exploring the qcd phase diagram · 2014. 6. 25. · droplets are stable in vacuum no stable...
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Exploring the QCD Phase Diagram
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The story gets more colorful ...
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Outline
● Introduction● Some remarks about the phase diagram● First order phase co-existence
– Dynamical treatment– observables
● Remarks about some results from the BES
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The Paradigm
T
ε/T4 RHIC LHC
Paradigm seems in good shape but can we establish that there is indeed a transition
RHIC and LHC look qualitatively similar:● Flow● R
AA
● Particle production● ….
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What we always see.... What it really means....
The Lattice EOS
“Tc” ~ 160 MeV
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Tc
Tc
1nd order 5th order
3th order0th order
Derivatives
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How to measure derivatives
Z=tr e− E /T /T N B
At μ = 0: ⟨E ⟩= 1Z
tr E e− E /T /T N B=− ∂∂1 /T
ln Z
⟨ E 2⟩=⟨E 2⟩−⟨E ⟩2=− ∂∂1 /T 2
ln Z =− ∂∂1 /T ⟨E ⟩
⟨ E n⟩=− ∂∂1/T
n−1
⟨E ⟩
Cumulants of Energy measure the derivatives of the EOS
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Tc
Tc
2nd order 6th order
4th order1st order
Fluctuations / Cumulants
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Another way
F=F (r) , r=√T 2+aμ2
T
μ
a~ curvature of critical line
∂μ2 F (T ,μ)μ=0=
aT
∂T F (T ,0)
∂μ4 F (T ,μ)μ=0=3
a2
T(T ∂T
2 −∂T)F (T , 0)
Baryon number cumulants give same info. Less problem with flow etc.
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Comments on Phase diagram
Liquid-GasWater, nuclear matter, ...
T
μ
1“gas”
2“liquid”
T
μ
“QCD”
1“hadron gas”
2“QGP-liquid”
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T
μ
1“gas”
2“liquid”
T
μ
1“gas” 2
“liquid”
Liquid-gas
Temperature
Pressure
“QCD”
2“QGP-liquid”
1“hadron gas”
1“hadron gas”
2“QGP-liquid”
Temperature
Pressure
“QCD”
Liquid-gas
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Difference between Liquid Gas and QCD PT
Dexheimer et al, arXiv:1302.2835
Clausius-Clapeyron: dPdT
=S1 /B1−S 2/ B2
1 /ρ1−1/ρ2
ρ2>ρ1 → (1 /ρ1−1/ρ2 )>0
dPdT
>0 →S 1/ B1>S 2/ B2
(SB)
gas>( S
B )liquid
dPdT
>0 →S 1/B1<S 2 /B2
( SB )
hadron−gas
<( SB )
QGP−liquid
1“gas” 2
“liquid”
Liquid-gas
Temperature
Pressure
1“hadron gas”
2“QGP-liquid”
Temperature
Pressure
“QCD”
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Liquid-gas vs QCD
T
P(T=0)co-exist
> 0!!!
T
P(T=0)co-exist
= 0
Droplets are stable in vacuum No stable droplets in vacuum
(SB )
gas>( S
B)liquid ( S
B )hadron−gas
<( SB )
QGP−liquid
μ μ
dPdt
<0dPdt
>0
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Liquid-gas vs QCD
QCD: pressure at T=Tc and μ=0 same as at T=0 and ρ ~ 2.5 ρ
0
If T=0 phase transition happens above 2.5 ρ0 → dP
dT<0
Note: virtually ALL model predicting a QCD critical point have dPdT
>0
Steinheimer et al, Phys.Rev. C89 (2014) 034901
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Liquid-gas vs QCD
Liquid Gas:T=0: Liquid co-exists with vacuum
QCD:T=0: Liquid co-exists with high
density nuclear matterSteinheimer et al, Phys.Rev. C89 (2014) 034901
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Lattice to the rescue?
