Life Above the Hagedorn Temperature Quark-Gluon Plasma at SPS, RHIC & LHC
Berndt Mueller Brookhaven National Laboratory & Duke University
Hagedorn Symposium CERN 13 November 2015 1965 was a momentous year
cosmic microwave background Hagedorn mass spectrum
2 2015 almost unimaginable progress
RHIC 3He+Au
Planck: cosmological parameters PHENIX: QGP in p/d/3He+Au
3 Three things are needed…
…to reach the summit: good equipment, good strategy, determination.
In the study of hot, dense QCD matter this means:
• High luminosity colliders • Large acceptance, high DAQ rate detectors with good particle ID • Realistic lattice QCD for thermo- dynamic quantities • Realistic transport codes • Weak (pQCD) and strong (AdS/CFT) coupling dynamical models • Multivariate model-data comparison
After several decades of experimental and theoretical development, the necessary tools are now all in place.
4 The Relativistic Heavy Ion Collider
…is hexagonal and 3.8 km long
RHIC-AGS Complex at BNL
5 The Relativistic Heavy Ion Collider
…is hexagonal and 3.8 km long
RHIC-AGS Complex at BNL
5 The highest energies…
6 The highest energies…
CMS
ATLAS
6 Equation of State of QCD Matter
7 Equation of State
EOS of flowing matter has conservative and dissipative contributions:
(cons) (diss) Tµν = Tµν + Tµν
= (ε + p)uµuν − pgµν
2 α α +η(∂µ uν + ∂ν uµ − 3 gµν ∂α u ) +ζ gµν ∂α u
α When ζ(∂αu ) > p, the matter becomes unstable and cavitates.
In general, Tµν is a dynamical quantity that relaxes to its equilibrium value on a time scale τπ that itself is related to the viscosity.
While the shear viscosity η has a lower quantum bound, the bulk viscosity ζ vanishes for conformally invariant matter.
8 QCD EOS at μB = 0
Results (true quark masses, continuum extrapolated) have converged; full agreement found between groups (HotQCD, Wuppertal-Budapest) using different quark actions.
9 (Pseudo-) Critical temperature
Transition between hadron gas and quark-gluon plasma is a cross-over at µB = 0 and for small µB. Precise value of Tc depends on the quantity used to define it.
Pseudo-critical temperature from chiral susceptibility peak:
Tc = 154 ± 9 MeV
Uncertainty in Tc, not width of cross-over region!
10 Hadron mass spectrum
Below Tc, the quantity (ε−3p)/T4 measures the Hagedorn spectrum (TH ≈ 180 MeV): level density of massive hadronic excitations Aem/TH of the QCD vacuum. ρ m = H ( ) 2 2 5/4 (m + m0 ) Lines: Hadron resonance gas using only PDG resonances Data points: Lattice QCD LQCD lies above HRG for T > 140 MeV Indicates additional hadron resonances
11 Hadron mass spectrum
Below Tc, the quantity (ε−3p)/T4 measures the Hagedorn spectrum (TH ≈ 180 MeV): level density of massive hadronic excitations Aem/TH of the QCD vacuum. ρ m = H ( ) 2 2 5/4 (m + m0 ) Lines: Hadron resonance gas using only PDG resonances In good agreement with lattice results Data points: Lattice QCD Hadrons up to 3 GeV mass contribute LQCD lies above HRG for T > 140 MeV 4 Indicates additional hadron resonances Ê
Ê mcut = 3.0 GeV
3 Ê
mcut = 2.5 GeV 4 Ê T ê L Ê mcut = 2.0 GeV P 2 3 -
e Ê H mcut = 1.7 GeV
1 Ê
Ê Ê 0 100 110 120 130 140 150 160 170 T MeV
11
H L Probing the baryon spectrum
Consistency of µs/µB and µB/T with chemical composition of emitted hadrons and Lattice QCD requires additional strange baryon resonances beyond those in the PDG tables.
