Heavy Quark/onium in Hot Nuclear Matter Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA INT Program (Week.
Post on 20-Dec-2015
216 Views
Preview:
Transcript
Heavy Quark/onium
in Hot Nuclear Matter
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
INT Program (Week 7) on “Quantifying the Properties of Hot QCD Matter”
INT (Seattle), 06.-09.07.10
1.) Introduction: Virtues of Heavy Quarks (c,b)
• “Large” scale mQ >> QCD , T
- factorization in production; thermal medium: pth2 ~ 2mQ T >> T2
• Interactions spacelike (“low” pt):
- quarkonium: potential QCD - heavy-quark diffusion: Brownian motion
→ unified framework
• Beyond perturbation theory (s expansion)
→ resummations, bound + scattering states
• Constraints essential (latQCD, pQCD, vacuum spectrum,…)
• Heavy-ion collisions: - “initial-state” effects - medium effects: equilibrium properties, expansion collectivity
2220
2 kkkk
Q Q
1.2 Charm/onium Suppression at SPS + RHIC
• Same force operative for quarkonium (un)binding + heavy-quark transport?
Anomalous J/ Suppression Heavy-Quark Suppression+Flow
1.) Introduction
2.) T-Matrix for Heavy Quark/onium in QGP
Vacuum Spectroscopy, In-Medium Potentials Spectral + Correlation Functions
3.) Quarkonia in Heavy-Ion Collisions
Thermal Rate Equation Suppression vs. Regeneration
4.) Heavy-Quark Diffusion in QGP
Fokker-Planck + Thermalization Observables at RHIC
5.) Conclusions
Outline
• Lippmann-Schwinger equation
In-Medium Q-Q T-Matrix: -
2.) Heavy-Quark Potential + Thermal 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 ’06, Riek+RR ‘09]
- Q-Q propagator: - importance of threshold effects
• HQ potential well established in vacuum (EFT, lattice, spectroscopy)
• Quark-Gluon Plasma: bound+scattering states (quarkonia + HQ transport)
])(E/[)k,E(G QQkkQQ220 24 -
• 2-body potential VL at finite temperature?
2.2 Heavy-Quark Free Energy in Lattice QCD
F1(r,T) = U1(r,T) – T S1(r,T)
• Potential “Choices” : (a) Free energy F1 => weak potential, B(1.1Tc) ~ 50 MeV mQ(TF1(r=∞,T) small
(b) Internal Energy U1 ( U = ‹Hint› )
=> strong potential, B(1.1Tc) ~ 500 MeV mQ(T) ~ U1(r=∞,T) large
• approximate compensation in bound-state mass: E = 2mc
0 + 2mQ B
[Kaczmarek+Zantow ’05]• need improved ways to extract HQ potential
• Relativistic effects - kinematics - magnetic interaction → “Breit” correction: VQ1Q2(r) → VQ1Q2(r) ( 1 – v1 · v2 ) (↔ Poincaré-invariance, pQCD)
• Retardation effects - 4-D → 3-D reduction of Bethe-Salpeter equation - energy transfer fixed (q0=0), off-shell behavior ambiguous
• Gauge dependence of color-singlet free energy
• Field-theoretic ansatz: [Megias et al ‘07]
color-Coulomb: vector , string:
- fit color-average free energy to lat. QCD scalar
implement into “extended T-Matrix approach”
2.3 Corrections to Heavy-Quark Potential
[Riek+RR ‘10]
222
2
22001
)m~k(
m
mk)k(D
D
G
D
22
20 8
1G
c
NPa, m
g)N(
A
[Brown et al ‘52, ‘05]
[Philipsen ‘08]
In-Medium HQ Free Energies Model Parameters
2.3.2 Temperature Dependence of Fit Parameters
• s ~ 0.3
• screening of color-Coulomb + string term
• “Debye masses” ~ T
2.4.1 Constraints I: Vacuum Spectroscopy Quarkonia D-Mesons
• no hyperfine splitting• (bare) masses adjusted to ground state • ~ ±50 MeV accuracy
Born Approximation compared to Perturbative QCD
2.4.2 Constraints II: High-Energy Q-q Scattering
• Breit correction essential
2.5 Quarkonium Spectral Functions in Medium2.5.1 Lattice-QCD Correlators
]T/[)]T/([
)T,(d)T,(G2sinh
21cosh
0
• direct computation of Euclidean Correlation Fct.
spectral function
[Asakawa et al ’03, Iida et al ’06, Aarts et al ‘07, Jakovac et al ‘07]
[Datta et al ‘04]
• ~20% variation for S-wave charmonia ~ 0.9-3 Tc
• Bound states survive above Tc?!
