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Searching for QCD critical point theoretical overview M. Stephanov - - PowerPoint PPT Presentation

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Searching for QCD critical point theoretical overview M. Stephanov M. Stephanov QCD critical point search Fudan 2017 1 / 40 History Cagniard de la Tour (1822): discovered continuos transition from liquid to vapour by heating alcohol, water,

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Searching for QCD critical point

theoretical overview

  • M. Stephanov
  • M. Stephanov

QCD critical point search Fudan 2017 1 / 40

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History

Cagniard de la Tour (1822): discovered continuos transition from liquid to vapour by heating alcohol, water, etc. in a gun barrel, glass tubes.

  • M. Stephanov

QCD critical point search Fudan 2017 2 / 40

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Name

Faraday (1844) – liquefying gases:

“Cagniard de la Tour made an experiment some years ago which gave me

  • ccasion to want a new word.”

Mendeleev (1860) – measured vanishing of liquid-vapour surface tension: “Absolute boiling temperature”. Andrews (1869) – systematic studies of many substances established continuity of vapour-liquid phases. Coined the name “critical point”.

  • M. Stephanov

QCD critical point search Fudan 2017 3 / 40

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Theory

van der Waals (1879) – in “On the continuity of the gas and liquid state” (PhD thesis) wrote e.o.s. with a critical point. Smoluchowski, Einstein (1908,1910) – explained critical opalescence. Landau – classical theory of critical phenomena Fisher, Kadanoff, Wilson – scaling, full fluctuation theory based on RG.

  • M. Stephanov

QCD critical point search Fudan 2017 4 / 40

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Critical point is a ubiquitous phenomenon

  • M. Stephanov

QCD critical point search Fudan 2017 5 / 40

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Critical point between the QGP and hadron gas phases?

QCD is a relativistic theory of a fundamental force. CP is a singularity of EOS, anchors the 1st order transition.

Quarkyonic regime

QGP (liquid)

critical point

nuclear matter

hadron gas ? CFL+ ?

  • M. Stephanov

QCD critical point search Fudan 2017 6 / 40

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Critical point between the QGP and hadron gas phases?

QCD is a relativistic theory of a fundamental force. CP is a singularity of EOS, anchors the 1st order transition.

Quarkyonic regime

QGP (liquid)

critical point

nuclear matter

hadron gas ? CFL+ ?

Lattice QCD at µB 2T – a crossover. C.P . is ubiquitous in models (NJL, RM, Holog., Strong coupl. LQCD, . . . )

  • M. Stephanov

QCD critical point search Fudan 2017 6 / 40

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Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. The sign problem restricts reliable lat- tice calculations to µB = 0. Under different assumptions one can estimate the position of the critical point, assuming it exists, by extrapo- lation from µ = 0.

LTE03 LR01 LR04 LTE08 LTE04 50 100 150 200 400 800 600 200

T, MeV µB, MeV

Heavy-ion collisions.

  • M. Stephanov

QCD critical point search Fudan 2017 7 / 40

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Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. The sign problem restricts reliable lat- tice calculations to µB = 0. Under different assumptions one can estimate the position of the critical point, assuming it exists, by extrapo- lation from µ = 0.

LTE03 LR01 LR04 LTE08 LTE04 130 9 5 2 17 50 100 150 200 400 800 600 200

T, MeV µB, MeV

Heavy-ion collisions.

  • M. Stephanov

QCD critical point search Fudan 2017 7 / 40

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Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. The sign problem restricts reliable lat- tice calculations to µB = 0. Under different assumptions one can estimate the position of the critical point, assuming it exists, by extrapo- lation from µ = 0.

LTE03 LR01 LR04 LTE08 LTE04 130 9 5 2 17 50 100 150 200 400 800 600 200

R H I C s c a n T, MeV µB, MeV

Heavy-ion collisions.

  • M. Stephanov

QCD critical point search Fudan 2017 7 / 40

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Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. The sign problem restricts reliable lat- tice calculations to µB = 0. Under different assumptions one can estimate the position of the critical point, assuming it exists, by extrapo- lation from µ = 0.

