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:

QQ

• 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?!

QQ

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!?