Fluctuations and the QCD Critical Point M. Stephanov UIC M. - - PowerPoint PPT Presentation

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Fluctuations and the QCD Critical Point M. Stephanov UIC M. - - PowerPoint PPT Presentation

Oct 18, 2023 327 likes •616 views

Fluctuations and the QCD Critical Point M. Stephanov UIC M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 1 / 15 Outline QCD phase diagram, critical point and fluctuations 1 Critical fluctuations and correlation

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Fluctuations and the QCD Critical Point

  • M. Stephanov

UIC

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 1 / 15

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Outline

1

QCD phase diagram, critical point and fluctuations Critical fluctuations and correlation length Non-gaussian moments and universality

2

Beam energy scan Mapping to QCD and observables Intriguing data from RHIC BES I Acceptance dependence

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 2 / 15

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QCD Phase Diagram (a theorist’s view)

Quarkyonic regime

QGP (liquid)

critical point

nuclear matter

hadron gas ? CFL+ ?

Lattice at µB 2T

Critical point – a fundamental feature of QCD phase diagram and a major goal for H.I.C.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 3 / 15

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Why fluctuations are large at a critical point?

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

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 4 / 15

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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 (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 4 / 15

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SLIDE 6

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 (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 4 / 15

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SLIDE 7

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 (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 4 / 15

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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 Higher moments also depend on which side of the CP we are. This dependence is also universal. Using Ising model variables:

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 5 / 15

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Why ξ is finite

System expands and is out of equilibrium In this talk – equilibrium fluctuations. The only dynamical effect we consider is the one which makes ξ finite: Critical slowing down. Universal scaling law: ξ ∼ τ 1/z, where 1/τ is expansion rate and z ≈ 3 (Son-MS).

Estimates: ξ ∼ 2 − 3 fm (Berdnikov-Rajagopal, Asakawa-Nonaka).

Dynamical description of fluctuations is essential and is work in progress.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 6 / 15

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Experiments do not measure σ.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 7 / 15

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Mapping to QCD and experimental observables

Observed fluctuations are not the same as σ, but related: 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:

κ4[M] = M

  • baseline

+ κ4[σ] × g4 4

  • ∼M4

+ . . . , g – coupling of the critical mode (g = dm/dσ).

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 8 / 15

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Mapping to QCD and experimental observables

Observed fluctuations are not the same as σ, but related: 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:

κ4[M] = M

  • baseline

+ κ4[σ] × g4 4

  • ∼M4

+ . . . , g – coupling of the critical mode (g = dm/dσ). κ4[σ] < 0 means κ4[M] < baseline

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 8 / 15

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Mapping to QCD and experimental observables

Observed fluctuations are not the same as σ, but related: 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:

κ4[M] = M

  • baseline

+ κ4[σ] × g4 4

  • ∼M4

+ . . . , g – coupling of the critical mode (g = dm/dσ). κ4[σ] < 0 means κ4[M] < baseline NB: Sensitivity to Maccepted: (κ4)σ ∼ M4 (number of 4-tets).

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 8 / 15

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Beam Energy Scan

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15

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Beam Energy Scan

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15

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Beam Energy Scan

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15

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SLIDE 17

Beam Energy Scan

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15

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Beam Energy Scan

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15

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Beam Energy Scan

“intriguing hint” (2015 LRPNS)

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15

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QM2017 update: another intriguing hint

Preliminary, but very interesting: Non-monotonous √s dependence with max near 19 GeV. Charge/isospin blind. ∆φ (in)dependence is as expected from critical correlations. Width ∆η suggests soft thermal pions – but pT dependence need to be checked. But: no signal in R2 for K or p.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 10 / 15

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Acceptance dependence

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 11 / 15

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Correlations – spatial vs kinematic

ξ ∼ 1 − 3 fm ∆ηcorr = ξ τf ∼ 0.1 − 0.3 Particles within ∆ηcorr have thermal rapidity

  • spread. Thus

∆ycorr ∼ 1 ≫ ∆ηcorr

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 12 / 15

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Acceptance dependence – two regimes

How do cumulants depend on acceptance? Let κn(M) be a cumulant of M – multiplicity of accepted, say, protons. ∆y ≫ ∆ycorr – CLT applies. κn ∼ M

  • r ωn ≡ κn

M → const – an “intensive”, or volume indep. measure

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 13 / 15

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Acceptance dependence – two regimes

How do cumulants depend on acceptance? Let κn(M) be a cumulant of M – multiplicity of accepted, say, protons. ∆y ≫ ∆ycorr – CLT applies. κn ∼ M

  • r ωn ≡ κn

M → const – an “intensive”, or volume indep. measure ∆y ≪ ∆ycorr – more typical in experiment. Subtracting trivial (uncorrelated, Poisson) contribution: κn − M ∼ Mn – proportional to number of correlated n-plets;

  • r ωn − 1 ∼ Mn−1.
  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 13 / 15

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Critical point fluctuations vs acceptance

Proton multiplicity cumulants ratio at 19.6 GeV: ωn,σ ≡ ωn − 1 grows as (∆y)n−1 and saturates at ∆y ∼ 1 − 2.

PT ∈ (0, 2) GeV PT ∈ (0.4, 2) GeV PT ∈ (0.4, 0.8) GeV 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 Δy ω2,σ (Δy) ω2,σ (∞) PT ∈ (0, 2) GeV PT ∈ (0.4, 2) GeV PT ∈ (0.4, 0.8) GeV 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 Δy ω4,σ (Δy) ω4,σ (∞)

pT and rapidity cuts have qualitatively similar effects.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 14 / 15

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Critical point fluctuations vs acceptance

Proton multiplicity cumulants ratio at 19.6 GeV: ωn,σ ≡ ωn − 1 grows as (∆y)n−1 and saturates at ∆y ∼ 1 − 2.

PT ∈ (0, 2) GeV PT ∈ (0.4, 2) GeV PT ∈ (0.4, 0.8) GeV 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 Δy ω2,σ (Δy) ω2,σ (∞) PT ∈ (0, 2) GeV PT ∈ (0.4, 2) GeV PT ∈ (0.4, 0.8) GeV 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 Δy ω4,σ (Δy) ω4,σ (∞)

pT and rapidity cuts have qualitatively similar effects. Wider acceptance improves signal/error: errors grow slower than Mn.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 14 / 15

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Concluding summary

A fundamental question for Heavy-Ion collision experiments: Is there a critical point on the boundary between QGP and hadron gas phases? Intriguing data from RHIC BES I. Needed: better understanding. More data from BES II. Critical fluctuations have many universal properties. Characteristic non-monotonic √s dependence of fluctuations (with sign change for non-gaussian moments) – a CP signature. Increase of signal with rapidity acceptance is characteristic of critical fluctuations. Dynamical description of fluctuations is essential and is work in progress.

  • M. Stephanov (UIC)

Fluctuations and the QCD Critical Point Weizmann 2017 15 / 15