SMASH transport approach as afterburner

Dmytro (Dima) Oliinychenko

29 June 2018

LBNL with Prof. V. Koch

PhD at FIAS with Prof. H. Petersen

Thanks to SMASH team!

Thanks to SMASH team! (incomplete on the pic)

Weil et al, PRC 94 (2016) no.5, 054905

Hybrid (hydrodynamics + hadronic afterburner) approaches

Relativistic FluidInitial State

Pre-equilibrium Dynamics Hadronization Transport/Freeze-out

• Hydrodynamics: local thermal equilibrium,

∂µTµν = 0, ∂µj

µ = 0, EoS, boundary conditionsApplicability: mean free path� system size =⇒ high density

• Afterburner: Monte-Carlo solution of Boltzmann equationsApplicability: mean free path� λCompton =⇒ low density

• Hybrid: hydro at high density + afterburner at low density1

Does hadronic afterburner

matter?

2

Does hadronic afterburner matter?

Hydro + decaysHydro + SMASH (σBB x1)Hydro + SMASH (σBB x2)ALICE, PbPb, 0-10%

p x 0.2

K

π x 5

1/2π

pT d

2 Nd/d

ydp T

10−4

10−3

1

1000

104

pT [GeV]0 1 2 3 4 5

DO, ongoing work

It matters: proton spectra (and kaon too!)

Effects: pion wind, isotropization, BB̄ annihilation 3

Does hadronic afterburner matter?

Hannah Petersen et al, QM’18 proceedings, thanks to Sangwook Ryu

It matters: proton spectra (and kaon too!)

Effects: pion wind, isotropization, BB̄ annihilation 3

Does hadronic afterburner matter?

Hannah Petersen et al, QM’18 proceedings, thanks to Sangwook Ryu

It matters: mass splitting of the flow increases

4

Does hadronic afterburner

matter for jets?

5

Does hadronic afterburner

matter for (mini-)jets?

5

Does hadronic afterburner matter for (mini-)jets?

Sangwook Ryu PhD thesis

It matters: spectra and flow 6

SMASH transport approach

Simulating

Multiple

Accelerated

Strongly-interacting

Hadrons

7

SMASH transport approach J. Weil et al., Phys.Rev. C94 (2016) no.5, 054905

• Monte-Carlo solver of relativistic Boltzmann equations

BUU type approach, testparticles ansatz: N → N · Ntest , σ → σ/Ntest

• Degrees of freedom

• most of established hadrons from PDG up to mass 2.3 GeV

• strings: do not propagate, only form and decay to hadrons

• Propagate from action to action (timesteps only for potentials)

action ≡ collision, decay, wall crossing

• Geometrical collision criterion: dij ≤√σ/π

• Interactions: 2↔ 2 and 2→ 1 collisions, decays, potentials, string

formation (soft - SMASH, hard - Pythia 8) and fragmentation via

Pythia 8

8

SMASH: initialization

• “collider” - elementary or AA reactions, Ebeam & 0.5 A GeV

• “box” - infinite matter simulationsdetailed balance tests, computing transport coefficients, thermodynamics of hadron gas

Rose et al., PRC 97 (2018) no.5, 055204

• “sphere” - expanding systemcomparison to analytical solution of Boltzmann equation,

Tindall et al., Phys.Lett. B770 (2017) 532-538

• “list” - hadronic afterburner after hydrodynamics

9

SMASH: degrees of freedom

Hadrons and decaymodes configurable via human-readable files

10

SMASH: technical facts

• C++, over 50k lines of code (including comments)

• git for version control

• Doxygen for documentation

• Redmine issue tracker

• Supports different output formats:

• Text

• Binary

• ROOT

• VTK - for visualization

• Will be open-source in 2018

see H. Petersen, QM’18 talk

• Under constant development and tuning

11

Interactions in SMASH

• Resonance formation and decayEx. ππ → ρ→ ππ, quasielastic scattering

ππ → f2 → ρρ→ ππππ

• (In-)elastic 2→ 2 scatteringparametrized cross-sections σ(

√s, t) or

isospin-dependent matrix elements |M|2(√s, I )

