SMASH - A new hadron transport approach for heavy ion collisions - - PowerPoint PPT Presentation

SMASH - A new hadron transport approach for heavy ion collisions

54th International Winter Meeting on Nuclear Physics, Bormio January 26, 2016 Vinzent Steinberg

HGS-HIRe

Helmholtz Graduate School for Hadron and Ion Research

1 / 22

Outline

◮ Overview of the SMASH project ◮ Comparison to HADES and FOPI results

◮ Gold-gold at Elab ∈ [0.4, 1.5]A GeV ◮ Carbon-carbon at Elab ∈ {1, 2}A GeV ◮ Rapidity and transverse mass spectra

◮ Predictions for HADES pion beam

◮ π−p at Elab = 1.7 GeV ◮ Reaction rates and particle production ◮ Transverse mass spectra 2 / 22

Transport Approach: Big Picture

◮ Microscopic simulation of hadronic reactions ◮ Solve relativistic Boltzmann equation:

pµ∂µfi(x, p) = Ci

coll

(1)

◮ Each particle represented by a number of point-like test

particles

◮ Use Gaussian wave packets when calculating thermodynamic

quantities

3 / 22

The SMASH Team

Currently:

◮ Hannah Petersen (group leader) ◮ Janus Weil, Long-Gang Pang (postdocs) ◮ Dima Oliinychenko, Jean-Bernard Rose, Vinzent Steinberg

(PhD students)

◮ Anna Schäfer, Jan Staudenmeyer, Markus Mayer (master

students) Previously:

◮ Max Attems, Jussi Auvinen, Björn Bäuchle, Matthias Kretz,

Marcel Lauf

4 / 22

Motivation

◮ Understanding hadronic phase in heavy-ion collisions ◮ Modeling non-equilibrium phenomena and microscopic physics ◮ Open, maintainable, extensible code

5 / 22

Movie: Energy Density and Velocity in CuCu collision

√s = 3A GeV b = 3 fm

6 / 22

Implemented Particles

◮ Mesons:

◮ π, ρ, η, ω, φ, σ, f2 ◮ K, K ∗(892), K ∗(1410)

◮ Baryons:

◮ N, N∗, up to 2.25 GeV ◮ ∆, ∆∗, up to 1.95 GeV ◮ Λ, Λ∗, up to 1.89 GeV ◮ Σ, Σ∗, up to 1.915 GeV ◮ Ξ, Ω 7 / 22

Cross Sections

1.2 1.4 1.6 1.8 2.0

s[GeV]

10 20 30 40 50 60 70 80

[mb] p

SMASH-0.85-57-gf097a90 total N *

*

data (total) data (elast) 8 / 22

Cross Sections

2.0 2.5 3.0 3.5 4.0 4.5

s[GeV]

10 20 30 40 50 60 70 80

[mb] pp

SMASH-0.85-57-gf097a90 total N+N N+N * N+ N+

*

N * + + +

*

data (total) data (elast) 9 / 22

Detailed Balance: πρσ Box

count reactions π0 π+ π- ρ+ ρ0 ρ- σ

multiplicity

5 10 15 70 80 90 100

t [fm/c]

20 40 60 80 100

10 / 22

Detailed Balance: πρσ Box

Forward and backward reactions

π-π+→ρ0 ρ0→π-π+

dNρ↔ππ/dMinv

102 103 104 105 106 107

Minv [GeV/c2]

1 2 3 4 5 π π

+

↔ ρ

+

π

• π

↔ ρ

• π
• π

+

↔ ρ 2 × ( π π ↔ σ ) π

• π

+

↔ σ

Nππ↔σ/(π+π-→σ) Nππ↔ρ/(π0π-→ρ-)

0.99 1 1.01

11 / 22

FOPI Measurements

◮ Gold-gold collisions at various energies ◮ Centrality selections using energy-ratio cuts

ERAT = ET EL =

• i p2

Ti/(mi + Ei)

• i pLi/(mi + Ei)

(2)

