3.3.1 Observables I: Centrality Dependence at RHIC
[Grandchamp etal ’03]
→ solve rate equation for expanding fireball (QGP-mix-hadron gas)
Original Predictions
[PHENIX ‘05]
• nuc=1.5mb • sensitive to: c-quark diff., Tdiss
• shape of RAA a problem?! precise data!
[X.Zhao+RR in prep]
Update and Further Studies
• nontrivial “flat” dependence• similar interplay in rapidity!? (need accurate dNc/dy)
3.3.2 Observables II: Excitation Function + Rapidity
J/ Suppression vs. Regeneration
[Grandchamp +RR ’01]
• direct J/ essentially survive (even at RHIC)
Sequential ’+ c Suppression
[Karsch,Kharzeev+Satz ‘06]
RHIC
[Grandchamp etal ’05]
3.3.3 Bottomonium at RHIC and LHC
• 50% feeddown from Y’, b
• importance of color-screening!• bottomonium suppression as unique QGP signature ?!
LHC
5.) Summary• strong color-screening from lQCD heavy-quark potentials • short quarkonium lifetimes (X=1-5 fm/c)
• open-charm masses: open problem
• Heavy-Ion Collisions: - J/ above Tc : gain term! sensitive to c-quark diffusion, Tdiss
- flat excitation fct.: suppr. vs regeneration or (’, c) only?
elliptic flow: v2(J/) up to ~10% ?!
- Y suppression (very) sensitive to screening - sQGP signature: Y more suppressed than J/ at RHIC+LHC !
• Euclidean Correlation Functions: - quantitative constraints on model spectral functions - importance of nonperturbative threshold effects (T-matrix!) - moderate sensitivity to width effects
2.4.4 Eucl. Correlators from T-Matrix Approach• lattice U1-potential, mc=1.8GeV fix, Grecon(Ethr=2mD) [Cabrera+RR
in prep]
• trends roughly agree with lattice, except T-dep. of c – threshold?!
c c
• QGP-suppression prevalent• “jumps” / ”plateaus” in centrality?
3.5 Charmonium Observables at SPS Pb(158AGeV)-Pb In(158AGeV) –In
[Grandchamp etal ’03]
Satz, Digal, FortunatoRapp, Grandchamp, BrownCapella, Ferreiro
• Percolation• Plasma• Comovers NA60 preliminary
2.1 Onia in QGP: Color Screening and Binding Energies[Karsch,Mehr+Satz ’88, Wong ’04, …]
• binding energies much reduced above Tc
• similar for lattice U1(r) , smaller(!) for F1
e.g. screened Cornell potential (linear+confining)
CharmoniumBottomonium
~Tc
~ gT [GeV]
~ gT [GeV]
~Tc
2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA
[van Hees,Greco+RR ’05]
Resonances vs. pQCD Charm-pQCD (s, D=1.5T)s , g
1 , 3.5
0.5 , 2.5
0.25,1.8
[Moore and Teaney ’04]
• hydro with Tc=165MeV, ≈ 9fm/c
• s and Debye mass independent
• expanding fireball ≈ hydro • pQCD elastic scatt. moderate • resonance effects substantial
3.4.3 Scrutinizing Charmonium Regeneration II: J/ Elliptic Flow
Suppression only Thermal Coalescence at Tc
[Wang+Yuan ’02]
[Greco etal ’04]
MB Au-Au
• factor ~5 different! • transition in pt!?