• String formation/fragmentation2→ n processes

• Potentialsonly change equations of motion

12

Interactions in SMASH

• Resonance formation and decayEx. ππ → ρ→ ππ, quasielastic scattering

ππ → f2 → ρρ→ ππππ

• (In-)elastic 2→ 2 scatteringparametrized cross-sections σ(

√s, t) or

isospin-dependent matrix elements |M|2(√s, I )

• String formation/fragmentation2→ n processes

• Potentialsonly change equations of motion

N (1440)+

1.0 1.2 1.4 1.6 1.8

m [GeV]

10-3

10-2

10-1

100

Γ [

GeV

]

total

π+ n

π0 p

π+ ∆0

π0 ∆+

π− ∆+ +

σp

For every resonance:

• Breit-Wigner spectral function A(m) = 2Nπ

m2Γ(m)(m2−M2

0 )2+m2Γ(m)2

• Mass dependent partial widths Γi (m)Manley formalism for off-shell width Manley and Saleski, Phys. Rev. D 45, 4002 (1992)

Total width Γ(m) =∑

i Γi (m)

• 2→ 1 cross-sections from detailed balance relations

12

Interactions in SMASH

• Resonance formation and decayEx. ππ → ρ→ ππ, quasielastic scattering

ππ → f2 → ρρ→ ππππ

• (In-)elastic 2→ 2 scatteringparametrized cross-sections σ(

√s, t) or

isospin-dependent matrix elements |M|2(√s, I )

• String formation/fragmentation2→ n processes

• Potentialsonly change equations of motion

0.4 0.6 0.8 1.0 1.2 1.40

20

40

60

80

100

120

140

σ [

mb]

π+ π−

total

elasticω

ρ

σ

f2

data (total)

data (elast)

For every resonance:

• Breit-Wigner spectral function A(m) = 2Nπ

m2Γ(m)(m2−M2

0 )2+m2Γ(m)2

• Mass dependent partial widths Γi (m)Manley formalism for off-shell width Manley and Saleski, Phys. Rev. D 45, 4002 (1992)

Total width Γ(m) =∑

i Γi (m)

• 2→ 1 cross-sections from detailed balance relations 12

Interactions in SMASH

• Resonance formation and decayEx. ππ → ρ→ ππ, quasielastic scattering

ππ → f2 → ρρ→ ππππ

• (In-)elastic 2→ 2 scatteringparametrized cross-sections σ(

√s, t) or

isospin-dependent matrix elements |M|2(√s, I )

• String formation/fragmentation2→ n processes

• Potentialsonly change equations of motion

2.0 2.5 3.0 3.5 4.0 4.5√s [GeV]

0

10

20

30

40

50

60

σ [

mb]

pptotalN+N

N+N ∗

N+∆

N+∆ ∗

N ∗+∆

∆+∆

∆+∆ ∗data (total)data (elast)

• NN → NN∗, NN → N∆∗, NN → ∆∆, NN → ∆N∗,

NN → ∆∆∗

angular dependencies of NN → XX cross-sections implemented

• Strangeness exchange KN → K∆, KN → Λπ, KN → Σπ

12

Interactions in SMASH

• Resonance formation and decayEx. ππ → ρ→ ππ, quasielastic scattering

ππ → f2 → ρρ→ ππππ

• (In-)elastic 2→ 2 scatteringparametrized cross-sections σ(

√s, t) or

isospin-dependent matrix elements |M|2(√s, I )

• String formation/fragmentation2→ n processes

• Potentialsonly change equations of motion

parameters of the string

model currently tuned to

p-p data at SPS energies

(work ongoing)