LTE03 LR01 LR04 LTE08 LTE04 130 9 5 2 17 50 100 150 200 400 800 600 200

R H I C s c a n T, MeV µB, MeV

Heavy-ion collisions. Non-equilibrium.

  • M. Stephanov

QCD critical point search Fudan 2017 7 / 40

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Outline

Equilibrium Non-equilibrium Experimental hints

  • M. Stephanov

QCD critical point search Fudan 2017 8 / 40

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Why fluctuations are large at a critical point?

The key equation: P(σ) ∼ eS(σ) (Einstein 1910)

  • M. Stephanov

QCD critical point search Fudan 2017 9 / 40

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Why fluctuations are large at a critical point?

The key equation: P(σ) ∼ eS(σ) (Einstein 1910)

  • M. Stephanov

QCD critical point search Fudan 2017 9 / 40

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Why fluctuations are large at a critical point?

The key equation: P(σ) ∼ eS(σ) (Einstein 1910) At the critical point S(σ) “flattens”. And χ ≡ σ2/V → ∞.

CLT?

  • M. Stephanov

QCD critical point search Fudan 2017 9 / 40

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Why fluctuations are large at a critical point?

The key equation: P(σ) ∼ eS(σ) (Einstein 1910) At the critical point S(σ) “flattens”. And χ ≡ σ2/V → ∞.

CLT? σ is not a sum of ∞ many uncorrelated contributions: ξ → ∞

  • M. Stephanov

QCD critical point search Fudan 2017 9 / 40

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Higher order cumulants

Higher cumulants (shape of P(σ)) depend stronger on ξ. E.g., σ2 ∼ V ξ2 while σ4c ∼ V ξ7

[PRL102(2009)032301]

Higher moment sign depends on which side of the CP we are. This dependence is also universal.

[PRL107(2011)052301]

Using Ising model variables:

  • M. Stephanov

QCD critical point search Fudan 2017 10 / 40

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Experiments do not measure σ.

  • M. Stephanov

QCD critical point search Fudan 2017 11 / 40

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Critical fluctuations and experimental observables

Observed fluctuations are related to fluctuations of σ.

[MS-Rajagopal-Shuryak PRD60(1999)114028; MS PRL102(2009)032301]

Think of a collective mode described by field σ such that m = m(σ): δnp = δnfree

p

+ ∂np ∂σ × δσ The cumulants of multiplicity M ≡

  • p np:

(MP ∼ nB × ∆y) κ4[M] = M

  • baseline

+ κ4[σ] × g4 4

  • ∼M4
  • this is ˆ

κ4(a.k.a.CBzdak-Koch

4

)

+ . . . ,

  • M. Stephanov

QCD critical point search Fudan 2017 12 / 40

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Mapping Ising to QCD phase diagram

T vs µB: In QCD (t, H) → (µ − µCP, T − TCP)

  • M. Stephanov

QCD critical point search Fudan 2017 13 / 40

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Mapping Ising to QCD phase diagram

T vs µB: In QCD (t, H) → (µ − µCP, T − TCP)

  • M. Stephanov

QCD critical point search Fudan 2017 13 / 40

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Mapping Ising to QCD phase diagram

T vs µB: In QCD (t, H) → (µ − µCP, T − TCP) κn(N) = N + O(κn(σ))

  • M. Stephanov

QCD critical point search Fudan 2017 13 / 40

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Beam Energy Scan

  • M. Stephanov

QCD critical point search Fudan 2017 14 / 40

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Beam Energy Scan

  • M. Stephanov

QCD critical point search Fudan 2017 14 / 40

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Beam Energy Scan

  • M. Stephanov

QCD critical point search Fudan 2017 14 / 40

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Beam Energy Scan

“intriguing hint” (2015 LRPNS)

  • M. Stephanov

QCD critical point search Fudan 2017 14 / 40

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Large µB: n4

B vs ξ7

The cumulants of multiplicity M ≡

  • p np:

(MP ∼ nB × ∆y) κ4[M] = M

  • baseline

+ κ4[σ] × g4 4

  • ∼M4

+ . . . , ˆ κ4[M] ≈ g4κ4[σ]M4 ∼ ξ7 × n4

B

  • compete at large µB

× (∆y)4.

