hot and dense qcd matter and heavy-ion collisions
DESCRIPTION
Hot and Dense QCD Matter and Heavy-Ion Collisions. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA MLL Colloquium TU M ünchen , 22.10.09. = g 2 /4 p. Quantum Chromo Dynamics: “ strong” coupling for Q < 2GeV ( r > 0.1fm ) - PowerPoint PPT PresentationTRANSCRIPT
Hot and Dense QCD Matter
and Heavy-Ion Collisions
Ralf Rapp
Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
MLL Colloquium TU München, 22.10.09
1.) Introduction: Pillars of the Strong Force
• Stable Matter: u , d , e- mu,d ≈ 5-10 MeV
But:
00 |h|G d,u
• quarks “glued” together ► Confinement
• proton mass Mp= 940 MeV >> 3mq ≈ 20 MeV
► Mass Generation (>95% visible mass)
u
d u
Quantum Chromo Dynamics:
• “strong” coupling for Q < 2GeV (r > 0.1fm)• QCD vacuum filled by condensates
2
41
aq Gq)m̂Agi(q QCDL
GeV.~|qq|G~*mq 35000 “constituent” quark mass
= g2/4
• hadrons overlap, quarks liberated Deconfinement (energy density ~ (# d.o.f )T4 , crit ≈ 1 GeV / fm3 )
/ T4 free gas
[Cheng et al ’08]
1.2 Quark-Gluon Plasma
Excite vacuum (hot+dense matter)
But:
• matter around Tc strongly coupled: “sQGP” ( – 3p ≠ 0 !)
-• ‹0|qq|0› condensate “melts”, mq* → 0
Mass Degeneration (hadron masses?)
‹qq›T / ‹qq›vac --
3p / T4
LatticeQCD ’08
|
|
1.3 QCD Phase Diagram and NatureEarly Universe(few s after Big Bang) Compact
Stellar Objects(Neutron Stars)
Unique opportunity to study:• primordial Big Bang matter • quark (de-) confinement and mass (de-) generation• matter with smallest known viscosity (/s): “near perfect fluid”• phase structure of non-abelian gauge theory (↔ string theory!?)
1.) Introduction: QCD and QGP Quark Confinement + Hadron Mass Quark-Gluon Plasma + QCD Phase Diagram
2.) Experimental Probes of QCD Matter
Particle Spectra in Heavy-Ion Collisions
3.) Heavy-Quark Probes (c,b) Heavy-Quark Diffusion in the QGP Viscosity?!
4.) Electromagnetic Radiation The Visible Mass in the Universe?! Melting Vector Mesons + Dilepton Spectra
5.) Conclusions
Outline
“Freeze-Out”Hadron Gas (≈ 10fm/c)
QGP ?! (≈ 5fm/c)
Au + Au
2.1 The “Little Bang” in the Laboratory
Au + Au → X
e+
e-
Questions:• Thermalization?• QGP Signatures??• QGP Properties???
c,b
2.2 Basic Findings at RHIC: Hadron Spectra
(1) Ideal Hydrodynamics: pT ≤ 2GeV [Shuryak, Heinz, …]
v2had
early thermalization, 0 ≤ 1fm/c
...])cos()p(v[dp
dNpd
dNT
TT
221 222
∂ T = 0 T= (+P) u u – P g
Input: equation of state (P), initial conditions, freezeout
Output: collective flow u
radial + elliptic (v2)
2 GeV ≤ pT ≤ 6 GeV(2) Quark Coalescence:
• baryon-to-meson “anomaly” • “quark-number scaling” of elliptic flow
)p(f)p(f|)q(|qd)(
pdg
pd
dNE qqqqMM
M 2333 2
[Greco et al ‘03 Fries et al ‘03, Hwa et al ’03]
hadronization via qq → M, qqq → B
(instantaneous, no spatial dependence of v2 in fq )
_
matter at RHIC thermalizes, 0 > c , small viscosity, partonic
ET - m =
Rati
o
2.3 Problems + Advanced Tools
• Key Questions:
- microscopic origin of “near perfect fluid”? How “perfect”? - matter constituents / spectral functions? …
• Heavy Quarks (charm, bottom): created early, Brownian particle traversing QGP fluid ► transport coefficients ↔ thermalization and “flow” ► Q-Q bound states (J/, Y) in QGP?
