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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

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SLIDE 1

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

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SLIDE 2

Nucleons and Quark-gluon-plasma

Christoph Herold (SUT) Fairness, September 22, 2014 2 / 20

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SLIDE 3

The QCD critical point

Christoph Herold (SUT) Fairness, September 22, 2014 3 / 20

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SLIDE 4

Finding the CP - I

  • 1. From the QCD Lagrangian

Solve partition function Z on a lattice (sign problem) Solve Dyson-Schwinger equations

50 100 150 200 250 µ [Mev] 50 100 150 200 T [MeV] Chiral crossover Chiral 1st order CEP Deconfinement

− 1 = + − 1 − 1

= − 1 + + + + + + − 1

(Fischer, Luecker, Phys. Lett. B 718 (2013) 1036-1043) Christoph Herold (SUT) Fairness, September 22, 2014 4 / 20

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SLIDE 5

Finding the CP - II

  • 2. From effective models

Respect chiral symmetry (Sigma model, NJL model, ...) Existence/location of CP not universal!

50 100 150 200 50 100 150 200 250 300 350 T [MeV] µ [MeV] χ crossover Φ crossover

—

Φ crossover CEP χ first order

(Herbst, Pawlowski, Schaefer, Phys. Lett. B 696 (2011) 58-67)

500 1000 1500 2000 µB (MeV) 50 100 150 200 T (MeV) symmetric matter neutron star matter

(Dexheimer, Schramm, Phys. Rev. C 81 (2010) 045201) Christoph Herold (SUT) Fairness, September 22, 2014 5 / 20

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SLIDE 6

Finding the CP - III

  • 3. From experiment

Fluctuations sensitive to critical region

0.2 0.4 0.6 0.8 1.0 1.2

Au+Au Collisions at RHIC

Net-proton

<0.8 (GeV/c),|y|<0.5

T

0.4<p

Skellam Distribution

70-80% 0-5% 0.4 0.6 0.8 1.0 1.2

p+p data Au+Au 70-80% Au+Au 0-5% Au+Au 0-5% (UrQMD)

  • Ind. Prod. (0-5%)

5 6 7 8 10 20 30 40 100 200 0.85 0.90 0.95 1.00 1.05

σ S

2

σ κ

)/Skellam σ (S

(GeV)

NN

s Colliding Energy (STAR collaboration, Phys. Rev. Lett. 112 (2014) 032302) ω

1 1.5 2 [MeV]

B

µ

200 300 400 500

1 1.5 2 all charged

beam *

< y

π *

1 < y

  • fluct. at CEP:

=3 fm ξ all charged; =6 fm ξ all charged;

[MeV]

B

µ

200 300 400 500

1 1.5 2 negatively charged positively charged

beam *

< y

π *

1 < y

  • fluct. at CEP:

=3 fm ξ

  • neg. charged;

=6 fm ξ

  • neg. charged;

(NA49 collaboration, Nucl. Phys. A 830 (2009))

σ2 = δN2 ∼ ξ2 Sσ = δN3 δN2 ∼ ξ2.5 κσ2 = δN4 δN2 − 3δN2 ∼ ξ5

(Stephanov, Phys. Rev. Lett. 102 (2009)) Christoph Herold (SUT) Fairness, September 22, 2014 6 / 20

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SLIDE 7

CP and first-order phase transition

  • 10
  • 5

5 10 15 20 0.4 0.6 0.8 1 1.2 1.4

−3 µµ / Λ2 χ q

n [fm ]

1 10 100 1000 1e-007 1e-006 1e-005 0.0001 0.001 0.01

µµ / Λ2 χ

m = 5.6 MeV 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 χµµ ∼ (µ − µ0)−γ

(Sasaki, Friman, Redlcih, Phys. Rev. D 77 (2008)) Christoph Herold (SUT) Fairness, September 22, 2014 7 / 20

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SLIDE 8

Latent heat in heavy-ion collisions?