[Athanasiou-Rajagopal-MS]

The ratio ˆ κ4[M] n4

B

  • r ˆ

κ4[M] M4 ∼ κ4[σ] ∼ ξ7.

  • M. Stephanov

QCD critical point search Fudan 2017 15 / 40

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Bzdak

ˆ κ4/M 4 Speculative, but: qualitatively (signs of) deviations from the baseline seem in agreement with C.P . expectations.

  • M. Stephanov

QCD critical point search Fudan 2017 16 / 40

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Non-equilibrium physics is essential near the critical point. The goal for

  • M. Stephanov

QCD critical point search Fudan 2017 17 / 40

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Why ξ is finite

System expands and is out of equilibrium Kibble-Zurek mechanism: Critical slowing down means τrelax ∼ ξz. Given τrelax τ (expansion time scale): ξ τ 1/z, z ≈ 3 (universal).

  • M. Stephanov

QCD critical point search Fudan 2017 18 / 40

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Why ξ is finite

System expands and is out of equilibrium Kibble-Zurek mechanism: Critical slowing down means τrelax ∼ ξz. Given τrelax τ (expansion time scale): ξ τ 1/z, z ≈ 3 (universal).

Estimates: ξ ∼ 2 − 3 fm (Berdnikov-Rajagopal) KZ scaling for ξ(t) and cumulants (Mukherjee-Venugopalan-Yin)

  • M. Stephanov

QCD critical point search Fudan 2017 18 / 40

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Lessons

κn ∼ ξp and ξmax ∼ τ 1/z Therefore, the magnitude of fluctuation signals is determined by non-equilibrium physics.

  • M. Stephanov

QCD critical point search Fudan 2017 19 / 40

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Lessons

κn ∼ ξp and ξmax ∼ τ 1/z Therefore, the magnitude of fluctuation signals is determined by non-equilibrium physics. Logic so far: Equilibrium fluctuations + a non-equilibrium effect (finite ξ) − → Observable critical fluctuations

  • M. Stephanov

QCD critical point search Fudan 2017 19 / 40

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Lessons

κn ∼ ξp and ξmax ∼ τ 1/z Therefore, the magnitude of fluctuation signals is determined by non-equilibrium physics. Logic so far: Equilibrium fluctuations + a non-equilibrium effect (finite ξ) − → Observable critical fluctuations Can we get critical fluctuations from hydrodynamics directly?

  • M. Stephanov

QCD critical point search Fudan 2017 19 / 40

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Time evolution of cumulants (memory)

Mukherjee-Venugopalan-Yin Relaxation to equilibrium dP(σ0) dτ = F[P(σ0)] ⇓ dκn dτ = L[κn, κn−1, . . .]

  • M. Stephanov

QCD critical point search Fudan 2017 20 / 40

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Time evolution of cumulants (memory)

Mukherjee-Venugopalan-Yin Relaxation to equilibrium dP(σ0) dτ = F[P(σ0)] ⇓ dκn dτ = L[κn, κn−1, . . .]

κ3 κ4 Signs of cumulants can depend on off-equilibrium dynamics. Memory.

  • M. Stephanov

QCD critical point search Fudan 2017 20 / 40

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Time evolution of cumulants (memory)

Mukherjee-Venugopalan-Yin Relaxation to equilibrium dP(σ0) dτ = F[P(σ0)] ⇓ dκn dτ = L[κn, κn−1, . . .]

κ3 κ4 Signs of cumulants can depend on off-equilibrium dynamics. Memory.

  • M. Stephanov

QCD critical point search Fudan 2017 20 / 40

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Time evolution of cumulants (memory)

Mukherjee-Venugopalan-Yin Relaxation to equilibrium dP(σ0) dτ = F[P(σ0)] ⇓ dκn dτ = L[κn, κn−1, . . .]

κ3 κ4 Signs of cumulants can depend on off-equilibrium dynamics. Memory.

