Multiplicity fluctuations within nonequilibrium chiral fluid dynamics Christoph Herold based on CH, Nahrgang, Yan, Kobdaj, arXiv: 1407.8277, accepted by JPG School of Physics, Suranaree University of Technology Fairness, September 22, 2014 Christoph Herold (SUT) Fairness, September 22, 2014 1 / 20
Nucleons and Quark-gluon-plasma Christoph Herold (SUT) Fairness, September 22, 2014 2 / 20
The QCD critical point Christoph Herold (SUT) Fairness, September 22, 2014 3 / 20
Finding the CP - I 1. From the QCD Lagrangian Solve partition function Z on a lattice (sign problem) Solve Dyson-Schwinger equations 200 − − 1 1 − 1 = + 150 T [MeV] − 1 − 1 = + + 100 Chiral crossover + + Chiral 1st order 50 CEP Deconfinement + + 0 0 50 100 150 200 250 µ [Mev] (Fischer, Luecker, Phys. Lett. B 718 (2013) 1036-1043) Christoph Herold (SUT) Fairness, September 22, 2014 4 / 20
Finding the CP - II 2. From effective models Respect chiral symmetry (Sigma model, NJL model, ...) Existence/location of CP not universal! 200 symmetric matter neutron star matter 200 150 150 T (MeV) T [MeV] 100 100 χ crossover Φ crossover — 50 Φ crossover 50 CEP χ first order 0 0 0 50 100 150 200 250 300 350 0 500 1000 1500 2000 µ B (MeV) µ [MeV] (Herbst, Pawlowski, Schaefer, Phys. Lett. B 696 (2011) 58-67) (Dexheimer, Schramm, Phys. Rev. C 81 (2010) 045201) Christoph Herold (SUT) Fairness, September 22, 2014 5 / 20
Finding the CP - III 3. From experiment Fluctuations sensitive to critical region ω 1.2 Au+Au Collisions at RHIC negatively charged fluct. at CEP: all charged fluct. at CEP: 1.0 2 2 2 positively charged all charged; ξ =3 fm neg. charged; ξ =3 fm * * 1 < y < y Skellam Distribution π σ all charged; ξ =6 fm beam neg. charged; ξ =6 fm 0.8 * * 1 < y < y S π beam 70-80% 0.6 0-5% 1.5 1.5 1.5 0.4 Net-proton 0.2 0.4<p <0.8 (GeV/c),|y|<0.5 T 1 1 1 1.2 1.0 200 300 400 500 200 300 400 500 2 σ µ [MeV] µ [MeV] 0.8 B B κ p+p data 0.6 Au+Au 70-80% Au+Au 0-5% (NA49 collaboration, Nucl. Phys. A 830 (2009)) Au+Au 0-5% (UrQMD) 0.4 Ind. Prod. (0-5%) 1.05 σ 2 = � δ N 2 � ∼ ξ 2 )/Skellam 1.00 S σ = � δ N 3 � 0.95 � δ N 2 � ∼ ξ 2 . 5 σ 0.90 (S 0.85 κσ 2 = � δ N 4 � 5 6 7 8 10 20 30 40 100 200 � δ N 2 � − 3 � δ N 2 � ∼ ξ 5 Colliding Energy s (GeV) NN (STAR collaboration, Phys. Rev. Lett. 112 (2014) 032302) (Stephanov, Phys. Rev. Lett. 102 (2009)) Christoph Herold (SUT) Fairness, September 22, 2014 6 / 20
CP and first-order phase transition 20 1000 m = 5.6 MeV 15 10 100 µµ / Λ 2 µµ / Λ 2 5 χ χ 0 10 -5 -10 1 0.4 0.6 0.8 1 1.2 1.4 1e-007 1e-006 1e-005 0.0001 0.001 0.01 −3 n [fm ] q t Net quark number suscpetibility at CP (solid) and first-order phase transition (dashed) from NJL model Change of universality class, γ = 2 / 3 for CP , γ = 1 / 2 for first-order χ µµ ∼ ( µ − µ 0 ) − γ (Sasaki, Friman, Redlcih, Phys. Rev. D 77 (2008)) Christoph Herold (SUT) Fairness, September 22, 2014 7 / 20
Latent heat in heavy-ion collisions? 0 10-40% Centrality -0.02 a) antiproton -0.04 0.01 b) proton y=0 /dy| 1 0 dv c) net proton 2 10 10 0.01 0 Data UrQMD 2 10 10 √ s (GeV) NN Latent heat might influence directed flow v 1 , strength of expansion Measured by STAR collaboration (STAR collaboration, Phys. Rev. Lett. 112 (2014) 162301) Christoph Herold (SUT) Fairness, September 22, 2014 8 / 20
Scope of this work Start from effective chiral model with CEP and first-order phase transition 1. Study thermodynamics: Calculate susceptibility and compare with NJL Calculate kurtosis Determine critical indices 2. Study fluid dynamics (heavy-ion collisions): Quark and chiral fields → quark fluid and explicitly propagated fields Ensemble fluctuations event-by-event Christoph Herold (SUT) Fairness, September 22, 2014 9 / 20
A chiral model with dilatons Potential and equation of state from q + 1 / 2 ( ∂ µ σ ) 2 + 1 / 2 ( ∂ µ χ ) 2 − U ( σ ) − U ( χ ) γ µ ∂ µ − i g s γ 0 A 0 � � � � L = q i − g σ (Sasaki, Mishustin, Phys. Rev. C 85 (2012) 025202) 0.35 chiral crossover 14 0.3 chiral 1st-order melting gluon cond. 0.25 12 T [GeV] 0.2 E/T 4 10 0.15 8 0.1 m σ =600 MeV 0.05 900 MeV 6 Stefan-Boltzmann 0 0 0.1 0.2 0.3 0.4 0.5 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 µ [GeV] T/T chiral Christoph Herold (SUT) Fairness, September 22, 2014 10 / 20