  • 0.04
  • 0.02

10-40% Centrality a) antiproton

10

2

10 y=0

/dy|

1

dv 0.01

b) proton

10

2

10 0.01

c) net proton

Data UrQMD

(GeV)

NN

s √

Latent heat might influence directed flow v1, strength of expansion Measured by STAR collaboration

(STAR collaboration, Phys. Rev. Lett. 112 (2014) 162301) Christoph Herold (SUT) Fairness, September 22, 2014 8 / 20

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SLIDE 9

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

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SLIDE 10

A chiral model with dilatons

Potential and equation of state from L = q

  • i
  • γµ∂µ − igsγ0A0
  • − gσ
  • q + 1/2 (∂µσ)2 + 1/2 (∂µχ)2 − U (σ) − U(χ)

(Sasaki, Mishustin, Phys. Rev. C 85 (2012) 025202)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.1 0.2 0.3 0.4 0.5 T [GeV] µ [GeV] chiral crossover chiral 1st-order melting gluon cond. 6 8 10 12 14 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 E/T4 T/Tchiral mσ=600 MeV 900 MeV Stefan-Boltzmann

Christoph Herold (SUT) Fairness, September 22, 2014 10 / 20

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Spinodal instabilities at T = 40 MeV

10 20 30 40 50 60 70 80 360 362 364 366 368 370 372 σ (MeV) µ (MeV) 10 20 30 40 50 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p (MeV/fm3) nq (1/fm3)

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

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Spinodal instabilities at T = 40 MeV

  • 2000
  • 1500
  • 1000
  • 500

500 1000 1500 2000 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 χq/T2 nq (1/fm3) 2000 4000 6000 8000 10000 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 κ nq (1/fm3)

χq T 2 = 1 VT 3 δN2 q proportional to quark number fluctuations

κ =

δN4

q

δN2

q − 3δN2

q

Expect: Enhancement of fluctuations at CP AND 1st order transition

Christoph Herold (SUT) Fairness, September 22, 2014 12 / 20

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SLIDE 13

Critical indices

101 102 103 104 10-6 10-5 10-4 10-3 χq/T2 µr 104 105 106 107 108 109 1010 10-6 10-5 10-4 10-3 κ µr

χq ∼ (µ − µ0)−γ with γ = 1/2 for first-order and γ = 2/3 for CEP κ ∼ (µ − µ0)−ζ with ζ = 2 for first-order and ζ = 2 for CEP

Christoph Herold (SUT) Fairness, September 22, 2014 13 / 20

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SLIDE 14

A chiral model with dilatons ... dynamically

Ingredients for fully dynamical model: Hot medium (quarks) Fluctuations (chiral fields) Chiral fluid dynamics −δScl δσ − D = ξ , ∂µT µν

q

= Sν

σ

(Nahrgang, Leupold, Herold, Bleicher, Phys. Rev. C 84 (2011))

Potential and equation of state from L = q

  • i
  • γµ∂µ − igsγ0A0
  • − gσ
  • q + 1/2 (∂µσ)2 + 1/2 (∂µχ)2 − U (σ) − U(χ)

(Sasaki, Mishustin, Phys. Rev. C 85 (2012) 025202) Christoph Herold (SUT) Fairness, September 22, 2014 14 / 20

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SLIDE 15

Event-by-event fluctuations: variance

0.002 0.004 0.006 0.008 0.01 0.012 0.014 1 2 3 4 5 6 7 8 σ2 t (fm) first-order CEP crossover 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5 6 7 8 σ2 t (fm) first-order CEP crossover

Fixed volume vs. rapidity (y < 0.5) and pT cut (100 MeV/fm3 < pT < 500 MeV/fm3) Different scales due to different volumes Fluctuating volume for rapidity and momentum cut

Christoph Herold (SUT) Fairness, September 22, 2014 15 / 20

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SLIDE 16

Event-by-event fluctuations: kurtosis

  • 0.002
  • 0.001

0.001 0.002 0.003 0.004 0.005 1 2 3 4 5 6 7 8 κ t (fm) first-order CEP crossover

  • 0.2
  • 0.15
  • 0.1
  • 0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 1 2 3 4 5 6 7 8 κ t (fm) first-order CEP crossover

Fixed volume vs. rapidity (y < 0.5) and pT cut (100 MeV/fm3 < pT < 500 MeV/fm3) 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

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SLIDE 17

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

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SLIDE 18

SU(3) chiral quark-hadron (QH) model

include 3 quarks (u, d, s), baryon octet scalar mesons σ, ζ, vector meson ω L =

  • i

ψi

  • iγµ∂µ − γ0giωω − Mi
  • ψi + 1

2 (∂µσ)2−U (σ, ζ, ω)−U(ℓ) with effective masses generated by σ and ℓ Mq = gqσσ + gqζζ + M0q + gqℓ(1 − ℓ) MB = gBσσ + gBζζ + M0B + gBℓℓ2

(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

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SLIDE 19

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

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SLIDE 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