  • M. Stephanov

QCD critical point search Fudan 2017 20 / 40

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Connecting theory and experiment

(talks at CPOD2017)

Develop EOS with critical point which also matches available lat- tice data Schmidt,Parotto Implement it into a realistic hydro simulation Shen, Yin, Song, . . . Compare with experiments to constrain parameters of the critical point: position, non-universal amplitudes, angles, etc. Auvinen

  • M. Stephanov

QCD critical point search Fudan 2017 21 / 40

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Lattice

Schmidt

Ratios of Taylor coeffs. are estimators of the radius of conver- gence. Cannot predict, or exclude, C.P . without assumptions about asymptotics.

  • M. Stephanov

QCD critical point search Fudan 2017 22 / 40

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Lattice

Schmidt

Critical point is not always the nearest singularity. E.g.: The convergence radius at Tc for mq = 0 is zero (hep-lat/0603014).

  • M. Stephanov

QCD critical point search Fudan 2017 23 / 40

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Parameterized EOS for hydro simulations

  • M. Stephanov

QCD critical point search Fudan 2017 24 / 40

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Hydrodynamic simulations

Baryon stopping and diffusion:

Shen

Hydrodynamical evolution with sources

net baryon density

24/32 Chun Shen McGill Nuclear seminar Chun Shen 15/24 CPOD 2017

valence quark + LEXUS x η

psNN = 19.6 GeV

  • M. Stephanov

QCD critical point search Fudan 2017 25 / 40

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Hydrodynamic simulations

Baryon stopping and diffusion:

Shen

Effects of net baryon diffusion on particle yields

  • More net baryon numbers are transported to mid-rapidity

with a larger diffusion constant

0-5% 0-5%

Constraints on net baryon diffusion and initial condition

Chun Shen 20/24

AuAu@19.6 GeV

  • C. Shen, G. Denicol, C. Gale, S. Jeon, A. Monnai, B. Schenke, in preparation

κB = CB T ρB 1 3 coth µB T

  • − ρBT

e + P

  • CPOD 2017
  • M. Stephanov

QCD critical point search Fudan 2017 25 / 40

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Critical slowing down and hydrodynamics

Yin

  • M. Stephanov

QCD critical point search Fudan 2017 26 / 40

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Hydro+

  • M. Stephanov

QCD critical point search Fudan 2017 27 / 40

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Hydro+

  • M. Stephanov

QCD critical point search Fudan 2017 28 / 40

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Hydrodynamic fluctuations

Initial state fluctuations: Long rapidity correlations vn’s Thermo/hydro-dynamic fluctuations. Correlations over rapidity ∆ycorr ∼ 1. Critical fluctuations. Even for ξ = 2 − 3 fm ∆η = ξ/τ ≪ 1.

  • M. Stephanov

QCD critical point search Fudan 2017 29 / 40

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Dynamics of fluctuations

Thermal fluctuations need time to equilibrate.

initial geometry fluctuation

late times earlier times

Some modes could remain out of eqlbm. Dynamics of fluctuations: Mazeliauskas, Teaney, Lau, Song (Hydro with noise [Mueller-Kapusta-MS], but deterministic description.) This is especially true near critical point due to critical slowing down. This is the origin of the Hydro+ modes (more in Yin’s talk)

  • M. Stephanov

QCD critical point search Fudan 2017 30 / 40

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Experiments

  • M. Stephanov

QCD critical point search Fudan 2017 31 / 40

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STAR

Net-Proton Fourth-Order Fluctuation

Ø Non-monotonic energy dependence is observed for 4th order net-proton, proton fluctuations in most central Au+Au collisions. Ø UrQMD results show monotonic decrease with decreasing collision energy.

STAR Preliminary

𝜆𝜏5 = 𝐷2 𝐷5

Roli Esha (UCLA) August 7, 2017 11

  • M. Stephanov

QCD critical point search Fudan 2017 32 / 40

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  • M. Stephanov. J. Physics G.: Nucl. Part. Phys. 38 (2011) 124147

Control Measurements for CEP Sig ignatures

Need data here!