Spinodal instabilities at T = 40 MeV 50 80 70 40 p (MeV/fm 3 ) 60 30 σ (MeV) 50 20 40 30 10 20 0 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 360 362 364 366 368 370 372 n q (1/fm 3 ) µ (MeV) Phase transition in the presence of spinodal instabilities Mechanically instable region in the equation of state Christoph Herold (SUT) Fairness, September 22, 2014 11 / 20
Spinodal instabilities at T = 40 MeV 2000 10000 1500 8000 1000 500 6000 χ q / T 2 0 κ 4000 -500 -1000 2000 -1500 -2000 0 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 n q (1/fm 3 ) n q (1/fm 3 ) χ q VT 3 � δ N 2 1 T 2 = q � proportional to quark number fluctuations � δ N 4 q � q � − 3 � δ N 2 κ = q � � δ N 2 Expect: Enhancement of fluctuations at CP AND 1st order transition Christoph Herold (SUT) Fairness, September 22, 2014 12 / 20
Critical indices 10 4 10 10 10 9 10 3 10 8 χ q / T 2 10 7 κ 10 2 10 6 10 5 10 1 10 4 10 -6 10 -5 10 -4 10 -3 10 -6 10 -5 10 -4 10 -3 µ r µ r χ q ∼ ( µ − µ 0 ) − γ κ ∼ ( µ − µ 0 ) − ζ with γ = 1 / 2 for first-order with ζ = 2 for first-order and γ = 2 / 3 for CEP and ζ = 2 for CEP Christoph Herold (SUT) Fairness, September 22, 2014 13 / 20
A chiral model with dilatons ... dynamically Ingredients for fully dynamical model: Hot medium (quarks) Fluctuations (chiral fields) Chiral fluid dynamics − δ S cl δσ − D = ξ , ∂ µ T µν = S ν q σ (Nahrgang, Leupold, Herold, Bleicher, Phys. Rev. C 84 (2011)) Potential and equation of state from q + 1 / 2 ( ∂ µ σ ) 2 + 1 / 2 ( ∂ µ χ ) 2 − U ( σ ) − U ( χ ) γ µ ∂ µ − i g s γ 0 A 0 � � � � L = q i − g σ (Sasaki, Mishustin, Phys. Rev. C 85 (2012) 025202) Christoph Herold (SUT) Fairness, September 22, 2014 14 / 20
Event-by-event fluctuations: variance 0.014 0.6 first-order first-order 0.012 CEP CEP 0.5 crossover crossover 0.01 0.4 0.008 σ 2 σ 2 0.3 0.006 0.2 0.004 0.1 0.002 0 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 t (fm) t (fm) Fixed volume vs. rapidity ( y < 0 . 5) and p T cut (100 MeV/fm 3 < p T < 500 MeV/fm 3 ) Different scales due to different volumes Fluctuating volume for rapidity and momentum cut Christoph Herold (SUT) Fairness, September 22, 2014 15 / 20
Event-by-event fluctuations: kurtosis 0.005 0.35 first-order first-order 0.3 0.004 CEP CEP 0.25 crossover crossover 0.2 0.003 0.15 0.002 0.1 κ κ 0.05 0.001 0 0 -0.05 -0.1 -0.001 -0.15 -0.002 -0.2 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 t (fm) t (fm) Fixed volume vs. rapidity ( y < 0 . 5) and p T cut (100 MeV/fm 3 < p T < 500 MeV/fm 3 ) Different scales due baryon number conservation Ratios of cumulants depend on fraction of measured to total baryons Christoph Herold (SUT) Fairness, September 22, 2014 16 / 20
From fluctuations to observables ... ... some more things need to be considered in the future Freeze out over hypersurface with constant energy density or temperature Final state interactions Evolution of fluctuations in the hadronic phase Christoph Herold (SUT) Fairness, September 22, 2014 17 / 20
SU(3) chiral quark-hadron (QH) model include 3 quarks ( u , d , s ) , baryon octet scalar mesons σ , ζ , vector meson ω ψ i + 1 � 2 ( ∂ µ σ ) 2 − U ( σ, ζ, ω ) −U ( ℓ ) i γ µ ∂ µ − γ 0 g i ω ω − M i � � L = ψ i i with effective masses generated by σ and ℓ M q = g q σ σ + g q ζ ζ + M 0 q + g q ℓ ( 1 − ℓ ) g B σ σ + g B ζ ζ + M 0 B + g B ℓ ℓ 2 M B = (Dexheimer, Schramm, Phys. Rev. C 81 (2010), 045201) Improves equation of state, plus: Chiral phase transition at larger chemical potentials Disentangled from liquid-gas phase transition Christoph Herold (SUT) Fairness, September 22, 2014 18 / 20
QH model - phase diagram Chiral phase transition at larger chemical potentials Disentangled from liquid-gas phase transition (Herold, Limphirat, Kobdaj, Yan, SPC 2014) Christoph Herold (SUT) Fairness, September 22, 2014 19 / 20
Summary and Conclusions Event-by-event fluctuations become enhanced in hydrodynamic phase for CEP and first-order phase transition Effects of hadronic phase have to be taken into account for reliable predictions THANK YOU Christoph Herold (SUT) Fairness, September 22, 2014 20 / 20
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