Comprehensive Analysis of

In-Medium Quarkonia at SPS, RHIC + LHC

Ralf Rapp Cyclotron Institute +

Dept. of Physics & Astronomy Texas A&M University

College Station, TX USA

With: X. Zhao, A. Emerick

Quark Matter 2012 ConferenceWashington (DC), 12.-18.08.12

1.) Introduction: A “Calibrated” QCD Force

•Vacuum charm- + bottomonium spectroscopy well described

• Non-perturbative force (EBCoul(J/) ~ 0.05 GeV vs. 0.6 GeV expt.)

• Persists in medium to at least ~2Tc

• Potential approach in medium?

[Kaczmarek et al ‘03]

V [½ GeV]

r [½ fm]

• Lippmann-Schwinger equation

In-Medium Q-Q T-Matrix: -

2.) Thermodynamic T-Matrix for Quarkonia in QGP

)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T QQ 02

[Mannarelli,Cabrera,Riek+RR ‘05,‘06,‘10]

• potential V strictly real

• imaginary parts: unitarization (cuts in in-med. QQ propagator GQQ) -

q q

• gluo-dissosciation (coupled channel) [Bhanot+Peskin ‘85] • Landau damping (HQ selfenergy)

2.2 Brueckner Theory of Heavy Quarks in QGP

2-body potential QQ

T-matrix

QqT-matrix

Q → Q0-modes

Quarkselfenergy

QQ evolution (rate equation)

Q spectra + v2

(Langevin)

spectral fcts./eucl. correlat.

quark-no.susceptibility

latticedata

exp.data

Input Process Output Test

-

-

reaction rate equilibrium limit ( -width) )m,m,dp/dN( cTc

3.) Transport Approach to Quarkonium Evolution

J/ D

D-

J/c- c

)NN(d

dN eq

[PBM et al ’01, Gorenstein et al ’02,Thews et al ’01, Grandchamp+RR ’01, Ko et al ’02, Cassing et al ’03, Zhuang et al ’05, …]

J/ + g c + c + X←→ -• Regeneration in QGP + HG:

detailed balance:

mc*

B

• Input from T-Matrix (weak/strong binding)

• Rate Equation:

3.1 Inputs + Parameters• Input

- J/ c, ’, bb + cc production cross sections [p-p]

- “Cold Nuclear Matter” effects (shadowing, nucl. abs., Cronin) [p/d-A]

- Medium evolution: thermal fireball [A-A, hydrodynamics]

• Parameters

- strong coupling s controls diss

- incomplete c-quark equilibration: N

eq () ~ Ntherm() · [1-exp(-/c

eq)]

-

q q

-

3.2 Inclusive J/ at SPS + RHIC

• s~0.3, charm relax. ceq = 6(3) fm/c for U(F) vs. ~5(10) from T-matrix

• different composition in two scenarios

Strong Binding (U) Weak Binding (F)

[Zhao+RR ‘10]

3.2.2 J/ pT Spectra + Elliptic Flow at RHIC

• small v2 limits regeneration, but does not exclude it [Zhao+RR ‘08]

(U potential)

• shallow minimum at low pT

• high pT: formation time, b feeddown, Cronin

3.3 J/ at LHC: Centrality

• regeneration increases, still net suppression• uncertainty from “shadowing”• good consistency of transport approaches [Zhao+RR ‘11]

Mid-Rapidity Forward Rapidity

3.3.2 J/ at LHC: pT-Spectra + v2

• maximum at low pT confirms expected regeneration level

• room for additional regeneration with harder pT spectra…

• b-feeddown prevalent at high pT

3.4 (1S) and (2S) at LHC

• sensitive to color-screening + early evolution times• clear preference for strong binding (U potential)

(1S) →

(2S) →

[Grandchamp et al ’06, Emerick et al ‘11]

Weak Binding Strong Binding

4.) Conclusions

• Thermodynamic T-matrix approach → quarkonium spectral fcts. + HQ transport in QGP, benchmarks: lattice QCD, vacuum spectroscopy, pQCD

• Kinetic rate equation with in-medium quarkonia → dissociation + formation in QGP / hadronization inputs: HQ cross-secs., cold-nuclear-matter effects,…

• “Weak-binding” scenario disfavored - inconsistent with: HF transport, (1S) suppression, …

• Manifestations of J/ regeneration - RAA

SPS(Ti~220) ~ RAARHIC(Ti~350) < RAA

LHC(Ti~550) ~ 0.5

- low-pT enhancement of RAALHC, finite v2

3.3.3 J/ at LHC III: High-pt – ATLAS+CMS

• underestimate for peripheral (expected from RHIC) (spherical fireball reduces surface effects …)

[Zhao+RR ‘11]

3.3.4 Time Evolution of J/ at LHC

• finite “cooking-time” window, determined by inelastic width

[Zhao+RR ‘11]

Strong Binding (U) Weak Binding (F)

3.4 at RHIC and LHC

• sensitive to color-screening + early evolution times

RHIC →

LHC →

[Grandchamp et al ’06, Emerick et al ‘11]

Weak Binding Strong Binding

• U-potential, selfconsist. c-quark width

• Spectral Functions - J/ melting at ~1.5Tc

- c melting at ~Tc

- c ~ 100MeV

• Correlator Ratios

- rough agreement with lQCD within uncertainties

3.2 Charmonia in QGP: T-Matrix Approach

[Mocsy+ Petreczky ’05+’08, Wong ’06, Cabrera+RR ’06, Beraudo et al ’06, Satz et al ’08, Lee et al ’09, Riek+RR ’10, …]

[Aarts et al ‘07]

• selfcons. c-quark width

• Spectral Functions - J/ melting at ~1.1Tc

- c melting at ≤ Tc

- c ~ 50MeV

• Correlator Ratios

- slightly worse agreement with lQCD

3.2.2 T-matrix Approach with F-Potential

[Riek+RR ’10]

[Aarts et al ‘07]

3.3 Charm-Quark Susceptibility in QGP

• sensitive to in-medium charm-quark mass • finite-width effects can compensate in-medium mass increase

[Riek+RR ‘10]

2→ →

→ 0 m « T

4.2.5.2 Thermalization Rate from T-Matrix

• thermalization 4 (2) times faster using U (F) as potential than pert. QCD

• momentum dependence essential (nonpert. effect ≠ K-factor!)

[Riek+RR ‘10]

c [

1/fm

]

4.5 Summary of Charm Diffusion in Matter

• Shallow minimun around Tc ?!

• Quark-Hadron Continuity?!• 20% reduction by non-perturbative HQ-gluon scattering

Hadronic Matter vs. QGP vs. Lattice QCD (quenched)

[He et al ’11, Riek+RR ’10, Ding et al ‘11, Gavai et al ‘11]

AdS/CFT

• dashed lines: gluo-dissociation

• solid lines: quasifree dissociation

• similar to full NLO calculation

3.1.3 Momentum Dependence of Inelastic Width

_

[Zhao+RR ‘07] [Park et al ‘07]

4.3 J/ at Forward Rapidity at RHIC

[Zhao+RR ‘10]