c
J/
)T,(G
)T,(G)T,(RG
rec
2.5.2 T-Matrix Spectral Functions with Potential U
• S-wave ground state “melts” at Tdiss ≈ 2 Tc
• correlator ratios within 30% (3D reduction scheme)
S-Wave Spectral Function Euclidean Correlator Ratio(narrow-width
limit)
2.5.3 T-Matrix Spectral Functions with Potential F
• S-wave ground state “melts” at Tdiss ≈ 1.3 Tc
• reduced c-c threshold → low-energy strength
S-Wave Spectral Function Euclidean Correlator Ratio
[Cabrera+RR ’06, Riek+RR ‘09]
-
2.5.4 Importance of Confining Force
J/
Υ
2.6 Charmonium Widths in QGP
→ sensitive to binding energy (i.e., color screening)
• J/ lifetime ~ 1-4 fm/c
)s()T;(f)(
kd disspk
p
g,qp
3
3
2
s~0.25
q q
J/ Dissociation Rates
[Grandchamp+RR ’01]
J/
S-Wave Spectral Function
• accelerates “melting”: Tdiss ≈ 1.6 Tc
• correlator ratio temperature-stable
med=200MeV
• dashed lines: gluo-dissociation
• solid lines: quasifree dissociation
• similar to full NLO calculation
2.6.2 Momentum Dependence of Inelastic Width
_
[Zhao+RR ‘07][Park et al ‘07]
q q
2.6.3 Relation of Quarkonium Widths to EFT
•Landau damping
• Singlet-octet transition
q q
reaction rate equilibrium limit ( -width) )m,m,dp/dN( cTc
3.) Quarkonium Production in URHICs
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 Thermodynamic T-Matrix (weak/strong binding)
3.1 Inputs and Parameters• Input
- J/ (c, ’), c-c production cross sections [p-p data [PHENIX] ]
- “Cold Nuclear Matter”: shadowing, nuclear absorption, pt broadening [p-A data]
- Thermal fireball evolution: thermalization time (↔ initial T0),
expansion rate, lifetime, Tc , freezeout …
[hadron data, hydrodynamics]
• Parameters
- strong coupling s controls diss
- schematic relaxation for c-quark equilibration: N
eq ()~ Ntherm() · [1-exp(-/c
eq)] _
-
3.2 Centrality Dependence of J/ at SPS + RHIC
• regeneration controlled by c-quark relaxation time (ceq
= 6 vs. 3 fm/c)• similar total yield, but different composition
[Zhao+RR in prep]
Strong-Binding Scenario (U) Weak-Binding Scenario (F)
3.3 pT-Dependence of J/ at SPS + RHIC
• weak binding problematic with pt-dependence?!
Strong Binding (U) Weak Binding (F)
3.3.2 pT-Dependence II: Blast Wave at RHIC
• blast wave at ~Tc too soft?
• lever arm for direct prod. at high pT?
Regeneration only (Stat. Model) Rate-Equation (strong bind.)Au-Au
200AGeV
[Andronic et al. ‘07]
3.3.3 Charm-Quark pT-Spectra and Regeneration
• supports sensitivity to thermal relaxation time of c quarks
• microscopic calculation of gain term c + c + g → J/ + g-
QmDT
2
2
p
fD
p)pf(
tf
• Brownian
Motion:
thermalization rate diffusion coefficient
4.) Heavy-Quark Diffusion in the QGP
Fokker Planck Eq.[Svetitsky ’88,…]
Q
k)p,k(wkdp Q3
23
21 k)p,k(wkdD Q
• In-medium heavy-light T-matrix:
)E(T)E(GVdkkV)E(T LQqLLL 2
• pQCD elastic scattering:
1= therm ≥ 20 fm/c slow
q,g
c
2
2elast
D
scg ~
direct connection to quarkonia!
[Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore ’04, Peshier,Gossiaux+Aichelin ‘09]
[van Hees et al ’07, Riek+RR ‘10]
4.2 Charm-Quark T-Matrix + Thermalization
• meson/diquark resonances for T < 1.5 Tc
• factor 3-4 (~2) larger than pert. QCD for U (F) potential
Thermalization RateThermal Q-q T-Matrix
[Riek+RR ‘10]
T [GeV]
[1
/fm
]
4.3 e± Spectra at RHIC
• hadronic resonances at ~Tc ↔ quark coalescence
• connects 2 “pillars” of RHIC: strong coupl. + coalescence
[van Hees et al ‘07]
T-mat
T-mat
5.) Conclusions
• Thermodynamic T-matrix for heavy quarks + quarkonia - vacuum: spectroscopy + pQCD limit - in-medium potential from lattice QCD? U1 (Td
~2Tc) , F1 (Td~1.3Tc) , or else …
- confining force mandatory for realistic calculations
• Quarkonium phenomenology - “strong” vs. “weak” J/ binding (pt-data, lever arm, …)
- bottomonium suppression? (less regeneration …)
• Open heavy flavor - resonances close to Tc ? (strong coupling + coalescence …)
- RHIC non-photonic e±Ds (2T) ≈ 5 - scrutinize medium evolution, Fokker-Planck, d-Au …
3.2.3 Rapidity Dependence at RHIC
• regeneration yield sensitive to dNc/dy
• hot matter effects insufficient • additional shadowing at forward y (assuming constant abs)
Thermal Rate-Eq Approach
[Kharzeev et al. ‘07, Ferreiro et al. ‘08] [Zhao+RR in prep]
• regeneration at low pT
3.2.5 Momentum Spectra
• regeneration part → blast-wave at Tc
Au-Au200AGeV
• high pT: formation time ( ), bottom feeddown, …
[Karsch+Petronzio ’87, Blaizot+Ollitrault ‘87]
[Zhao+RR ’07, ‘08]
3.2.4 Momentum Spectra and Elliptic Flow
• regeneration at low pt → small v2
• direct component at high pt → small v2
[Zhao+RR ’08, Zhuang et al ‘06]
2.4.2 Example from “Extended T-Matrix Model”
c
• cc propagator with c= 100 MeV:
• S-wave “melting” Tdiss ≈ 1.5-2 Tc
• correlator ratio temperature-stable
- ])(s/[)s(G cckkcc20 24
S-Wave Spectral Function Euclidean Correlator Ratio
4.3 Thermalization Rate and Diffusion Coefficient
• Factor ~3-4 larger thermalization rates than in pert. QCD
•“different” approaches related, e.g. AdS/CFT ↔ Coulomb
T [GeV]
[1
/fm
]
T [GeV]
2.4 Mesonic Spectral Functions + Correlators
• Euclidean Correlation Function (precise lat-QCD data avail.!)
Correlator Ratio:
2.2.2 Potential Models in the QGP
U1 potential
• F1 low threshold (2mc~ 2.7GeV), ground state Tdiss ~ 1.2 Tc
• U1 decreasing threshold and B, Tdiss ~2.5Tc
both scenarios compatible with lat-QCD
~F1 potential [Cabrera +RR ‘06]
[Mocsy+ Petreczky ’05,‘08]
mc=1.7GeVmc=1.7GeVmc*
c
212
3 3
32
,N)T,m(f)(
qdVN cccFB
eq
3.1.3 Equilibrium Limit (Statistical Model)
eq
opc
opcD,copcFBcc N
)N(I)N(I
)T;m(nVN0
1
21• fixed c-c number:
• equilibrium number:
• (very) sensitive to open-charm spectrum
• thermal relaxation for c-quark spectra:
[Grandchamp et al ’03, Andronic et al ’07, …]
-
]/)T(N)(N eqc
eqeq exp[-
2.1.3 In-Medium Charm-Quark Mass in LQCD
• U: large variation close to Tc – mass interpretation?!
[Kaczmarek+Zantow ’05]
F
• fit quark-number fluctuations with zero-width quasiparticle model (T) ~ ∂2P / ∂2c
[Velytsky et al ’09]
3.3.4 Rapidity Dependence at RHIC
• reproduced in statistical hadronization model (GC ensemble) [Andronic et al. ’07]
• more problematic in dynamic approaches
• additional shadowing at forward y?
Statistical Model Thermal Rate-Eq Approach
[Capella et al. ’07, Zhao+RR ‘08]
[Kharzeev et al. ‘07, Ferreiro et al. ‘08]
3.4 Upsilon at RHIC
• (1S,2S) suppression unambiguous QGP signature ?!• NB: 50% feed-down on (1S)
No Color-Debye Screening With Color-Debye Screening
[Grandchamp et al. ’05]
3.3 Heavy-Quark Spectra at RHIC
• T-matrix approach ≈ effective resonance model • similar to “coll. dissoc.” [Adil+Vitev ’07]; radiative E-loss? (2↔3), …
• relativistic Langevin simulation in elliptic expanding fireball background
pT [GeV]
Nuclear Modification Factor Elliptic Flow
pT [GeV]
2.3.2 Bottomonium Reaction Rates in QGP
[Grandchamp et al. ’05]
• color-screening accelerates dissociation• significance at RHIC: Y ≈ 50 → 5 fm/c
top related