Cooper-Frye negative contributions at FAIR energies Dmytro - - PowerPoint PPT Presentation

Cooper-Frye negative contributions at FAIR energies

Dmytro Oliinychenko

Frankfurt Institute of Advanced Studies

• liiny@fias.uni-frankfurt.de

In collaboration with Pasi Huovinen and Hannah Petersen

HGS-HIRe

Helmholtz Graduate School for Hadron and Ion Research

September 22, 2014

Description of heavy ion collision: hybrid models

Relativistic Fluid Initial State Pre-equilibrium Dynamics Hadronization Transport/Freeze-out

Hydro: local thermal equilibrium, mean free path ≪ system size ∂µT µν = 0, ∂µjµ = 0, EoS, boundary conditions Transport: Monte-Carlo solution of Boltzmann equation Hydrodynamics and transport are solved independently Transition - on a predefined hypersurface

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Transition in hybrid models

H y d r

• B
• l

t z m a n n

Criterion for transition surface: ”hydro equivalent to transport”

◮ Constant energy density surface ǫ(t, x, y, z) = ǫ0 = 0.3 − 0.6 GeV/fm3

• H. Petersen, Phys.Rev. C78 (2008)

◮ Constant temperature surface T = 150 − 170 MeV

• D. Teaney et al., 2001, nucl-th/0110037; T. Hirano Phys.Lett.B636, 2006
• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Particlization and negative contributions

v

"positive" "negative"

dσµ - normal 4-vector uµ = (γ, γ− → v ) - 4-velocity T - temperature µ - chemical potential

Particlization

◮ know ǫ, p, uµ on the surface ◮ from EoS - T, µ ◮ want particles

”Cooper-Frye formula”

d3N(p) = f (p)

d3p (2π)3 pµ p0 dσµ pµ p0 · dσµ - analog of n · V

e.g. ideal hydro f (p) =

• e

pµuµ−µ T

± 1 −1

Negative contribution

◮ pµdσµ > 0: positive contribution,

particles fly out

◮ pµdσµ < 0: negative contribution,

particles fly in

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Negative contributions: options

Account feedback to hydro - great increase in complexity

• K. Bugaev, Phys Rev Lett. 2003; L. Czernai, Acta Phys. Hung., 2005

Account effectively - artificial constructions

• S. Pratt, 2014, nucl-th1401.0136

Neglect - violate conservation laws

How large are negative contributions? What changes if we neglect them and how much? How much does the choice of transition surface influence results? Is hydro equivalent to cascade in the transition region?

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Negative contributions: possible solution

Hybrid model Assume: transport equivalent to hydrodynamics Neglect negative Cooper-Frye contributions + remove particles from cascade if they fly to hydrodynamical region

Cooper-Frye

Is it possible to compensate negative Cooper-Frye contributions? That would solve problem with conservation laws.

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

6 / 19

Coarse-grained microscopic transport approach

Hypersurface of constant Landau rest frame energy density: mimic hybrid model transition surface Generate many UrQMD events On a (t,x,y,z) grid calculate T µν =

• 1

Vcell

• i∈cell

pµ

i pν i

p0

i

• event average

In each cell go to Landau frame: T 0ν

L

= (ǫL, 0, 0, 0) Construct surface ǫL(t, x, y, z) = ǫ0 Example: E = 160 AGeV, Au+Au central collision, ǫ0 = 0.3 GeV/fm3 t = 4 fm/c t = 11 fm/c t = 13 fm/c t = 18 fm/c

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

7 / 19

Definitions for negative contributions

Hypersurface Σ: ǫL(t, x, y, z) = const

◮ A) Cooper-Frye formula on Σ ◮ B) count UrQMD particles crossing Σ

A ≡ B if particle distribution from UrQMD is exactly equilibrated A) Cooper-Frye p0 d3N+ dp3 = pµdσµ exp(pνuν/T) ± 1θ(pνdσν) p0 d3N− dp3 = pµdσµ exp(pνuν/T) ± 1θ(−pνdσν) B) ”by particles”

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

8 / 19

Gaussian smearing and statistics

Results are very sensitive to surface lumpiness

E = 10 A GeV, b =0, σ = 1 fm CF positive/10

• utward crossings/10

CF negative inward crossings

dNπ/dy|y=0

25

N

1 10 1000 104

Saturation of results against statistics To get a smooth surface gaussian smearing with σ = 1 fm was used.

