Suppression of anisotropic flow without viscosity Adam Takacs * - - PowerPoint PPT Presentation

Suppression of anisotropic flow without viscosity

Adam Takacs* University of Bergen (Norway) & Eotvos University (Hungary) Denes Molnar Purdue University (U.S.) Konrad Tywoniuk University of Bergen (Norway) Gergely G. Barnafoldi Wigner Institute (Hungary)

*takacs.adam@wigner.mta.hu

Supported by the 18-3 New National Excellence Program of the Ministry of Human Capacities and OTKA K120660.

COST Workshop Lund 28-02-2019 1

Outline

• 1. Motivation:

relativistic hydrodynamics to understand heavy ion collisions

• 2. Particlization:

basics, shortcomings, influence on observables

• 3. How much does f matter?
• 4. Results: 4-source model and 2+1D hydro
• 5. Conclusion and outlook

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Motivation

MADAI Collaboration

For students: see Gabriel Denicol’s talk about hydro from Hot Quarks 2018 https://indico.cern.ch/event/7 03015/contributions/3095199/

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Motivation

Adam Takacs COST Workshop Lund 28-02-2019

• Shear viscosity is sensitive to the

particlization method

• There is no unique way to do the

particlization

• Thermal equilibrium is an assumption
• D. Molnar & P. Huovien, J.Phys. G35 104125 (2008)
• K. Dusling, G.D. Moore, D. Teaney, Phys. Rev. C81, 034907 (2010)
• D. Molnar & Z. Wolff, Phys. Rev. C95, 024903 (2017)

0.1 0.2 0.3 0.4 0.5 0.5 1 1.5 2 2.5 3 3.5 4 v2 (pT) pT [GeV]

Ideal Linear Quadratic

Pure Glue Reprint: Phys. Rev. C81, 034907 (2010)

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Motivation

Adam Takacs COST Workshop Lund 28-02-2019

• Shear viscosity is sensitive to the way of

particlization

• There is no unique way to do the

particlization

• Thermal equilibrium is an assumption

Questions:

• 1. How sensitive is ideal hydro?
• 2. Is thermal equilibrium a legitimate assumption?
• D. Molnar & P. Huovien, J.Phys. G35 104125 (2008)
• K. Dusling, G.D. Moore, D. Teaney, Phys. Rev. C81, 034907 (2010)
• D. Molnar & Z. Wolff, Phys. Rev. C95, 024903 (2017)

0.1 0.2 0.3 0.4 0.5 0.5 1 1.5 2 2.5 3 3.5 4 v2 (pT) pT [GeV]

Ideal Linear Quadratic

Pure Glue Reprint: Phys. Rev. C81, 034907 (2010)

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Particlization How is it done?

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Particlization: from hydro to particles

• L. Csernai, Introduction Relativistic Heavy Ion Collisions (1994)

Conversion of fluid → particles on a 3D hypersurface: Inside: fluid (uµ(x), ε(x), P(x), n(x))

dσµ

dσµ

Adam Takacs COST Workshop Lund 28-02-2019

N µ(x) = (n(x),~ j(x)) T µν(x) = ["(x) + P(x)]uµuν − P(x)gµν

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Particlization: from hydro to particles

• L. Csernai, Introduction Relativistic Heavy Ion Collisions (1994)

Conversion of fluid → particles on a 3D hypersurface: Inside: fluid Outside: particle (uµ(x), ε(x), P(x), n(x))

f(x, p)

N µ(x) = Z d3p p0 pµf(x, p) T µν(x) = Z d3p p0 pµpνf(x, p)

dσµ

Adam Takacs COST Workshop Lund 28-02-2019

dσµ

N µ(x) = (n(x),~ j(x)) T µν(x) = ["(x) + P(x)]uµuν − P(x)gµν

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Particlization: from hydro to particles

• L. Csernai, Introduction Relativistic Heavy Ion Collisions (1994)

Conversion of fluid → particles on a 3D hypersurface: Inside: fluid Outside: particle Boundary: conservation laws (uµ(x), ε(x), P(x), n(x))

f(x, p)

N µ(x) = Z d3p p0 pµf(x, p) T µν(x) = Z d3p p0 pµpνf(x, p)

dσµ

[N µdσµ]in−out = 0 [T µνdσµ]in−out = 0

Adam Takacs COST Workshop Lund 28-02-2019

dσµ

N µ(x) = (n(x),~ j(x)) T µν(x) = ["(x) + P(x)]uµuν − P(x)gµν

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Particlization: from hydro to particles

• L. Csernai, Introduction Relativistic Heavy Ion Collisions (1994)

Conversion of fluid → particles on a 3D hypersurface: Inside: fluid Outside: particle Cooper-Frye formula: momentum spectrum (measurable) (uµ(x), ε(x), P(x), n(x))

f(x, p)