Quark model states of strange baryons
12 QCD EOS at μB ≠ 0 Borszanyi et al., arXiv:1204:6710
Approximate trajectories in QCD phase diagram 13 Probing the QCD Phase Boundary
14 QCD Phase Diagram
Lattice QCD LHC equation of state RHIC Borsanyi et al. Quark-Gluon
Critical end point ? 154±9 MeV Tc Plasma RHIC BES
Hadronic Matter Color Super- conductor
Nuclei Neutron µB stars
15 Thermodynamic fluctuations
Susceptibilities measure thermodynamic fluctuations. Interesting because they exhibit singularities at a critical point. Fluctuations of conserved quantities (charge Q, baryon number B,…) cannot be changed by local final-state processes.
Lattice gauge theory:
Ratios are independent of the (unknown) freeze-out volume:
16 Chemical freeze-out
… from fluctuations of conserved quantum numbers (Q, B):
Compare lattice results with the STAR data for the fluctuation ratios in the temperature range 140−150 MeV permits to read off µB. Both methods are consistent with each other and with the measured baryon/antibaryon ratios, if additional strange baryon states beyond those in the PDG tables (e.g. in the quark model) are accounted for.
17 Chemical freeze-out
hadron abundances fluctuations
Consistency of freeze-out parameters from mean hadron abundances and from fluctuations (Q, B) opens the door to search for a critical point in the QCD phase diagram by looking for enhanced critical fluctuations as function of beam energy.
18 Probing the Quark-Gluon Plasma
19 Hot QCD matter properties
Which properties of hot QCD matter can we hope to determine and how ?
20 Hot QCD matter properties
Which properties of hot QCD matter can we hope to determine and how ?
Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD
20 Hot QCD matter properties
Which properties of hot QCD matter can we hope to determine and how ?
Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 1 4 η = d x Txy (x)Txy (0) Shear viscosity: anisotropic collective flow T ∫ 4π 2α C ⎫ Very qˆ = s R dy− U †F a+i (y− )UF a+ (0) N 2 −1 ∫ i ⎪ Hard c ⎪ for 4π 2α C ⎪ eˆ = s R dy− iU † ∂− Aa+ (y− )UAa+ (0) Momentum/energy diffusion: LQCD 2 ∫ ⎬ Nc −1 ⎪ parton energy loss, jet fragmentation
4πα s † a0i a b0i b ⎪ κ = ∫ dτ U F (τ )t UF (0)t ⎪ 3Nc ⎭
20 Hot QCD matter properties
Which properties of hot QCD matter can we hope to determine and how ?
Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 1 4 η = d x Txy (x)Txy (0) Shear viscosity: anisotropic collective flow T ∫ 4π 2α C ⎫ Very qˆ = s R dy− U †F a+i (y− )UF a+ (0) N 2 −1 ∫ i ⎪ Hard c ⎪ for 4π 2α C ⎪ eˆ = s R dy− iU † ∂− Aa+ (y− )UAa+ (0) Momentum/energy diffusion: LQCD 2 ∫ ⎬ Nc −1 ⎪ parton energy loss, jet fragmentation
4πα s † a0i a b0i b ⎪ κ = ∫ dτ U F (τ )t UF (0)t ⎪ 3Nc ⎭ Hard Πµν (k) = d 4 x eikx j µ (x) jν (0) QGP Radiance: Lepton pairs, photons for em ∫ LQCD
20 Hot QCD matter properties
Which properties of hot QCD matter can we hope to determine and how ?
Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 1 4 η = d x Txy (x)Txy (0) Shear viscosity: anisotropic collective flow T ∫ 4π 2α C ⎫ Very qˆ = s R dy− U †F a+i (y− )UF a+ (0) N 2 −1 ∫ i ⎪ Hard c ⎪ for 4π 2α C ⎪ eˆ = s R dy− iU † ∂− Aa+ (y− )UAa+ (0) Momentum/energy diffusion: LQCD 2 ∫ ⎬ Nc −1 ⎪ parton energy loss, jet fragmentation
4πα s † a0i a b0i b ⎪ κ = ∫ dτ U F (τ )t UF (0)t ⎪ 3Nc ⎭ Hard Πµν (k) = d 4 x eikx j µ (x) jν (0) QGP Radiance: Lepton pairs, photons for em ∫ LQCD
Easy 1 † a a mD = − lim ln U E (x)UE (0) Color screening: Quarkonium states for |x|→∞ | x | LQCD 20 The “perfect” fluid
21 Viscous hydrodynamics
Hydrodynamics = effective theory of energy and momentum conservation
energy-momentum tensor = ideal fluid + dissipation
µν µν µ ν µν µν ∂µT = 0 with T = (ε + P)u u − Pg + Π µν λ ⎡ dΠ µ νλ ν µλ du ⎤ µ ν ν µ µν τ ⎢ + u Π + u Π ⎥ = η ∂ u + ∂ u − trace − Π Π d ( ) d ( ) ⎣ τ τ ⎦ Input: Equation of state P(ε), shear viscosity, initial conditions ε(x,0), uμ(x,0)
Shear viscosity η is normalized by density: kinematic viscosity η/ρ.
Relativistically, the appropriate normalization factor is the entropy density s = (ε+P)/T, because the particle density is not conserved: η/s.
22 Elliptic flow
• two nuclei collide rarely head-on, but mostly with an offset: Reaction z plane
only matter in the overlap area gets compressed and heated y
x
dN ⎛ ⎞ 2π = N0 ⎜1+ 2∑vn (pT ,η)cosn(φ −ψ n (pT ,η))⎟ dφ ⎝ n ⎠
anisotropic flow coefficients event plane angle
23 Event-by-event fluctuations
Initial state generated in A+A collision is grainy event plane ≠ reaction plane WMAP ⇒ eccentricities ε1, ε2, ε3, ε4, etc. ≠ 0
Idea: Energy density fluctuations in transverse plane from initial state quantum fluctuations. These thermalize to different temperatures locally and then propagate hydrodynamically to generate angular flow velocity fluctuations in the final state.
⇒ flows v1, v2, v3, v4,...
24 Elliptic flow “measures” ηQGP
Universal strong coupling limit of
Schenke, Jeon, Gale, PRL 106 (2011) 042301 non-abelian gauge theories with a gravity dual:
/s=0 η/s → 1/4π v η/s = 0 2 /s=0.08 /s=0.16 η/s = 1/4π aka: the “perfect” liquid 0.2 η/s = 2/4π 0.15
0.1 Au+Au 200 GeV 0.05 30-40% central STAR data 0 0 0.5 1 1.5 2 2.5
pT [GeV]
Schenke, Jeon, Gale, PRC 85 (2012) 024901
25 RHIC vs. LHC
Saturated Glasma Gale, Jeon, Schenke, Tribedy, Venugopalan, arXiv:1209.6330
LHC MC-Glauber
0.7 0.6 BM & A. Schäfer, PRD 85 (2012) 114030 0.5 RHIC e ê 0.4 De 0.3 0.2 0.1 0.0 0.2 0.4 0.6 0.8 z fm
26 H L Shape engineering: U+U collisions
STAR
Constituent-quark Glauber model and IP-Glasma model are consistent with the observations, but not the nucleon-nucleon based Glauber model.
→ Initial state fluctuations are driven by interactions at the sub-nucleonic level
27 Discovery by model-data comparison
Data: Model: initial conditions, τ0, η/s, ζ/s, ….
