Hydro+: Hydrodynamics for QCD critical point M. Stephanov with Y. - PowerPoint PPT Presentation

Hydro+: Hydrodynamics for QCD critical point M. Stephanov with Y. Yin (MIT), 1712.10305 M. Stephanov Hydro+ SEWM 2018 1 / 21

Critical point – end of phase coexistence – is a ubiquitous phenomenon Water: Is there one in QCD? M. Stephanov Hydro+ SEWM 2018 2 / 21

QCD critical point QCD is a relativistic QFT of a fundamental force, not quite like non-relativistic fluids. But a critical point is a very universal phenomenon – it takes 2 phases whose coexistence (first-order transition) ends. M. Stephanov Hydro+ SEWM 2018 3 / 21

QCD critical point QCD is a relativistic QFT of a fundamental force, not quite like non-relativistic fluids. But a critical point is a very universal phenomenon – it takes 2 phases whose coexistence (first-order transition) ends. In QCD: The two phases: quark-gluon plasma and hadron gas. Experiments: QGP has liquid properties – almost perfect fluidity. If the phases are separated by a first-order phase transition, there must also be a critical point! M. Stephanov Hydro+ SEWM 2018 3 / 21

QCD phase diagram (sketch) QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter M. Stephanov Hydro+ SEWM 2018 4 / 21

QCD phase diagram (sketch) QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter Lattice QCD at µ B � 2 T – a crossover Therefore, if at larger µ B ∃ first-order transition ⇒ ∃ critical point M. Stephanov Hydro+ SEWM 2018 4 / 21

QCD phase diagram (sketch) QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter Lattice QCD at µ B � 2 T – a crossover Therefore, if at larger µ B ∃ first-order transition ⇔ ∃ critical point M. Stephanov Hydro+ SEWM 2018 4 / 21

Critical point discovery challenges Essentially two approaches to discovering the QCD critical point. Each with its own challenges. 200 130 LTE04 LTE03 T , LTE08 LR01 MeV 17 LR04 150 R H I C 9 s c a n Lattice simulations. Sign problem. 5 100 Heavy-ion collisions. Encouraging progress 50 2 and intriguing new results. 0 0 200 400 600 800 µ B , MeV Challenge in connecting the two: non-equilibrium dynamics. M. Stephanov Hydro+ SEWM 2018 5 / 21

Fluctuations as signatures of the critical point Fluctuations are observables on the lattice and in heavy-ion collisions. The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) M. Stephanov Hydro+ SEWM 2018 6 / 21

Fluctuations as signatures of the critical point Fluctuations are observables on the lattice and in heavy-ion collisions. The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) M. Stephanov Hydro+ SEWM 2018 6 / 21

Fluctuations as signatures of the critical point Fluctuations are observables on the lattice and in heavy-ion collisions. The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) At the critical point S ( σ ) “flattens”. And χ ≡ � δσ 2 � V → ∞ . CLT? M. Stephanov Hydro+ SEWM 2018 6 / 21

Fluctuations as signatures of the critical point Fluctuations are observables on the lattice and in heavy-ion collisions. The key equation: P ( σ ) ∼ e S ( σ ) (Einstein 1910) At the critical point S ( σ ) “flattens”. And χ ≡ � δσ 2 � V → ∞ . CLT? δσ is not an average of ∞ many uncorrelated contributions: ξ → ∞ In fact, � δσ 2 � ∼ ξ 2 /V . M. Stephanov Hydro+ SEWM 2018 6 / 21

Higher order cumulants n > 2 cumulants (shape of P ( σ ) ) depend stronger on ξ . E.g., � σ 2 � ∼ ξ 2 while κ 4 = � σ 4 � c ∼ ξ 7 [PRL102(2009)032301] For n > 2 , sign depends on which side of the CP we are. This dependence is also universal. [PRL107(2011)052301] Using Ising model variables: M. Stephanov Hydro+ SEWM 2018 7 / 21

Mapping Ising to QCD phase diagram Equilibrium κ 4 vs T and µ B : In QCD ( t, H ) → ( µ − µ CP , T − T CP ) κ n ( N ) = N + O ( κ n ( σ )) M. Stephanov Hydro+ SEWM 2018 8 / 21

Beam Energy Scan I: intriguing hints Equilibrium κ 4 vs T and µ B : M. Stephanov Hydro+ SEWM 2018 9 / 21

Beam Energy Scan I: intriguing hints Equilibrium κ 4 vs T and µ B : M. Stephanov Hydro+ SEWM 2018 9 / 21

Beam Energy Scan I: intriguing hints Equilibrium κ 4 vs T and µ B : “intriguing hint” (2015 LRPNS) M. Stephanov Hydro+ SEWM 2018 9 / 21

Non-equilibrium physics is essential near the critical point. The challenge taken on by Goal: build a quantitative theoretical framework describing criti- cal point signatures for comparison with experiment. Strategy: Parameterize QCD equation of state with unknown T CP and µ CP as variable parameters. Use it in a hydrodynamic simulation and compare with experi- ment to determine or constrain T CP and µ CP . M. Stephanov Hydro+ SEWM 2018 10 / 21