◮ Normalized rapidity:

y0 = y − ycm ycm (3)

◮ Simulated with SMASH

(with and without Skyrme potential, Fermi motion, Pauli blocking)

12 / 22

FOPI Pion Production

0.4 0.6 0.8 1.0 1.2 1.4 1.6

Ekin [AGeV]

10

1

10

2

M( ) = 3/2(N

+ + N

) Au + Au (b < 2 fm)

SMASH without potential SMASH with potential FOPI data 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Ekin [AGeV]

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

N /N

+

SMASH without potential SMASH with potential FOPI data 13 / 22

FOPI Rapidity Spectra at Elab = 0.8A GeV

2 1 1 2

y0

1 2 3 4 5

dN/dy0

SMASH FOPI 14 / 22

HADES Measurements

◮ Carbon-carbon collisions at Elab ∈ {1, 2} A GeV ◮ Impact parameter distribution provided by HADES

(reconstructed from another transport model)

◮ Simulated with SMASH

(no potentials, no Fermi motion, no Pauli blocking)

15 / 22

HADES Transverse Mass Spectra vs. SMASH (1A GeV)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

mT m0 [GeV]

10

3

10

2

10

1

10 10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

8

1 m2

T

dN dmT [GeV]

Elab = 1AGeV,

y0 [1. 05, 1. 35] y0 [0. 75, 1. 05] y0 [0. 45, 0. 75] y0 [0. 15, 0. 45] y0 [

• 0. 15, 0. 15]

y0 [

• 0. 45,
• 0. 15]

y0 [

• 0. 75,
• 0. 45]

16 / 22

HADES Transverse Mass Spectra vs. SMASH (2A GeV)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

mT m0 [GeV]

10

2

10

1

10 10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

1 m2

T

dN dmT [GeV]

Elab = 2AGeV,

y0 [0. 5, 0. 7] y0 [0. 3, 0. 5] y0 [0. 1, 0. 3] y0 [

• 0. 1, 0. 1]

y0 [

• 0. 3,
• 0. 1]

y0 [

• 0. 5,
• 0. 3]

y0 [

• 0. 7,
• 0. 5]

17 / 22

HADES Pion Beam

◮ Upcoming HADES data: π−C (and π−W ) collisions at

Elab = 1.7 GeV

◮ Corresponds to √s ≈ 2.1 GeV,

requires heavy N∗ resonances for π−p cross section (little experimental data on branching ratios)

◮ Simulated with SMASH for b ∈ [0, 2] fm ◮ No potentials, no Fermi motion, no Pauli blocking ◮ Spectators (particles that only interact elastically) are ignored

18 / 22

HADES Pion Beam: Predicted Reactions

5 10 15 20 25 30

t / fm

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

dNreact/dt/event [fm 1]

1e 3 SMASH-0.85-54-gf6cab38

NN NN N N

*

N N *

• ther

NN NN N N

* *

N

*

N N * N * N N *

• ther

inelastic

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Nreact/event

reaction rates, 50000 events 19 / 22

HADES Pion Beam: Pion Transverse Mass

0.0 0.1 0.2 0.3 0.4 0.5 0.6

mT m0 [GeV]

10

2

10

1

10 10

1

10

2

1 m2

T

dN dmT [GeV]

+ SMASH

SMASH 20 / 22

HADES Pion Beam: Nucleon Transverse Mass

0.0 0.1 0.2 0.3 0.4 0.5 0.6

mT m0 [GeV]

10

3

10

2

10

1

10 10

1

10

2

1 m2

T

dN dmT [GeV] p SMASH n SMASH 21 / 22

Conclusion

◮ Clean and future-proof implementation of hadronic transport ◮ Work in progress:

◮ Strangeness ◮ String fragmentation

◮ Future work:

◮ Interface to hydro ◮ Parallelization ◮ Many-particle interactions, stochastic rates 22 / 22

Transport Approach: Reactions

◮ Inelastic low energy reactions:

◮ Resonance excitations and decays ◮ Need cross sections and branching ratios

→ Data available from PDG, but very little on heavy resonances

◮ Different options at high energies:

◮ String fragmentation (color flux tubes) ◮ Hagedorn states 23 / 22

SMASH: Current Status

◮ Simulating Many Accelerated Strongly-interacting Hadrons ◮ Roughly three years old ◮ Ca. 20 000 source lines of code,

7 active contributors

◮ Almost feature parity with UrQMD

(missing: string fragmentation)

24 / 22

I/O and Tests

◮ Input

◮ Configuration file for simulation parameters and options ◮ Configuration files for particles and decays ◮ Very concise ◮ Easy to switch

◮ Output

◮ OSCAR, VTK, ROOT, binary ◮ Easy to make movies or analyze in ROOT

◮ Tests

◮ Separate analysis repository for regular consistency tests and

comparison to experiment

◮ Unit tests to check code correctness 25 / 22

Collision Criterion

◮ Geometric collision criterion (as used by UrQMD)

using the transverse distance in c.o.m. frame: dtrans < dint =

σtot

π (4) d2

trans = (

ra − rb)2 −

• (

ra − rb)( pa − pb)

2

( pa − pb)2 (5) tcoll = −( xa − xb)( va − vb) ( va − vb)2 (6)

◮ Not Lorentz-invariant

26 / 22

Frame Dependence of Particle Production

0.01 0.02 0.04 0.06 0.08 0.1

time step size dt

480 490 500 510 520 530 540 550

total number of interactions

center of mass frame center of velocity frame fixed target frame 27 / 22

Decay Width

◮ Manley-Saleski ansatz for off-shell decay branching ratio:

ΓR→ab = Γ0

R→ab

ρab(m) ρab(m0) (7) ρab(m) =

• dm2

adm2 bAa(m2 a)Ab(m2 b)pf

m B2

L(pf R)Fab(m)

(8)

◮ Example: L=1 decay with stable daughters (e.g. ∆ → πN)

Γ(m) = Γ0 m0 m

pf

pf 0

3 p2

f 0 + Λ2

p2

f + Λ2

(9)

28 / 22

Cross Sections

◮ 2 → 1 resonance production (Breit-Wigner)

σab→R(s) = 2JR + 1 (2Ja + 1)(2Jb + 1)Sab 4π p2

cm

sΓab→R(s)ΓR(s) (s − M0)2 + sΓR(s)2 (10)

◮ 2 → 2

σab→Rc(s) = C2

I

|M|2

ab→Rc

64π2s 4π pi

cm

• dm2A(m2)pf

cm

(11) where A(m) = 1 π mΓ(m) (m2 − M2

0)2 + m2Γ(m)2

(12)

29 / 22

Skyrme Potentials

U = a ρ ρ0 + b

ρ

ρ0

τ

+ 2Spot ρp − ρn ρ0 I3 I (13) Hi =

• p2

i + m2 i + U(

ri) (14) where a = −209.2 MeV b = 156.4 MeV τ = 1.53 Spot = 18 MeV

30 / 22

FOPI Rapidity Spectra at Elab = 0.8A GeV

2 1 1 2

y0

0.0 0.5 1.0 1.5 2.0 2.5

dN/dy0

+ SMASH FOPI 31 / 22

HADES Transverse Mass Spectra vs. UrQMD (1A GeV)

Agakishiev et al, Eur.Phys.J. A40 (2009) 45-59

32 / 22

HADES Transverse Mass Spectra vs. UrQMD (2A GeV)

Agakishiev et al, Eur.Phys.J. A40 (2009) 45-59

33 / 22

HADES Pion Beam: Predicted Particle Production

π N ∆ N ∗ ∆ ∗ ρ σ K Λ η ω Σ γ f2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

most commonly produced particles per event

34 / 22

HADES Pion Beam: Nucleon Transverse Mass (p Target)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

mT m0 [GeV]

10

1

10 1 m2

T

dN dmT [GeV] p SMASH n SMASH 22 / 22