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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