STAR PRELIMINARY

FXT

κσ2 Preliminary HADES result, Quark Matter 2017

0-10% (QM 2017)

Systematic uncertainties included

 FXT measurements needed to determine shape of kσ2 observable at lower energies

8/11/2017 Kathryn Meehan -- UC Davis/LBNL -- CPOD 2017 6

Peak behavior predicted in critical region:

  • M. Stephanov

QCD critical point search Fudan 2017 33 / 40

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  • M. Stephanov. J. Physics G.: Nucl. Part. Phys. 38 (2011) 124147

Control Measurements for CEP Sig ignatures

Need data here!

STAR PRELIMINARY

FXT

κσ2 Preliminary HADES result, Quark Matter 2017

0-10% (QM 2017)

Systematic uncertainties included

 FXT measurements needed to determine shape of kσ2 observable at lower energies

8/11/2017 Kathryn Meehan -- UC Davis/LBNL -- CPOD 2017 6

Peak behavior predicted in critical region:

To draw physics conclusions from this comparison, one needs to take into account rapidity acceptance ∆y, different in the experiments.

Bzdak, Holzmann

  • M. Stephanov

QCD critical point search Fudan 2017 33 / 40

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Acceptance dependence

The acceptance dependence consistent with ∆yn−1

(Ling-MS 1512.09125; Bzdak-Koch 1607.07375)

As long as ∆y ≪ ∆ycorr the correlators ˆ κn count the number of n-plets in acceptance.

  • M. Stephanov

QCD critical point search Fudan 2017 34 / 40

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Factorial cumulants

More precisely, the scaling with ∆y is for factorial cumulants (ˆ κn or Cn). Because they isolate irreducible n-point correlations. Normal cumulants (n > 2) are deviations from normal distribution. Factorial cumulants – from Poisson distribution.

  • M. Stephanov

QCD critical point search Fudan 2017 35 / 40

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Physics of correlations

One can describe the correlations in the language of “clusters” (Bzdak). Or, more physically, repuslive mean-field (Petreczky). The correlations induced by critical mode have similar effect. Isospin blind n-particle correlations. Characteristic non-monotonous √s dependence. The size of the “cluster” of order number of particles within ξ3 (qualitatively).

  • M. Stephanov

QCD critical point search Fudan 2017 36 / 40

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QM/CPOD-2017 update: two-point correlations

Preliminary, but very interesting:

Rapidity Correlations Click to edit Master subtitle style W.J. Llope for STAR, CPOD2017, Aug. 8-11, 2017, Stony Brook, NY 21

R2(Δy,Δφ) for LS pions vs. √sNN, 0-5% central, convolution

✩Preliminary

7.7 GeV 11.5 GeV 14.5 GeV 19.6 GeV 27 GeV 39 GeV 62.4 GeV 200 GeV

  • W. Llope

Why this is interesting: Non-monotonous √s dependence with max near 19 GeV. Charge/isospin blind. ∆φ “ridge” as expected from critical correlations. Width ∆η suggests soft pions – but pT dependence need to be checked. Why no signal in R2 for K or p?

  • M. Stephanov

QCD critical point search Fudan 2017 37 / 40

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Summary

A fundamental question for Heavy-Ion collision experiments: Is there a critical point on the boundary between QGP and hadron gas phases? Quantitative theoretical framework is needed ⇒ . Large (non-gaussian) fluctuations – universal signature of a crit- ical point. In H.I.C., the magnitude of the signatures is controlled by dy- namical non-equilibrium effects. The physics of the interplay of critical and dynamical phenomena can be captured in Hydro+. Intriguing results from experiments (BES-I). More to come (BES-II, FAIR/CBM, NICA, J-PARK).

  • M. Stephanov

QCD critical point search Fudan 2017 38 / 40

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More

  • M. Stephanov

QCD critical point search Fudan 2017 39 / 40

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Spinodal region

[An-Mesterhazy-MS]

Fonseca-Zamolodchikov conjecture: spinodal point is off the real axis

  • f H.

Spinodal singularity is an artefact of the mean field approximation. No thermodynamics in the metastabe/unstable region. Question: What is the meaning of EOS?

  • M. Stephanov

QCD critical point search Fudan 2017 40 / 40