• String (soft or hard) fragmentation: always via Pythia 8

• Hard scattering and string formation: Pythia• Soft string formation: SMASH

• single/double diffractive

• BB̄ annihilation

• non-diffractive 12

Interactions in SMASH

• Resonance formation and decayEx. ππ → ρ→ ππ, quasielastic scattering

ππ → f2 → ρρ→ ππππ

• (In-)elastic 2→ 2 scatteringparametrized cross-sections σ(

√s, t) or

isospin-dependent matrix elements |M|2(√s, I )

• String formation/fragmentation2→ n processes

• Potentialsonly change equations of motion

Transverse radius of Cu

• Skyrme and symmetry potential

• U = a(ρ/ρ0) + b(ρ/ρ0)τ ± 2SpotρI3ρ0

ρ - Eckart rest frame baryon density

ρI3 - Eckart rest frame density of I3/I

a = −209.2 MeV, b = 156.4 MeV, τ = 1.35, Spot = 18 MeVcorresponds to incompressibility K = 240 MeV

assures stability of a nucleus with Fermi motion

12

Detailed balance testing in the box

count reactions

π0

π+

π-

ρ+

ρ0

ρ-

σ

mul

tipl

icit

y

0

5

10

15

70

80

90

100

t [fm/c]0 20 40 60 80 100

(a)

13

Detailed balance testing in the box

1 2 3 4 5Minv [GeV]

10 410 310 210 1100101102

dN dMdt

[GeV

1 fm1 ]

(b)

2 ×( )

0.991.001.011.021.03

N rea

ct/N i

sosp

ingr

oup

2×(

)(c)

13

SMASH thermodynamics: coarse-graining

• On a (t,x,y,z) grid compute

Tµν(~r) =1

Nev

∑events

∑i

pµi pνi

p0i

K (~r − ~ri , ui ); uµ = (u0, ~u) =pµ

m

K (~r − ~ri , u, σ) =u0

(2πσ2)3/2exp

(− (~r − ~ri )2 + (~u · (~r − ~ri ))2

2σ2

)• In each cell go to Landau frame: T 0ν

L = (εL, 0, 0, 0)

• Obtain T , µb, µs from ideal hadron gas EoS

Au

+A

u,√s N

N=

3G

eV,b

=5

fm

14

SMASH ideal hadron gas EoS

More hadron sorts - smaller pressure at given energy density

n b = 0.3 fm

-3

nb = 0 fm

-3

Huovinen, Petreczky s95p-v1UrQMD 3.4SMASH id. gasSMASH box

p [G

eV/fm

3 ]

0

0.05

0.15

0.2

ε [GeV/fm3]0 0.2 0.4 0.6 0.8 1

P. Huovinen, P. Petreczky, Nucl.Phys. A837 (2010) 26-53

UrQMD ≡ Hadron Gas EoS from UrQMD tables by J. Steinheimer15

Summary

• Hadronic afterburner matters

• SMASH is physically and technically mature

to be linked to JetScape

• SMASH can provide more than hadronic rescattering:

• Hadrons properties can be changed/retuned easily

• Built-in coarse-graining: themodynamics can be computed

• Dileptons and photons production

(not in the talk, see Staudenmaier et al., arXiv: 1711.10297 )

16

Backup: smearing kernel DO, HP, Phys.Rev. C93 (2016) no.3, 034905

The energy-momentum tensor Tµν is constructed as

Tµν(~r) =1

Nev

∑events

∑i

pµi pµi

p0i

K (~r − ~ri , pi ) (1)

Smearing kernel K (r): K (r)d3r should be Lorentz scalar

∆x i = Λij∆x ′j (2)

Λij = δij + (uiuj)/(1 + γ) (3)

(∆x i )2 = Λij∆x ′jΛi

k∆x ′k (4)

ΛijΛ

ik = δjk + ujuk (5)

(∆~x)2 = (∆~x ′)2 + (∆~x ′ · ~u)2 (6)

K (~r) = γ(2πσ2)−3/2exp

(−~r2 + (~r · ~u)2

2σ2

)(7)

Normalization using∫

(∏n

i=1 dxi ) e−xiAijxj = πn/2 (detA)−1/2

17