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 length Non-gaussian moments and universality Beam energy scan 2 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
QCD Phase Diagram (a theorist’s view) QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter Lattice at µ B � 2 T 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
Why fluctuations are large at a critical point? The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 4 / 15
Why fluctuations are large at a critical point? The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) At the critical point S ( σ ) “flattens”. And χ ≡ � σ 2 � /V → ∞ . CLT? M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 4 / 15
Why fluctuations are large at a critical point? The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) At the critical point S ( σ ) “flattens”. And χ ≡ � σ 2 � /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
Why fluctuations are large at a critical point? The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) At the critical point S ( σ ) “flattens”. And χ ≡ � σ 2 � /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
Higher order cumulants Higher cumulants (shape of P ( σ ) ) depend stronger on ξ . E.g., � σ 2 � ∼ V ξ 2 while � σ 4 � c ∼ V ξ 7 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
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
Experiments do not measure σ . M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 7 / 15
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 ) : + ∂ � n p � δn p = δn free × δσ p ∂σ � The cumulants of multiplicity M ≡ p n p : + κ 4 [ σ ] × g 4 � � 4 κ 4 [ M ] = � M � + . . . , ���� � �� � baseline ∼ M 4 g – coupling of the critical mode ( g = dm/dσ ). M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 8 / 15
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 ) : + ∂ � n p � δn p = δn free × δσ p ∂σ � The cumulants of multiplicity M ≡ p n p : + κ 4 [ σ ] × g 4 � � 4 κ 4 [ M ] = � M � + . . . , ���� � �� � baseline ∼ M 4 g – coupling of the critical mode ( g = dm/dσ ). κ 4 [ σ ] < 0 means κ 4 [ M ] < baseline M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 8 / 15
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 ) : + ∂ � n p � δn p = δn free × δσ p ∂σ � The cumulants of multiplicity M ≡ p n p : + κ 4 [ σ ] × g 4 � � 4 κ 4 [ M ] = � M � + . . . , ���� � �� � baseline ∼ M 4 g – coupling of the critical mode ( g = dm/dσ ). κ 4 [ σ ] < 0 means κ 4 [ M ] < baseline NB: Sensitivity to M accepted : ( κ 4 ) σ ∼ M 4 (number of 4-tets). M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 8 / 15
Beam Energy Scan M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15
Beam Energy Scan M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15
Beam Energy Scan M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15
Beam Energy Scan M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15
Beam Energy Scan M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15
Beam Energy Scan “intriguing hint” (2015 LRPNS) M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 9 / 15
QM2017 update: another intriguing hint Non-monotonous √ s Preliminary, but very interesting: 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 p T dependence need to be checked. But: no signal in R 2 for K or p . M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 10 / 15
Acceptance dependence M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 11 / 15
Correlations – spatial vs kinematic ξ ∼ 1 − 3 fm ∆ η corr = ξ ∼ 0 . 1 − 0 . 3 τ f Particles within ∆ η corr have thermal rapidity spread. Thus ∆ y corr ∼ 1 ≫ ∆ η corr M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 12 / 15
Acceptance dependence – two regimes How do cumulants depend on acceptance? Let κ n ( M ) be a cumulant of M – multiplicity of accepted , say, protons. ∆ y ≫ ∆ y corr – CLT applies. κ n ∼ M or ω n ≡ κ n M → const – an “intensive”, or volume indep. measure M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 13 / 15
Acceptance dependence – two regimes How do cumulants depend on acceptance? Let κ n ( M ) be a cumulant of M – multiplicity of accepted , say, protons. ∆ y ≫ ∆ y corr – CLT applies. κ n ∼ M or ω n ≡ κ n M → const – an “intensive”, or volume indep. measure ∆ y ≪ ∆ y corr – more typical in experiment. Subtracting trivial (uncorrelated, Poisson) contribution: κ n − M ∼ M n – proportional to number of correlated n -plets; or ω n − 1 ∼ M n − 1 . M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 13 / 15
Critical point fluctuations vs acceptance Proton multiplicity cumulants ratio at 19.6 GeV: ω n,σ ≡ ω n − 1 grows as (∆ y ) n − 1 and saturates at ∆ y ∼ 1 − 2 . 1.0 1.0 P T ∈ ( 0, 2 ) GeV P T ∈ ( 0, 2 ) GeV 0.8 0.8 P T ∈ ( 0.4, 2 ) GeV P T ∈ ( 0.4, 0.8 ) GeV ω 2, σ ( Δ y ) ω 4, σ ( Δ y ) 0.6 0.6 ω 2, σ ( ∞ ) ω 4, σ ( ∞ ) 0.4 0.4 0.2 P T ∈ ( 0.4, 2 ) GeV 0.2 P T ∈ ( 0.4, 0.8 ) GeV 0.0 0.0 0 1 2 3 4 0 1 2 3 4 Δ y Δ y p T and rapidity cuts have qualitatively similar effects. M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 14 / 15
Critical point fluctuations vs acceptance Proton multiplicity cumulants ratio at 19.6 GeV: ω n,σ ≡ ω n − 1 grows as (∆ y ) n − 1 and saturates at ∆ y ∼ 1 − 2 . 1.0 1.0 P T ∈ ( 0, 2 ) GeV P T ∈ ( 0, 2 ) GeV 0.8 0.8 P T ∈ ( 0.4, 2 ) GeV P T ∈ ( 0.4, 0.8 ) GeV ω 2, σ ( Δ y ) ω 4, σ ( Δ y ) 0.6 0.6 ω 2, σ ( ∞ ) ω 4, σ ( ∞ ) 0.4 0.4 0.2 P T ∈ ( 0.4, 2 ) GeV 0.2 P T ∈ ( 0.4, 0.8 ) GeV 0.0 0.0 0 1 2 3 4 0 1 2 3 4 Δ y Δ y p T and rapidity cuts have qualitatively similar effects. Wider acceptance improves signal/error: errors grow slower than M n . M. Stephanov (UIC) Fluctuations and the QCD Critical Point Weizmann 2017 14 / 15
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
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