• Electromagnetic Emission (photons, dileptons): escape medium unaffected, “thermal radiation”
► dilepton invariant mass: (Mee )2 = (pe++pe )2
↔ direct access to in-medium spectral functions
-c,b
e+
e-
1.) Introduction: QCD and QGP Quark Confinement + Hadron Mass Quark-Gluon Plasma + QCD Phase Diagram
2.) Experimental Probes of QCD Matter
Particle Spectra in Heavy-Ion Collisions
3.) Heavy-Quark Probes (c,b) Heavy-Quark Diffusion in the QGP Viscosity?!
4.) Electromagnetic Radiation The Visible Mass in the Universe?! Melting Vector Mesons + Dilepton Spectra
5.) Conclusions
Outline
3.1 The Virtue of Heavy Quarks (Q=b,c)
• Large scale mQ >> QCD
→ “factorization” even at low pT
→ QQ produced in primordial N-N collisions
→ well “calibrated” initial spectra at all pT
• Large scale mQ >> T
→ thermal momentum pth2 = 3mQT >> T2 ~ Q2 therm. mom. transfer
→ Brownian motion (elastic scattering) → thermalization delayed by mQ/T memory of rescattering
• Flavor conserved in hadronization → coalescence!?
• Elastic scattering Q2 = q02 – q2 ~ (q2/2mQ)2 – q2 ~ -q2
→ quasi-static potential approach!? → common framework for heavy-quark diffusion and quarkonia
-
QmDT
2
2
p
fD
p)pf(
tf
• Brownian
Motion:
scattering rate diffusion coefficient
3.2 Heavy Quark Diffusion in the QGP
Fokker Planck Eq.[Svetitsky ’88,…]Q
q)p,q(wqdp 3 23
21 q)p,q(wqdD
• pQCD elastic scattering:
1= therm ≥ 20 fm/c slow
q,g
c
Microscopic Calculations of Diffusion
2
2elast
D
scg ~
[Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore ‘04]
• D-/B-resonance model:
1= therm ~ 5 fm/c c
“D”
c
_q
_q
c)(
qG DDDcq 2
v1 L
parameters: mD , GD[van Hees+RR ’04]
3.2.2 Potential Scattering using Lattice QCD
• potential: use lattice QCD Q-Q internal energy (T>Tc):
TSUF QQQQ
• T-matrix for Q-q scatt. in QGP , GqQ: Q-q propagator
)E(T)E(GVdkkV)E(T LQqLLL 2
• HQ potential concept established in vacuum (EFT, lattice)
• 3-D reduced Bethe-Salpeter Eq.
QQQQQQ U)r(U)r(V
• Meson and diquark “resonances” for T ≤ 1.5 Tc
[Brambilla, Vairo et al]
3.3 Comparison of Drag Coefficients(Thermal Relaxation Rate)
• proliferation?! NB: pQCD ↔ Coulomb ↔ AdS/CFT T-matrix: Coulomb + ”string”(latQCD), resummed • “melting” resonances: relax = 1/ ~ 5-8 fm/c ~ constant
T [GeV]
[1
/fm
]
[Gubser ’06]
[Peshier ‘06; Gossiaux+Aichelin ’08]
[van Hees+RR ’04]
[van Hees,Mannarelli, Greco+RR ’07]
3.4 Heavy Flavor Phenomenology at RHIC
• Medium Evolution - hydrodynamics or parameterizations thereof
- realistic bulk-v2 (~5-6%)
- stop evolution after QGP; hadronic phase?
