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
Jan 12, 2016
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!?