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 E lab ∈ [0 . 4 , 1 . 5] A GeV ◮ Carbon-carbon at E lab ∈ { 1 , 2 } A GeV ◮ Rapidity and transverse mass spectra ◮ Predictions for HADES pion beam ◮ π − p at E lab = 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: p µ ∂ µ f i ( x , p ) = C i (1) coll ◮ 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 = 3 A GeV b = 3 fm 6 / 22

Implemented Particles ◮ Mesons: ◮ π , ρ , η , ω , φ , σ , f 2 ◮ 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 p 80 SMASH-0.85-57-gf097a90 total 70 N * * 60 data (total) data (elast) 50 [mb] 40 30 20 10 0 1.2 1.4 1.6 1.8 2.0 s [GeV] 8 / 22

Cross Sections pp 80 SMASH-0.85-57-gf097a90 total 70 N + N N + N * 60 N + N + * N * + 50 + [mb] * + 40 data (total) data (elast) 30 20 10 0 2.0 2.5 3.0 3.5 4.0 4.5 s [GeV] 9 / 22

Detailed Balance: πρσ Box 100 π 0 ρ + σ π + ρ 0 90 π - ρ - 80 multiplicity 70 15 10 5 count reactions 0 0 20 40 60 80 100 t [fm/c] 10 / 22

Detailed Balance: πρσ Box Forward and backward reactions 1.01 ) σ N ππ↔ρ /(π 0 π - →ρ - ) N ππ↔σ /(π + π - →σ) ↔ - 0 0 + ρ ρ π σ ρ ↔ 0 ↔ ↔ ↔ π 0 ( + + π × + - π π π π - 2 - 0 π π π 1 0.99 10 7 π - π + →ρ 0 dN ρ↔ππ /dM inv 10 6 ρ 0 →π - π + 10 5 10 4 10 3 10 2 0 1 2 3 4 5 M inv [GeV/c 2 ] 11 / 22

FOPI Measurements ◮ Gold-gold collisions at various energies ◮ Centrality selections using energy-ratio cuts i p 2 ERAT = E T � Ti / ( m i + E i ) = (2) E L � i p Li / ( m i + E i ) ◮ Normalized rapidity: y 0 = y − y cm (3) y cm ◮ Simulated with SMASH (with and without Skyrme potential, Fermi motion, Pauli blocking) 12 / 22

FOPI Pion Production Au + Au (b < 2 fm) 2 10 ) + + N M( ) = 3/2(N 1 10 SMASH without potential SMASH with potential FOPI data 0.4 0.6 0.8 1.0 1.2 1.4 1.6 E kin [AGeV] 3.2 3.0 SMASH without potential 2.8 SMASH with potential 2.6 FOPI data + 2.4 /N 2.2 N 2.0 1.8 1.6 1.4 0.4 0.6 0.8 1.0 1.2 1.4 1.6 E kin [AGeV] 13 / 22

FOPI Rapidity Spectra at E lab = 0 . 8 A GeV 5 SMASH FOPI 4 3 dN/dy 0 2 1 0 2 1 0 1 2 y 0 14 / 22

HADES Measurements ◮ Carbon-carbon collisions at E lab ∈ { 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 (1 A GeV) E lab = 1AGeV , 8 10 y 0 [1. 05, 1. 35] 7 10 y 0 [0. 75, 1. 05] y 0 [0. 45, 0. 75] 6 10 y 0 [0. 15, 0. 45] 5 y 0 [ 0. 15, 0. 15] 10 y 0 [ 0. 45, 0. 15] 4 10 y 0 [ 0. 75, 0. 45] dm T [ GeV ] 3 10 2 dN 10 T m 2 1 1 10 0 10 1 10 2 10 3 10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 m T m 0 [ GeV ] 16 / 22

HADES Transverse Mass Spectra vs. SMASH (2 A GeV) E lab = 2AGeV , 9 10 y 0 [0. 5, 0. 7] 8 10 y 0 [0. 3, 0. 5] y 0 [0. 1, 0. 3] 7 10 y 0 [ 0. 1, 0. 1] 6 y 0 [ 0. 3, 0. 1] 10 y 0 [ 0. 5, 0. 3] 5 10 y 0 [ 0. 7, 0. 5] dm T [ GeV ] 4 10 3 dN 10 T m 2 1 2 10 1 10 0 10 1 10 2 10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 m T m 0 [ GeV ] 17 / 22