• Hadronization - fragmentation: c → D + X
- coalescence: c + q → D, adds momentum and v2
• Semileptonic Electron Decays - D, B → e± X , ~ conserve v2 and RAA of parent meson
- charm/bottom composition in p-p
[Hirano et al ’06]
→ relativistic Langevin simulations of heavy quark in QGP:
3.4.2 Model Predictions vs. RHIC Data
Semileptonic e± Spectra [PHENIX ’06]
• c-q → D coalescence increases both RAA and v2
• radiative E-loss upscaled pQCD • Langevin with resonances + coalescence• Langevin with upscaled pQCD elastic (Ds ~ 30/2T)
RAA≡ (dN/dpT )AA / (dN/dpT )pp
no coal.
3.4.3 T-Matrix Approach vs. e± Spectra at RHIC
• hadronic resonances at ~Tc ↔ quark coalescence
• connects 2 pillars of RHIC! (strong coupl. + coalescence)
[van Hees,Mannarelli,Greco+RR ’07]
Spatial Diffusion Ds = T/(mQ
3.5 Viscosity in sQGP?• Conjectured bound of sCFT (string-theo. methods):
• use heavy-quark diffusion to estimate for QGP: kinetic theory: s ≈n <p> tr /s = 1/5 T Ds
sCFT:s≈ Ds= 1/2 T Ds
close toTc
41
s[Kovtun,Son +Starinets ’05]
462 )(
s
[Lacey et al ’06]
[RR+van Hees ‘08]
3.6 “Reinterpretation” of Quark Coalescence “Resonance Recombination Model”: resonance scattering q+q → M close to Tc using Boltzmann eq.-
[Ravagli et al ’08]
~pd
dNM3
• conserves energy, recovers thermal equilibrium, encodes v2(x) in fq(x,p)
• Langevin, interaction strength determines v2max ≈7%
• approximate scaling in KT=ET -m
Quarks Mesons
2
1.) Introduction: QCD and QGP Quark Confinement + Hadron Mass Quark-Gluon Plasma + QCD Phase Diagram
2.) Experimental Probes of QCD Matter
Particle Spectra in Heavy-Ion Collisions
3.) Heavy-Quark Probes (c,b) Heavy-Quark Diffusion in the QGP Viscosity?!
4.) Electromagnetic Radiation The Visible Mass in the Universe?! Melting Vector Mesons + Dilepton Spectra
5.) Conclusions
Outline
4.) Electromagnetic Radiation
Tiqx )(j)x(jexdi)q(Π 0emem
4em
EM Correlation Function:
e+
e-)T,q(f
Mqdxd
dN Bee023
2
44 Im Πem(M,q;B,T)
Dilepton Sources: Relevance:
- Quark-Gluon Plasma: high mass + temp. qq → e+e , … M > 1.5GeV, T >Tc
- Hot + Dense Hadron Gas: M ≤ 1 GeV → e+e , … T ≤ Tc
-
q
q
_
e+
e
e+
e
Im Πem ~ Im D
>>
B*,a1,K1
...
N,,K…
4.2 -Meson in Medium: Hadronic Interactions
D(M,q;B ,T) = [M 2 - m2 - - B - M ] -1-Propagator:
[Chanfray et al, Herrmann et al, RR et al, Weise et al, Koch et al, Mosel et al, Eletsky et al, Oset et al, Lutz et al…]
= B,M=Selfenergies:
Constraints: decays: B,M→ N, scattering: N → N, A, …
B /0
0 0.1 0.7 2.6
[RR,Wambach et al ’99]
Meson “Melting” Switch off Baryons
4.3 Dilepton “Excess” Spectra at SPS
• “average” (T~150MeV) ~ 350-400 MeV
(T~Tc) ≈ 600 MeV → m
• fireball lifetime: FB ~ (6.5±1) fm/c[van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08]
)y,M(Acc),T;q,M(qxdd
dNq
qMd)(Vd
dMdN
iFB
fo
44
therm
0
3therm
0
Thermal Emission Spectrum:
4.3.2 NA60 Data vs. In-Medium Dimuon Rates
• acceptance-corrected data directly reflect thermal rates!