ALICE
102 p >0.5 GeV, |η|<2.5 p >0.5 GeV, |η|<2.5 p >0.5 GeV, |η|<2.5 Glauber 20-25% .L1 20-25% T T T ATLAS Pb+Pb ATLAS Pb+Pb ATLAS Pb+Pb 10 0oGel sNN=2.76 TeV sNN=2.76 TeV sNN=2.76 TeV -1 10 -1 -1 ATLAS Lint = 7 µb Lint = 7 µb Lint = 7 µb
1 ) 2 v ) ) ) ( 2 3 4
10 P p(v p(v p(v 1 -1 10 centrality: centrality: centrality: 0-1% 0-1% 0-1% 5-10% 5-10% 5-10% 20-25% 20-25% 20-25% 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 -2 30-35% 30-35% 30-35% 10 v v 40-45% 10-1 40-45% 40-45% 2 2 60-65% 1 0 0.1 0.2 0 0.05 0.1 0 0.01 0.02 0.03 0.04 0.05
v2 v3 v4 extracted QGP properties:28 η/s, … Flow Analysis of QGP Properties at the LHC
Posterior: emulator predictions for Key Results: highest likelihood parameter values Data: • excellent agreement with data, • ALICE v2, v3 & v4 flow cumulants simultaneous description of v2, v3 • identified particle spectra and v4 data • identified particle mean pT • initial condition favors scaling properties of IP-Glasma Model: • non-zero bulk viscosity • EbE VISHNU • temperature dependence of η/s requires data at several beam Parameter Space: energies to pin down • Trento initial condition: • p: entropy deposition • k: nucleon fluctuation • w: Gaussian nucleon width • specific shear viscosity η/s slope and intercept at TC • normalization scale for ζ/s • hydro to micro switching temperature Tsw
Analysis Design: • 6 centrality bins • 300 point Latin Hypercube • total of 10,000,000 events • Gaussian Process Emulators for interpolation between LH points use MCMC for analysis 29 Calibrated Explicit model calculations (no emulator): posterior distributions:
Temperature-dependent viscosities J. Bernhard from the calibrated posterior: S. Moreland S.A. Bass
30 How small can a QGP be?
N saturation scale Q2 ∝ cl s π L2 Ncl mean free path ℓ ∝Q −1 mfp s
final multiplicity dN / dy ∝ Ncl
2L Basar & Teaney, 1312.6770 ℓ 1 1 Size scales out of Re = mfp ∝ ∝ Reynolds number: L Q L dN / dy s This does not mean that hydrodynamics applies for a given dN/dy, but it suggests that the transport is independent of size.
31 How small can a QGP droplet be? arXiv: 1404.7461v1
Very successful 3-week run resulted in RHIC 3He+Au 2.2 billion recorded minimum bias 3He +Au collisions (PHENIX)
Characteristic differential elliptic flow for hadrons of different mass
Evidence for strong coupling? 32 QGP Chemistry
33 Strangeness enhanced
2 N(s ) 1 ⎛ m ⎞ /(3T ) The original idea (Rafelski): = s K m / T eµB = 1! 5 ⎝⎜ ⎠⎟ 2 ( s ) N(q) 2 T
“We almost always have more s than u or d quarks. When quark matter reassembles into hadrons, some of the numerous s quarks may, instead of being bound into kaons, form multiply strange antibaryons, such as Λ , Ξ , Ω .”
gg → s s is essential for rapid strangeness equilibration ! (JR & BM)
Almost 30 years of investigation: The liberation of quark and gluon degrees of freedom (not necessarily thermalization) is required for strangeness equilibration.
34 s-enhancement at SPS
NA57 measured enhanced strange baryon yields in Pb+Pb collisions at 158 GeV/c
(sss)
(qss)
(qqs)
35 s-enhancement at RHIC
(sss)
(qss)
(qqs)
★ STAR ★ STAR
36 s-enhancement at LHC Strangeness enhancement grows with fireball size (or life-time) and saturates at grans canonical equilibrium in Pb+Pb collisions
37 Size dependence of s-enhancement
Canonical equilibrium gives reasonable fit, but effect of finite life-time of QGP needs to be also explored.
38 v2(pT) vs. hydrodynamics
39 v2(pT) vs. hydrodynamics
Mass splitting characteristic property of hydrodynamics
39 v2(pT) vs. hydrodynamics
Failure of ideal hydrodynamics tells us how hadrons form
Mass splitting characteristic property of hydrodynamics
39 Quark number scaling of v2
In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :
T,µ,v
40 Quark number scaling of v2
In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :
T,µ,v
Emitting medium is composed of unconfined, flowing quarks.