Slope of pressurealong pseudo-critical line
Lattice data from Wuppertal/Budapest: Sign depends on definition of pseudo-critical line
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DOES IT MATTER?
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Oh, YES!
“QCD”
“Liquid-gas”
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Co-existence region
T
ρ
SpinodalRegion
System should spent long timein spinodal region
Spinodal instability:Mechanical instability
∂ p∂ϵ <0
Exponential growth of clumping
Non-equilibrium phenomenon!
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Phase-transition dynamics: Density clumping
With phase transition: Without phase transition: Density enhancement:
Evolution of density moments
Insert the modified pressure into existingideal finite-density fluid dynamics code
Use UrQMD for pre-equilibrium stageto obtain fluctuating initial conditions
Simulate central Pb+Pb collisions at ≈3 GeV/A beam kinetic energy on fixed target,using an Equation of State either with a phase transition or without (Maxwell partner):
Phase transition
Phase coexistence: surface tension Introduce a gradient term:
Phase separation: instabilities=>
J. Steinheimer & J. Randrup, PRL 109, 212301(2012) PRC 87, 054903 (2013)
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PQM (“liquid-gas”) “QCD”
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Time evolution
Higher pressure leads to faster evolution of “QCD” EoS.
Oscillation of nearlystable droplets for “liquid-gas” EoS
Steinheimer et al, Phys.Rev. C89 (2014) 034901
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PQM (“liquid-gas”) “QCD”
Flow
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Flow
Coordinate space Momentum space
Coordinate space asymmetries sensitive to nearly stable dropletformation in “liquid gas” EoS
Small pressure of liquid: Weak mapping into momentum space hardly any effect of instabilitiesIn case of “QCD” EoS
Steinheimer et al, Phys.Rev. C89 (2014) 034901
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Cluster a.k.a. nuclei
Even if total baryon number doesnot fluctuate the baryon density does
Therefore measure production of NUCLEI: d, 3He, 4He, 7Li....
⟨d ⟩~⟨B2 ⟩ ⟨3 He ⟩~⟨B
3 ⟩ ⟨7 Li ⟩∼⟨ρB7 ⟩
Extracts higher moments of the baryon density at freeze out
Nice Idea, but...
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“Cluster” formation
Clumping in coordinate space is compensated by dilution on momentum space → tiny effect
“QCD” EoS
( SB )
hadron−gas
<( SB )
QGP−liquid
Steinheimer et al, Phys.Rev. C89 (2014) 034901
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Back to
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STAR net-proton cumulants(Phys.Rev.Lett. 112 (2014) 032302)
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Things to consider
● Fluctuations of conserved charges ?!● Higher cumulants probe the tails. Statistics!● The detector “fluctuates” ! ● Net-protons different from net-baryons
– Isospin fluctuations
● Auto-correlations● Beware of the “Poissonizer”
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Auto CorrelationsLuo et al, arXiv:1303.2332
Strong correlation between multiplicity determination and proton cumulantsDue to baryon resonances
Need to determine multiplicity far away in rapidity from cumulants
Y
Δ
pπ
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STAR net-proton cumulants(Phys.Rev.Lett. 112 (2014) 032302)
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The “Poissonizer”
K4/K
2=5
STAR acceptance
(protons)
Fraction of BARYONSobserved
K4/K
2=1
K4/K
2=-1
K4/K
2=-5
NA49 “sees” 32 protons per unit rapidity at top SPS energies!!!
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Flow
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Particle and Anti-particle flow
Steinheimer et al Phys.Rev. C86 (2012) 044903 :● Excitation function of v
2
● Centrality dependence of freeze out parameters
Both agree with STAR measurement
Essential: stopping of baryon numberExplains difference in elliptic flow between protons and anti-protons.