M[GeV] [RR,Wambach et al ’99]
[van Hees+RR ’07]
4.3.3 Low-Mass Dileptons at RHIC: PHENIX
• Successful approach at SPS fails at RHIC
5.) Conclusions
• Strong-Interaction (QCD) Matter
- Quark (de-) confinement, Mass (de-) generation
- Can be studied in heavy-ion collisions
- “Near perfect” liquid?!
• (Some) Recent Developments
- non-perturbative heavy-quark diffusion above Tc (“QGP liquid”)
- -resonance melts toward Tc (“hadron liquid”)
• Upcoming Experimental Programs:
- LHC (CERN), RHIC-2 (BNL), FAIR (GSI), NICA (Dubna), …
- “perturbative” QGP at high T?
- 1st order transition at finite B > 0?
3.2.3 AdS/CFT-QCD Correspondence
[Gubser ‘07]
pdtdp 2
2 SYMc
CFT/ADS Tm
cCFT/ADS m
T)..(2
5012
• match energy density (d.o.f = 120 vs. ~40) and coupling constant (heavy-quark potential) to QCD
3-momentum independent
[Herzog et al, Gubser ‘06]
≈ (4-2 fm/c)-1 at T=180-250 MeV
Lat-QCD
TQCD ~ 250 MeV
But: “Higgs” Mechanism in Strong Interactions:qq attraction “Bose” condensate fills QCD vacuum
Spontaneous Chiral Symmetry Breaking
3.1 Chiral Symmetry + QCD Vacuum
)m( d,u 0QCD L : isospin + “chiral” (left/right-handed) invariant
350000 fm|qqqq||qq| LRRL
>
>
>
>qLqR
qL-qR
--
Profound Consequences:• effective quark-mass: ↔ mass generation
• massless Goldstone bosons 0,± , pion pole-strength f= 93MeV
• “chiral partners” split, M ≈ 0.5GeV:
00 |qq|m*q
JP=0± 1± 1/2±
• Weinberg Sum Rule(s)
3.1.2 Hadron Spectra + Chiral Symm. Breaking
Axial-/Vector Correlators
)Im(Ims
dsf IA
IV
112
pQCD cont.
“Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85]
● chiral breaking: |q2| ≤ 1 GeV2
Constituent Quark Mass
3.2.2 Dilepton Rates: Hadronic vs. QGP
dRee /dM2 ~ ∫d3q f B(q0;T) Im em
• Hard-Thermal-Loop [Braaten et al ’90]
enhanced over Born rate
• Hadronic and QGP rates “degenerate” around ~Tc
• Quark-Hadron Duality at all M ?! ( degenerate axialvector SF!)