HADES Pion Beam ◮ Upcoming HADES data: π − C (and π − W ) collisions at E lab = 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 reaction rates, 50000 events 1e 3 dN react /dt /event [ fm 1 ] 3.5 SMASH-0.85-54-gf6cab38 3.0 2.5 N N * NN NN N 2.0 other N * 1.5 1.0 0.5 0.0 0 5 10 15 20 25 30 t / fm 1.2 1.0 N react /event 0.8 0.6 0.4 0.2 0.0 NN * * N * N * * N * other inelastic N NN N N N N 19 / 22

HADES Pion Beam: Pion Transverse Mass 2 10 + SMASH SMASH 1 10 dm T [ GeV ] 0 10 dN T m 2 1 1 10 2 10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 m T m 0 [ GeV ] 20 / 22

HADES Pion Beam: Nucleon Transverse Mass 2 10 p SMASH n SMASH 1 10 0 dm T [ GeV ] 10 dN 1 10 T m 2 1 2 10 3 10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 m T m 0 [ GeV ] 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 ◮ S imulating M any A ccelerated S trongly-interacting H adrons ◮ 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: � σ tot d trans < d int = (4) π � 2 � ( � r a − � r b )( � p a − � p b ) r b ) 2 − d 2 trans = ( � r a − � (5) p b ) 2 ( � p a − � t coll = − ( � x a − � x b )( � v a − � v b ) (6) v b ) 2 ( � v a − � ◮ Not Lorentz-invariant 26 / 22

Frame Dependence of Particle Production 550 center of mass frame center of velocity frame 540 fixed target frame total number of interactions 530 520 510 500 490 480 0.01 0.02 0.04 0.06 0.08 0.1 time step size dt 27 / 22

Decay Width ◮ Manley-Saleski ansatz for off-shell decay branching ratio: ρ ab ( m ) Γ R → ab = Γ 0 (7) R → ab ρ ab ( m 0 ) b ) p f � dm 2 a dm 2 b A a ( m 2 a ) A b ( m 2 m B 2 ρ ab ( m ) = L ( p f R ) F ab ( m ) (8) ◮ Example: L=1 decay with stable daughters (e.g. ∆ → π N ) � p f � 3 p 2 f 0 + Λ 2 m 0 Γ( m ) = Γ 0 (9) p 2 f + Λ 2 m p f 0 28 / 22

Cross Sections ◮ 2 → 1 resonance production (Breit-Wigner) 2 J R + 1 4 π s Γ ab → R ( s )Γ R ( s ) σ ab → R ( s ) = (2 J a + 1)(2 J b + 1) S ab ( s − M 0 ) 2 + s Γ R ( s ) 2 p 2 cm (10) ◮ 2 → 2 | M | 2 4 π � σ ab → Rc ( s ) = C 2 dm 2 A ( m 2 ) p f ab → Rc (11) cm I 64 π 2 s p i cm where A ( m ) = 1 m Γ( m ) (12) ( m 2 − M 2 0 ) 2 + m 2 Γ( m ) 2 π 29 / 22

Skyrme Potentials � ρ U = a ρ ρ p − ρ n � τ I 3 + b + 2 S pot (13) ρ 0 ρ 0 ρ 0 I � p 2 i + m 2 H i = � i + U ( � r i ) (14) where a = − 209 . 2 MeV b = 156 . 4 MeV τ = 1 . 53 S pot = 18 MeV 30 / 22

FOPI Rapidity Spectra at E lab = 0 . 8 A GeV + 2.5 SMASH FOPI 2.0 1.5 dN/dy 0 1.0 0.5 0.0 2 1 0 1 2 y 0 31 / 22

HADES Transverse Mass Spectra vs. UrQMD (1 A GeV) Agakishiev et al, Eur.Phys.J. A40 (2009) 45-59 32 / 22

HADES Transverse Mass Spectra vs. UrQMD (2 A GeV) Agakishiev et al, Eur.Phys.J. A40 (2009) 45-59 33 / 22

HADES Pion Beam: Predicted Particle Production most commonly produced particles per event 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ∆ N ∗ ∆ ∗ π N ρ σ K Λ η ω Σ γ f 2 34 / 22

HADES Pion Beam: Nucleon Transverse Mass ( p Target) 0 10 p SMASH n SMASH dm T [ GeV ] dN T m 2 1 1 10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 m T m 0 [ GeV ] 22 / 22