N µ(x) = Z d3p p0 pµf(x, p) T µν(x) = Z d3p p0 pµpνf(x, p)

dσµ

Adam Takacs COST Workshop Lund 28-02-2019

E d3N

d3p =

R dσµpµf(x, p)

dσµ

N µ(x) = (n(x),~ j(x)) T µν(x) = ["(x) + P(x)]uµuν − P(x)gµν

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N µ(x) = (n(x),~ j(x)) T µν(x) = ["(x) + P(x)]uµuν − P(x)gµν

dσµ

Particlization: from hydro to particles

• L. Csernai, Introduction Relativistic Heavy Ion Collisions (1994)

Conversion of fluid → particles on a 3D hypersurface: Inside: fluid Outside: particle Cooper-Frye formula: momentum spectrum (measurable) (uµ(x), ε(x), P(x), n(x))

dσµ

E d3N

d3p =

R dσµpµf(x, p)

f(x, p)

N µ(x) = Z d3p p0 pµf(x, p) T µν(x) = Z d3p p0 pµpνf(x, p)

What is ? f(x, p)

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Particlization: what is ?

• single-particle distribution

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

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Particlization: what is ?

• single-particle distribution
• We don’t know.

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

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Particlization: what is ?

• single-particle distribution
• Described by some kinetic transport theory

(assumption)

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

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Particlization: what is ?

• single-particle distribution
• Described by the Boltzman Transport Equation

(assumption of assumption)

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

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Particlization: what is ?

• single-particle distribution
• 0th solution of the BTE

(assumption of assumption of assumption) Relativistic Boltzmann (thermal) distribution: One field describes everything: temperature.

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

T(x)

f0(x, p) =

g (2π)3 e−

pµuµ(x) T (x)

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Particlization: what is ?

• single-particle distribution
• 0th solution of the BTE

(assumption of assumption of assumption) Relativistic Boltzmann (thermal) distribution: One field describes everything: temperature.

• Change a little to „non-extensive“: corrections

One field „temperature“ + non-ext. parameter . If we get back Boltzmann! Starts in exponential, end in power law!

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

T(x)

Tα(x)

α → 0

α

f0(x, p) =

g (2π)3 e−

pµuµ(x) T (x)

f(x, p) = A h 1 +

α Tα(x)pµuµ(x)

i− 1

α

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Particlization: what is ?

• single-particle distribution
• 0th solution of the BTE

(assumption of assumption of assumption) Relativistic Boltzmann (thermal) distribution: One field describes everything: temperature.

• Change a little to „non-extensive“: corrections

One field „temperature“ + non-ext. parameter . If we get back Boltzmann! Starts in exponential, end in power law!

f(x, p)

Adam Takacs COST Workshop Lund 28-02-2019

f(x, p)

T(x)

Tα(x)

α → 0

α

f0(x, p) =

g (2π)3 e−

pµuµ(x) T (x)

f(x, p) = A h 1 +

α Tα(x)pµuµ(x)

i− 1

α

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How does spectrum and flow change?

• Spectrum: exponential like → power-law tail (sounds good)

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How does spectrum and flow change?

• Spectrum: exponential like → power-law tail (sounds good)
• Flow:

Boltzmann: Tsallis: (looks interesting!) vn(p) =

R dφ cos(nφ)E d3N

d3p

R dφE d3N

d3p

vn(p) ∼ e−ap

e−bp = e−(a−b)p → 1

Adam Takacs COST Workshop Lund 28-02-2019

vn(p) ∼ (ap)−1/α

(bp)−1/α →

a

b

− 1

α ≤ 1

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How does spectrum and flow change?

• Spectrum: exponential like → power law tail
• Flow:
• Simple 4-source model:

4-uniform fireballs, no long. expansion, boosted sym. (vx, vy) and T=const freeze-

• ut

vn(p) =

R dφ cos(nφ)E d3N

d3p

R dφE d3N

d3p

f 4s(p) = f|vx + f|−vx + f|vy + f|−vy

Adam Takacs COST Workshop Lund 28-02-2019

• P. Houven et al Phys. Lett. B 503, 58 (2001)

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How does spectrum and flow change?

Result from 4-source model: suppression in v2!

Adam Takacs COST Workshop Lund 28-02-2019

0.0 0.5 1.0 1.5 2.0 2.5 3.0 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 v2 Pion vx = 0.5, vy = 0.45 Tq = 140 MeV α = 0 (Boltzmann) α = 0.01 α = 0.03 α = 0.1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 v2 Proton vx = 0.5, vy = 0.45 Tq = 140 MeV α = 0 (Boltzmann) α = 0.01 α = 0.03 α = 0.1

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Hydrodynamic Simulation

1. Initial condition: Au+Au @ 200 GeV optical Glauber model S0=110 fm-3. 2. 2+1D numerical ideal hydro with Azhydro. 3. Cooper–Frye freeze-out with Tsallis and q are fixed, 4. Resonance decays are included. Tf = 140 MeV

ε(x), P(x)

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Results: hydrodynamic simulation

1 2 3 4 pT [GeV/c] 10−3 10−2 10−1 100 101 102 103 104 105

1 2πpT d2N dydpT [c2/GeV2]