Parameterized EOS for hydro simulations Parotto et al , 1805.05249 Variable parameters ( T CP , µ CP , slopes, etc.) control Ising-QCD mapping near the QCD critical point: P = P Non-Ising + P Ising . Lattice data at µ B = 0 is matched: This EOS is ready to be used in a hydrodynamic simulation. M. Stephanov Hydro+ SEWM 2018 11 / 21

Hydrodynamics breaks down near the critical point Hydrodynamics, as an EFT, relies on separation of scales: Evolution rate (e.g., expansion time, O (10) fm) much slower than the local equilibration rate (typically, O (0 . 5 − 1) fm). M. Stephanov Hydro+ SEWM 2018 12 / 21

Hydrodynamics breaks down near the critical point Hydrodynamics, as an EFT, relies on separation of scales: Evolution rate (e.g., expansion time, O (10) fm) much slower than the local equilibration rate (typically, O (0 . 5 − 1) fm). Critical slowing down means relaxation time diverges: τ relaxation ∼ ξ z ( z ≈ 3 ). When τ relaxation ∼ τ expansion hydrodynamics breaks down. M. Stephanov Hydro+ SEWM 2018 12 / 21

Hydrodynamics breaks down near the critical point Hydrodynamics, as an EFT, relies on separation of scales: Evolution rate (e.g., expansion time, O (10) fm) much slower than the local equilibration rate (typically, O (0 . 5 − 1) fm). Critical slowing down means relaxation time diverges: τ relaxation ∼ ξ z ( z ≈ 3 ). When τ relaxation ∼ τ expansion hydrodynamics breaks down. In fact, magnitude of ξ , and thus fluctuations/cumulants κ n ∼ ξ p , is estimated using ξ ∼ τ 1 /z expansion . To be more quantitative we need to describe the breakdown of hydro due to critical slowing down. M. Stephanov Hydro+ SEWM 2018 12 / 21

Hydro+ [MS-Yin,1712.10305] This is similar to the breakdown of an effective theory when we consider processes faster than some modes (fields) which we integrated out. M. Stephanov Hydro+ SEWM 2018 13 / 21

Hydro+ [MS-Yin,1712.10305] This is similar to the breakdown of an effective theory when we consider processes faster than some modes (fields) which we integrated out. Breakdown of locality is manifested in large gradient corrections to pressure due to ζ ∼ ξ 3 → ∞ . p hydro = p equilibrium − ζ ∇ · v M. Stephanov Hydro+ SEWM 2018 13 / 21

Hydro+ [MS-Yin,1712.10305] This is similar to the breakdown of an effective theory when we consider processes faster than some modes (fields) which we integrated out. Breakdown of locality is manifested in large gradient corrections to pressure due to ζ ∼ ξ 3 → ∞ . p hydro = p equilibrium − ζ ∇ · v Extending hydro by adding the critically slow modes → Hydro+ M. Stephanov Hydro+ SEWM 2018 13 / 21

What are the additional slow modes? An equilibrium thermodynamic state is completely characterized by average values ¯ ε , ¯ n , . . . . Fluctuations of ε , n are given by eos: P ∼ exp( S eq ( ε, n )) . M. Stephanov Hydro+ SEWM 2018 14 / 21

What are the additional slow modes? An equilibrium thermodynamic state is completely characterized by average values ¯ ε , ¯ n , . . . . Fluctuations of ε , n are given by eos: P ∼ exp( S eq ( ε, n )) . Hydrodynamics describes partial-equilibrium states , i.e., equilibrium is only local, because equilibration time ∼ L 2 . Fluctuations in such states are not necessarily in equilibrium. M. Stephanov Hydro+ SEWM 2018 14 / 21

Nonequilibrium fluctuations Measures of fluctuations are additional variables needed to characterize the partial-equilibrium state. 2-point (and n -point) functions of fluctuating hydro variables: � δεδε � , � δnδn � , � δεδn � , . . . . (Or probability functional). M. Stephanov Hydro+ SEWM 2018 15 / 21

Nonequilibrium fluctuations Measures of fluctuations are additional variables needed to characterize the partial-equilibrium state. 2-point (and n -point) functions of fluctuating hydro variables: � δεδε � , � δnδn � , � δεδn � , . . . . (Or probability functional). Relaxation rates of 2pt functions is of the same order as that of corresponding 1pt functions (i.e., × 2 ). But effects of fluctuations are usually suppressed due to � ξ 3 /V ∼ ( kξ ) 3 / 2 ≪ 1 by CLT. averaging out: This is why 1st-order hydrodynamics exists (for d > 2 ). M. Stephanov Hydro+ SEWM 2018 15 / 21

Critical fluctuations Near CP there is parametric separation of relaxation time scales. The slowest and thus most out-of-equilibrium mode is charge diffusion at const p : s/n ≡ m . M. Stephanov Hydro+ SEWM 2018 16 / 21