[qq→ee] [HTL]
-
• Relativistic Langevin simulations for heavy quarks in QGP fireball
4.2 Heavy-Quark Spectra in Au-Au at RHIC
[van Hees,Greco+RR ’05]
Nuclear Modification Factor
• factor 3-4 stronger effects due to resonance interactions• bottom quarks little affected
Elliptic FlowRAA≡ (spec)AA /(spec)pp
4.4 Heavy-Light Quark T-Matrix in QGP
)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T Qq02
• lattice-QCD based quark “potentials” FQQ =UQQ –T SQQ
• meson + diquark “resonances” up to ~1.5 Tc
[van Hees et al ‘08]
3.2 EM Spectral Function in VacuumR = (e+e → hadrons) / (e+e→) ~ Im em(M)
Imem ~ [Im D+ Im D/10 + Im D/5]
M ≤ 1 GeV: non-perturbative (vector-meson resonance)
M > 1.5 GeV: perturbative (qq continuum)
Im em ~ Nc ∑(eq)2
C)T(fMqxdd
dN Bee23
2
44Low-mass
dilepton rate:-mesondominated! Im D
√s=M-
e+
e-
e+
e-
q
q
-
R
3.4Meson in Cold Nuclear Matter
+ A → e+e X e+
e
Nuclear Photo-Production:
invariantmass
spectra
[Riek et al ’08]Theoretical Approach:
Mee[GeV]
Fe - Ti
N ≈ 0.5 0
N
elementary production amplitude
in-medium spectral function+
[CLAS/JLab ‘08]
well tested at high energies, Q2 > 1 GeV2:
• perturbation theory (s = g2/4π << 1)
• degrees of freedom = quarks + gluons
1.2 Quantum Chromodynamics (QCD)
2
41
aq Gq)m̂Agi(q QCDL
(mu ≈ md ≈ 5-10MeV )
[Nobel approved, 2004]
Q2 ≤ 1 GeV2 → transition to “strong” QCD:
• effective d.o.f. = hadrons (Confinement)• massive “constituent” quarks, mq* ≈ 350 MeV ≈ ⅓ Mp (Chiral Symmetry Breaking)
↕ ⅔ fm
4.7 Q-Q Bound States in the QGP: J/
J/ + g c + c + X←→ -
Suppression +Regeneration:
-
J/D
D -
J/c- c reaction equilibrium rate limit
Nuclear Modification Factors
Centrality Dependence Momentum Dependence
[Zhao+RR ’08, ‘09]
)NN(d
dN eq
4.1 Heavy-Quarks and Single-e± Spectra• Radiative energy-loss of heavy quarks?• Thermalization and collective flow? • Consistency?• experimental tool: electron spectra D,B → eX
c,b
pT [GeV/c]
RA
A =
(A
A)
/ (p
p)
Djordjevic etal. ‘04
Armesto etal.‘05
Elliptic Flow Nuclear Modification Factor
• radiative transport coefficient larger than theory (~ 3-5)q̂
[Armesto et al ’05]
?
• origin of strong interactions?• bottom “contamination”?
• 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
4.) Heavy Quarkonia in Medium4.1 Basic Elements and Connections to URHICs
[PBM etal ’01, Gorenstein etal ’02,Thews etal ’01, Ko etal ’02, Grandchamp+RR ’02, Cassing etal ‘03] J/ + g c + c + X←→ -
for thermal c-quarks and gluons:
5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS
Expanding Fireball + pQCD
• pQCD+Cronin at qt >1.6GeV T0=205MeV suff., HG dom.
• addt’l meson-Bremsstrahlung → K→K substantial at low qt
[Liu+ RR’05]
WA98 “Low-qt Anomaly”
[Turbide,RR+Gale’04]
• thermal radiation qt<3GeV ?!
• QGP window 1.5<qt<3GeV ?!
5.1.2 Thermal Photons II: RHIC
• also: -radiation off jets• shrinks QGP window qt<2GeV ?!
[Gale,Fries,Turbide,Srivastava ’04]
3.3.5 Charmonium Width+Mass from Lattice QCD
[Umeda+ Matsufuru ’05]using constrained curve fitting (Breit-Wigner functions)
c and J/ Width
• ”jumps” across Tc
• qualitatively consistent with partonic dissociation
c and J/ Mass
• essentially constant
3.5 Dilepton Spectra in Heavy-Ion Collisions (SPS)→ Evolve dilepton rates over thermal fireball expansion
• show in-medium broadening• normalized• “distorted” by exp. acceptance
+ Mass Spectra [NA60, 2005]
drop. mass (norm.)
M[GeV]
• quantitative agreement • exhibits Boltzmann slope (T)• invariant-mass spectrum!
Acc.-corrected+ Spectra [NA60, 2009]
M[GeV]
[van Hees+RR ’08]