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

9 / 19

What changes if we neglect negative contributions

Conservation laws will be violated Spectra will change depending

• n

◮ collision energy ◮ centrality ◮ particle sort ◮ transition surface

We further investigate [dN−/dy]/[dN+/dy] in % Example:

π

E = 10 AGeV, b=0 fm

• nly positive

total Cooper-Frye

dNπ/dy

10 20 30 40 50

y

• 3
• 2
• 1

1 2 3

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

10 / 19

Negative contributions: particle mass dependence

E = 40 AGeV, b = 0, ǫ0 = 0.3 GeV/fm3, dN/dy distributions π (mπ = 139 MeV)

π

E = 40 AGeV, b=0 fm by particles Cooper-Frye

[dN-

π/dy]/[dN+ π/dy], %

2 4 6 8

y

• 3
• 2
• 1

1 2 3

K + (mK = 495 MeV)

K+

E = 40 AGeV, b=0 fm by particles Cooper-Frye

[dN-

K+/dy]/[dN+ K+/dy], %

2 4 6 8

y

• 3
• 2
• 1

1 2 3

N (mN = 938 MeV)

N

E = 40 AGeV, b=0 fm by particles Cooper-Frye

[dN-

N/dy]/[dN+ N/dy], %

2 4 6 8

y

• 3
• 2
• 1

1 2 3

Smaller mass - larger negative contribution

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

11 / 19

Negative contributions: energy dependence

Pions, ǫ0 = 0.3 GeV/fm3, dN/dy distributions 10 AGeV

E = 10 AGeV, b=0 fm by particles hydro-style

π

[dN-

π/dy]/[dNtot π /dy], %

2.5 5 7.5 10 12.5 15

y

• 3
• 2
• 1

1 2 3

40 AGeV

π

E = 40 AGeV, b=0 fm by particles Cooper-Frye

[dN-

π/dy]/[dN+ π/dy], %

2.5 5 7.5 10 12.5 15

y

• 3
• 2
• 1

1 2 3

160 AGeV

π

E = 160 AGeV, b=0 fm by particles Cooper-Frye

[dN-

π/dy]/[dN+ π/dy], %

2.5 5 7.5 10 12.5 15

y

• 3
• 2
• 1

1 2 3

Lower collision energy - slower expansion - larger negative contributions

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Negative contributions: dependence on surface ǫ0

E = 40 AGeV, b = 0

t, fm/c

E = 40 AGeV, b=0 fm ε0 = 0.6 GeV/fm3 ε0 = 0.3 GeV/fm3

5 10 15

z, fm

• 10
• 5

5 10

π

Cooper-Frye, ε0 = 0.3 GeV/fm3 Cooper-Frye, ε0 = 0.6 GeV/fm3 by particles, ε0 = 0.3 GeV/fm3 by particles, ε0 = 0.6 GeV/fm3 E = 40 AGeV, b=0 fm

[dN-

π/dy]/[dN+ π/dy], %

5 10 15

y

• 3
• 2
• 1

1 2 3

E = 40 AGeV, b=0 fm ε0 = 0.3 GeV/fm3 ε0 = 0.6 GeV/fm3

dN/dγ ⋅ 103

2 6 8

γ

0.5 1.0 2.0 2.5

Larger ǫ0 - slower surface expansion - larger negative contributions

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Negative contributions: dependence on centrality

E = 40 AGeV, b = 0

π

Cooper-Frye, b = 0 fm Cooper-Frye, b = 6 fm Cooper-Frye, b = 12 fm E = 40 AGeV, ε0 = 0.3 GeV/fm3

[dN-

π/dy]/[dN+ π/dy], %

5 10

y

• 3
• 2
• 1

1 2 3

More peripheral collision - smaller negative contributions

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Summary

Hydro-transport transition (”particlization”) was studied

◮ Coarse-grained UrQMD was used to construct ǫ(t, x, y, z) = ǫ0

isosurface

◮ Negative contributions on this surface are calculated in two ways:

from Cooper-Frye formula and explicitly counting particles

Negative contributions are larger

◮ for smaller collision energies ◮ for central collisions than for peripheral ◮ for smaller particle masses ◮ for larger ǫ0 ◮ for lumpy transition surface

