QCD critical point, fluctuations and hydrodynamics M. Stephanov M. - PowerPoint PPT Presentation

QCD critical point, fluctuations and hydrodynamics M. Stephanov M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 1 / 28

Critical point is a ubiquitous phenomenon M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 2 / 28

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. QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 3 / 28

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. QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter Lattice QCD at µ B � 2 T – a crossover. C.P . is ubiquitous in models (NJL, RM, Holog., Strong coupl. LQCD, . . . ) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 3 / 28

Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. 200 LTE04 LTE03 T , LTE08 The sign problem restricts reliable lat- LR01 MeV LR04 150 tice calculations to µ B = 0 . 100 Under different assumptions one can estimate the position of the critical 50 point, assuming it exists, by extrapo- lation from µ = 0 . 0 0 200 400 600 800 µ B , MeV Heavy-ion collisions. M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 4 / 28

Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. 200 130 LTE04 LTE03 T , LTE08 The sign problem restricts reliable lat- LR01 MeV 17 LR04 150 9 tice calculations to µ B = 0 . 5 100 Under different assumptions one can estimate the position of the critical 50 point, assuming it exists, by extrapo- 2 lation from µ = 0 . 0 0 200 400 600 800 µ B , MeV Heavy-ion collisions. M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 4 / 28

Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. 200 130 LTE04 LTE03 T , LTE08 The sign problem restricts reliable lat- LR01 MeV 17 LR04 150 R H I C 9 tice calculations to µ B = 0 . s c a n 5 100 Under different assumptions one can estimate the position of the critical 50 point, assuming it exists, by extrapo- 2 lation from µ = 0 . 0 0 200 400 600 800 µ B , MeV Heavy-ion collisions. M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 4 / 28

Essentially two approaches to discovering the QCD critical point. Each with its own challenges. Lattice simulations. 200 130 LTE04 LTE03 T , LTE08 The sign problem restricts reliable lat- LR01 MeV 17 LR04 150 R H I C 9 tice calculations to µ B = 0 . s c a n 5 100 Under different assumptions one can estimate the position of the critical 50 point, assuming it exists, by extrapo- 2 lation from µ = 0 . 0 0 200 400 600 800 µ B , MeV Heavy-ion collisions. Non-equilibrium. M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 4 / 28

Why fluctuations are large at a critical point? The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 5 / 28

Why fluctuations are large at a critical point? The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 5 / 28

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 QCD CP , fluctuations and hydrodynamics Trento 2017 5 / 28

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 QCD CP , fluctuations and hydrodynamics Trento 2017 5 / 28

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 [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 CP , fluctuations and hydrodynamics Trento 2017 6 / 28

Mapping Ising to QCD phase diagram T vs µ B : In QCD ( t, H ) → ( µ − µ CP , T − T CP ) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 7 / 28

Mapping Ising to QCD phase diagram T vs µ B : In QCD ( t, H ) → ( µ − µ CP , T − T CP ) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 7 / 28

Mapping Ising to QCD phase diagram T vs µ B : In QCD ( t, H ) → ( µ − µ CP , T − T CP ) κ n ( N ) = N + O ( κ n ( σ )) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 7 / 28

Beam Energy Scan M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 8 / 28

Beam Energy Scan M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 8 / 28

Beam Energy Scan M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 8 / 28

Beam Energy Scan “intriguing hint” (2015 LRPNS) M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 8 / 28

QM/CPOD2017: two-point correlations Preliminary, but very interesting: Why this is interesting: Non-monotonous √ s dependence with max near 19 GeV. Charge/isospin blind. ∆ φ (in)dependence is as expected from R2( Δ y, Δφ ) for LS pions vs. √ s NN , 0-5% central, convolution Rapidity Correlations critical correlations. Click to edit Master subtitle style 7.7 GeV 11.5 GeV 14.5 GeV 19.6 GeV C 2 ∼ f ( φ 1 ) f ( φ 2 ) . Width ∆ η suggests soft pions – but p T ✩ Preliminary 27 GeV 39 GeV 62.4 GeV 200 GeV dependence need to be checked. Why no signal in R 2 for K or p ? W.J. Llope for STAR, CPOD2017, Aug. 8-11, 2017, Stony Brook, NY 21 W. Llope M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 9 / 28

Non-equilibrium physics is essential near the critical point. The goal for M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 10 / 28

Why ξ is finite System expands and is out of equilibrium Kibble-Zurek mechanism: Critical slowing down means τ relax ∼ ξ z . Given τ relax � τ (expansion time scale): ξ � τ 1 /z , z ≈ 3 (universal). M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 11 / 28

Why ξ is finite System expands and is out of equilibrium Kibble-Zurek mechanism: Critical slowing down means τ relax ∼ ξ z . Given τ relax � 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 CP , fluctuations and hydrodynamics Trento 2017 11 / 28

Magnitude of observables and ξ κ n ∼ ξ p ξ max ∼ τ 1 /z and Therefore, the magnitude of fluctuation signals is determined by non-equilibrium physics. M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 12 / 28

Magnitude of observables and ξ κ n ∼ ξ p ξ max ∼ τ 1 /z and 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 CP , fluctuations and hydrodynamics Trento 2017 12 / 28

Magnitude of observables and ξ κ n ∼ ξ p ξ max ∼ τ 1 /z and 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 CP , fluctuations and hydrodynamics Trento 2017 12 / 28

Hydrodynamics breaks down at CP Hydrodynamics relies on gradient expansion: T µν = ǫu µ u ν + p ∆ µν + ˜ T µν visc T µν ˜ visc = − ζ ∆ µν ( ∇ · u ) + . . . � �� � O ( ζ k ) ≪ 1 M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 13 / 28

Hydrodynamics breaks down at CP Hydrodynamics relies on gradient expansion: T µν = ǫu µ u ν + p ∆ µν + ˜ T µν visc T µν ˜ visc = − ζ ∆ µν ( ∇ · u ) + . . . � �� � O ( ζ k ) ≪ 1 ζ ∼ ξ 3 → ∞ Near CP: ( z − α/ν ≈ 3 ). M. Stephanov QCD CP , fluctuations and hydrodynamics Trento 2017 13 / 28