Au+Au → p, ¯ p, √sNN = 200 GeV, |y| < 0.5

α = 0 0-5% ×100 20-30% ×10 30-40%

1 2 3 4 pT [GeV/c] 10−3 10−2 10−1 100 101 102 103 104 105

1 2πpT d2N dydpT [c2/GeV2]

Au+Au → K±, √sNN = 200 GeV, |y| < 0.5

α = 0 0-5% ×100 20-30% ×10 30-40%

1 2 3 4 pT [GeV/c] 10−3 10−2 10−1 100 101 102 103 104 105

1 2πpT d2N dydpT [c2/GeV2]

Au+Au → π±, √sNN = 200 GeV, |y| < 0.5

α = 0 0-5% ×100 20-30% × 10 30-40%

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Results: hydrodynamic simulation

1 2 3 4 pT [GeV/c] 10−3 10−2 10−1 100 101 102 103 104 105

1 2πpT d2N dydpT [c2/GeV2]

Au+Au → p, ¯ p, √sNN = 200 GeV, |y| < 0.5

α = 0 α = 0.01 α = 0.03 α = 0.05 0-5% ×100 20-30% ×10 30-40%

1 2 3 4 pT [GeV/c] 10−3 10−2 10−1 100 101 102 103 104 105

1 2πpT d2N dydpT [c2/GeV2]

Au+Au → K±, √sNN = 200 GeV, |y| < 0.5

α = 0 α = 0.01 α = 0.03 α = 0.05 0-5% ×100 20-30% ×10 30-40%

1 2 3 4 pT [GeV/c] 10−3 10−2 10−1 100 101 102 103 104 105

1 2πpT d2N dydpT [c2/GeV2]

Au+Au → π±, √sNN = 200 GeV, |y| < 0.5

α = 0 α = 0.01 α = 0.03 α = 0.05 0-5% ×100 20-30% × 10 30-40%

Adam Takacs COST Workshop Lund 28-02-2019

• Power-law tail appears
• Better agreement with data!

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Results: hydrodynamic simulation

1 2 3 4 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 v2 Au+Au → p, ¯ p, √sNN = 200 GeV, |y| < 0.5

α = 0 20-30%

1 2 3 4 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 v2 Au+Au → K±, √sNN = 200 GeV, |y| < 0.5

α = 0 20-30%

1 2 3 4 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 v2 Au+Au → π±, √sNN = 200 GeV, |y| < 0.5

α = 0 20-30%

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Results: hydrodynamic simulation

1 2 3 4 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 v2 Au+Au → p, ¯ p, √sNN = 200 GeV, |y| < 0.5

α = 0 α = 0.01 α = 0.03 α = 0.05 20-30%

1 2 3 4 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 v2 Au+Au → K±, √sNN = 200 GeV, |y| < 0.5

α = 0 α = 0.01 α = 0.03 α = 0.05 20-30%

1 2 3 4 pT [GeV/c] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 v2 Au+Au → π±, √sNN = 200 GeV, |y| < 0.5

α = 0 α = 0.01 α = 0.03 α = 0.05 20-30%

Adam Takacs COST Workshop Lund 28-02-2019

• Suppression in flow!
• Better agreement with data!
• Mass ordering in the suppression, like shear viscosity!

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Results: hydrodynamic simulation

Adam Takacs COST Workshop Lund 28-02-2019

Reprint: D.Molnar & Z.Wolff, Phys.Rev. C95, 024903 (2017)

• Non-ext. behaves like shear viscosity (no viscosity in the model)!
• Comparison to viscous calculation:
• From fits to spectra:

α ≈ 0.05 ↔ η/s = 0.05

Viscous calculation:

K.Urmossy, G.G.Barnafoldi, T.S.Biro, J.Phys. Conf.Ser. 612 012048 (2015)

α = 0 − 0.07

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Summary

Adam Takacs COST Workshop Lund 28-02-2019

• Relativistic Boltzmann distribution (thermal equilibrium) is an

approximation.

• To study a specific type of correction (using Tsallis distribution):

1. Finite size effects and correlations. 2. More suitable for the spectrum (power law tail) and the flow (vn < 1). 3. Isotropization? Conformal theories do not require equilibrium.

• The correction has important effects:
• Better spectra.
• Suppressed flow
• Mimic shear viscosity:
• Future:
• Extend to viscous calculation.
• Study kinetic transport for an exact correction. Better understand

α ≈ 0.05 ↔ η/s = 0.05

α

P.Arnold, J.Lenaghan, G.D.Moore, L.G. Yaffe, Phys. Rev.

• Lett. 94, 072302 (2005)

M.Luzum & P.Romatschke. Phys.Rev. C78 034915 (2008)

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Thank you for your attention!

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Backup: describing hydro fields with non-ext. distr.

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Backup: non-ext. parameter vs. shear viscosity

D.Molnar & Z.Wolff, Phys.Rev. C95, 024903 (2017) Z.Wolff & D.Molnar, Phys.Rev. C96, 044909 (2017)

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Backup: v4 with non-ext. f

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Backup: changes in other observables

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