Negative contributions by particles are smaller than Cooper-Frye ones

◮ no compensation by accident

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Backup: surface quality check

Surface - no holes or double counting: Cornelius routine Conservation laws on hypersurface: accuracy better than 1% Energy conservation

%

−5 0 5 5 10 15 20

%

−5 0 5

t, fm/c

5 15

discrep., %

−5 5 5 10 15

E = 160 AGeV, b=0 fm

GeV

E = 40 AGeV, b=0 fm Ein(t-dt) - Ein(t) ∫ dσμ Tμ 0

GeV

E = 10 AGeV, b=0 fm

GeV

25 50

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Backup: statistics matters

E = 160 AGeV, b = 0 Smooth surface

π

E = 160 AGeV, b=0 fm by particles Cooper-Frye

[dN-

π/dy]/[dN+ π/dy], %

5 10 15 20 25 30

y

• 3
• 2
• 1

1 2 3

Lumpy surface

π

E = 160 AGeV, b=0 fm by particles Cooper-Frye

[dN-

π/dy]/[dN+ π/dy], %

5 10 15 20 25 30

y

• 3
• 2
• 1

1 2 3

Lumpier surface - larger negative contributions

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

17 / 19

Spectra: nucleons

Red lines - by particles, blue lines - Cooper-Frye. ǫ0 = 0.3 GeV/fm3 Ecoll y pT Conclusion 10 AGeV

N

E = 10 AGeV, b=0 fm dNN

+/dy by particles

dNN

+/dy Cooper-Frye

dN+

N/dy

20 40 60 80

y

• 3
• 2
• 1

1 2 3

N

E = 10 AGeV, b=0 fm dN+

N/pTdpT by particles

dN+

N/pTdpT Cooper-Frye

dN+/pTdpT

10−4 10−3 10−2 10−1 100 101 102 103 104

pT, GeV

0.5 1 2 2.5 3

Cooper-Frye works well. Spectra are close. 160 AGeV

N

E = 160 AGeV, b=0 fm dNN

+/dy by particles

dNN

+/dy Cooper-Frye

dN+

N/dy

10 20

y

• 3
• 2
• 1

1 2 3

N

E = 160 AGeV, b=0 fm dN+

N/pTdpT by particles

dN+

N/pTdpT Cooper-Frye

dN+/pTdpT

10−4 10−3 10−2 10−1 100 101 102 103 104

pT, GeV

0.5 1 2 2.5 3

At high |y| distri- bution is not ther- mal. Similar picture for ∆, Λ, K +, K −, but ...

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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Spectra: pions

Red lines - by particles, blue lines - Cooper-Frye. ǫ0 = 0.3 GeV/fm3 Ecoll y pT Conclusion 10 AGeV

π

E = 10 AGeV, b=0 fm dN+

π/dy by particles

dN+

π/dy Cooper-Frye

dN+

π/dy

20 40 60 80

y

• 3
• 2
• 1

1 2 3

π

E = 10 AGeV, b=0 fm dN+

π/pTdpT by particles

dN+

π/pTdpT Cooper-Frye

dN+/pTdpT

10−3 100 103

pT, GeV

0.5 1 2 2.5 3

π out of chemical equilibrium: reso- nance decays 160 AGeV

π

E = 160 AGeV, b=0 fm dNπ

+/dy by particles

dNπ

+/dy Cooper-Frye

dN+

π/dy

50 100 150 200

y

• 3
• 2
• 1

1 2 3

π

E = 160 AGeV, b=0 fm dN+

π/pTdpT by particles

dN+

π/pTdpT Cooper-Frye

dN+/pTdpT

10−3 100 103

pT, GeV

0.5 1 2 2.5 3

π out of chemical equilibrium: reso- nance decays

• D. Oliinychenko (FIAS)

Cooper-Frye negative contributions

• Sep. 2014

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