40 Color screening & color opacity
41 Jet quenching Toward quantitative measurement of basic medium properties: q-hat
q T dE q dE = −C2α s qˆ L = −C2 eˆ dx dx Radiative Collisional
JET Collaboration
qˆ ⎧4.6 ±1.2 at RHIC 3 = ⎨ T ⎩3.7 ±1.4 at LHC Phys. Rev. C 90 (2014) 014909
QGP @ RHIC is slightly more strongly coupled than QGP@ LHC.
42 Quarkonium “melting” Color screening
Ionization
Charmonium states “melt” in the QGP but can be regenerated by recombination when Recombination the charm quark density is high (at LHC).
Resolved measurement of Upsilon states required at RHIC.
43 Future of RHIC
44 Completing the RHIC science mission
Status: RHIC-II configuration is complete • Vertex detectors in STAR (HFT) and PHENIX STAR HFT • Luminosity reaches 25x design luminosity Plan: Complete the RHIC mission in 3 campaigns: § 2014–17: Heavy flavor probes of the QGP using the micro-vertex detectors; Transverse spin physics § 2018: Install low energy e-cooling (LEReC) § 2019/20: High precision scan of the QCD phase diagram & search for critical point § Install sPHENIX § Probe QGP with precision measurements of jet quenching and Upsilon suppression sPHENIX § Spin physics and initial conditions at forward rapidities with p+p and p+A collisions ? § Transition to eRHIC ? LEReC
45 Critical fluctuations in BES-II Model independent structure of 300 200 √s = 62.4 GeV The Phases of QCD net baryon number kurtosis 2760 39 250 27 19.6 14.5 Quark-Gluon Plasma 200 11.5
BES-II 9.1 Possible Scenario 150 st 7.7 − 1 Near Critical Point 1 Orde r Ph 2 ase Tra 100 ns
Critical κσ itio Point? n Temperature (MeV) Color 50 Superconductor Hadron GasNuclear Vacuum Mater 0 0 200 400 600 800 1000 1200 1400 1600
Baryon Chemical Potential μB(MeV)
Top 5% Au+Au Collisions at RHIC
TPC iTPC STAR 19.6GeV Data 12.5 STAR 7.7GeV Data iTPC 0.4 < pT < 2 GeV/c 0.4 < pT < 2 GeV/c 2 0.4 < p < 0.8 GeV/c σ 10 T 1 Estimated BES-II Error
7.5 AMPT-SM 0 5 iTPC Net-proton k* 2.5 -1 Estimated BES-II Error 0 AMPT-SM TPC iTPC 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Proton Rapidity Width ∆yp 46 Probing scales in the medium
How does the perfect 50 sPHENIX fluidity of the QGP emerge from the asymptotically free vacuum theory of QCD?
10 LHC medium vacuum resolving power [1/fm] resolving thermal scale Jets probe sub-thermal medium 5RHIC Υ(1s) length scales microscopic Υ(2s) Upsilon states probe Υ(3s) thermal length scales 1 Tc 2Tc 3Tc perfect liquid temperature
47 Jets & Upsilon states
sPHENIX capabilities
Complete calorimetric jet spectroscopy
Completely resolved Upsilon spectroscopy
48 Beyond the Hagedorn temperature…
… lies the liquid QGP - a remarkable discovery by any measure.
Imagine: Heating a liquid (nuclear matter) turns it into vapor, i.e. a nucleon/hadron gas, at approximately 100 billion degrees.
But when we heat it to 20 times this temperature (2 trillion degrees) we find that it suddenly turns into a liquid again, in fact, into the most perfect liquid ever observed.
How is this possible?
It is still a mystery, but precise study of hard probes of various scales at RHIC and LHC, combined with comparative model-data analysis, will resolve the mystery within the next decade.
Rolf Hagedorn would surely be pleased!
49