Not yet included: Stopping of isospin.Qualitatively explains the trend seen for pions
Strangeness conservation: strangeness chemical Potential same sign as baryon chemical potential:Flow difference of kaons same sign as protons
Figure courtesy N. Xu
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Summary● Essential difference between liquid-gas and QCD EoS
● Important phenomenological consequences● Dynamical treatment of first order phase transition including
instabilities within fluid dynamics● Good tool for testing observables● So far no good observable for instabilities and droplet
formation● Higher order cumulants: Not there yet!
● Auto correlations● full therma phase space● Statistics at low energy
● Quark number scaling: Not rules out at low energy● Particle-anti particle v
2 : stopping!
● Need a statistically significant phi measurement
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BACKUP
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pt
dN/dpt
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Is there a critical point?
mu,d
ms
Cross Over
1storderpure glue
1storder
The worldwe live in
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Lattice and the critical pointForcrand, Philipsen
Favored by Lattice QCD
Note: Surface may bend back!!!
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Two Critical Points ?!M. Pinto et al, Phys.Rev. C82 (2010) 055205
Mπ~30 MeV
Two flavors
Seen in both Nambu and Linear Sigma Model
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Finite Acceptance(A. Bzdak and V.K., Phys.Rev. C86 (2012) 044904 and arXiv:1312.4574)
K4/K
2=5
STAR acceptance
(protons)
Fraction of BARYONSobserved
K4/K
2=1
K4/K
2=-1
K4/K
2=-5
Spoils the fun for Baryon cumulants
Electric Charge cumulants better. BUT issue with separation of (rapidity scales) at low energies
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pB, p
B_bar
Baryon Number ConservationA. Bzdak, V. Skokov, VK, Phys.Rev. C87 (2013) 014901
Protons only: < 1/2
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Finite AcceptanceA. Bzdak, VK; Phys.Rev. C86 (2012) 044904
Effect of conservation laws get reduced with finite acceptance:“Equilibration via ignorance”
Model with binomial distribution: p1,2
= probability to see particle, antiparticle
True distribution
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Finite Acceptance
True
Measured
Due to “acceptance” not only Cumulants of the the true distribution enter
N =N 1+N 2
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Requires measurement of factorial moments, f20
, f02
, f21
,.... with GOOD precision
Finite Acceptance
Unfolding?Can be done (in principle)
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Spinodal Multifragmentation
Ph Chomaz, M Colonna, J Randrup Nuclear Spinodal FragmentationPhysics Reports 389 (2004) 263
Fragments≈ equal!
Highly non-statistical => Good candidate signature
Nuclear EoS: Spinodal region:
1st order phase transtion
Spinodal instability
Density undulationsmay be amplified
Growth rates:
Spinodal pattern:
Tem
pera
ture
T (
MeV
)
J. RandrupCLUMPING of Baryon Density
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Input required for realistic estimate of conservation effects
Note: This is likely only to work at lower energies where we have baryon stoppingNote: at low energies anti-protons likely to be irrelevant
Need: ●Total number of protons and (anti-protons) (4 Pi)●Number of protons and (anti-protons) actually measured ●Total number of charged particles
Big Question: Over what rapidity range are the various charges conserved?● Balance Functions? Only averages!
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QCD vs HRG
QCD
“HRG”
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Generic Phase Diagram
T
μT,μ
σ, ρ
“Simply” use appropriate combination of T and μ
Requires: ⟨ E n⟩ ⟨ N Bn⟩ ⟨ E m N B
n ⟩ Mixed cumulants!
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Difference between Liquid Gas and QCD PT
Dexheimer et al, arXiv:1302.2835
Clausius-Clapeyron: dPdT
=S1 /B1−S 2/ B2
1 /ρ1−1/ρ2
11 2 2
ρ2>ρ1 → (1 /ρ1−1/ρ2 )>0
dPdT
>0 →S 1/ B1>S 2/ B2
(SB)
gas>( S
B )liquid
dPdT
>0 →S 1/B1<S 2 /B2
( SB )
hadron−gas
<( SB )
QGP−liquid
Liquid-gas “QCD”