Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Comparison between Different Transport Models Pawel Danielewicz National Superconducting Cyclotron Laboratory Michigan State University Probing Dense Baryonic Matter with Hadrons: Status and Perspective GSI, 11 - 13 February, 2019 Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Outline Introduction 1 Basics Types of Transport Models Successes & Failures 2 E 0 / A at ρ > ρ 0 S ( ρ ) from π − /π + Comparison Project 3 Code Comparison Effort Full-Run Comparisons Box Comparisons Impacts: TuQMD Example 4 5 Conclusions Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Need for Transport Many repeated elementary interactions outside equilibrium • Central Nuclear Collisions • Isotope Production • Energetic Hadron-Nucleus Collision • ν Detection • Supernova Explosion • Technological Applications • . . . Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Degrees of Freedom Choice depends on energy and application • Nucleons • Clusters • Pions, Baryon Resonances • Kaons, Strange Baryons • Photons • . . . Dominant degrees of freedom must be included; other might be treated perturbatively Phase-space distribution (in configuration space and momentum) ⇔ Wigner function � d r e − i pr � ˆ ψ † H ( R − r / 2 , T ) ˆ f ( p ; R , T ) = ψ H ( R + r / 2 , T ) � Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Statistical Description Phase-space distribution � d r e − i pr � ˆ ψ † H ( R − r / 2 , T ) ˆ f ( p ; R , T ) = ψ H ( R + r / 2 , T ) � Dynamics: Particles move through noisy medium: stochastic + deterministic impact of the medium on the particle - collisions + mean field Descriptions invoke Boltzmann equation: ∂ t + ∂ǫ ∂ f ∂ f r − ∂ǫ ∂ f p = K < ( 1 ∓ f ) − K > f ∂ p p p ∂ r r ∂ r r r ∂ p p Left-hand deterministic impact Right-hand stochastic Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Means of Learning on EOS at ρ > ρ 0 � ρ n − ρ p E A ( ρ n , ρ p ) = E 0 � 2 + O ( . . . 4 ) A ( ρ ) + S ( ρ ) ρ symmetric matter (a)symmetry energy ρ = ρ n + ρ p � ρ − ρ 0 ρ − ρ 0 E 0 A ( ρ ) = − B + K � 2 S ( ρ ) = S 0 + L + . . . + . . . 18 ρ 0 3 ρ 0 Known: B ≈ 16 MeV K ∼ 235 MeV Unknown: S 0 ? L ? Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions • Boltzmann Equation Type – Examples: GIBUU, IBUU, pBUU, RVUU – Pros: Well-defined equation, derivable from microscopic theory, solved; easy Pauli principle & mean-field – Cons: No fluctuations • Molecular Dynamics • Examples: IQMD, CoMD, TuQMD, UrQMD • Pros: Good fluctuations late in reactions • Cons: Wrong fluctuations initially, troubles with Pauli & mean-field, too much phenomenology? • Antisymmetrized Molecular Dynamics (AMD) – Pros: Excellent initial states, good mean field & Pauli – Cons: Troubles with final states, dose of phenomenology Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions EOS and Flow Anisotropies EOS assessed through reaction plane anisotropies characterizing particle collective motion v = − � Hydro? Euler eq. in � v = 0 frame: m N ρ ∂ ∂ t � ∇ p where p - pressure. From features of v , knowing ∆ t , we may learn about p in relation to ρ . ∆ t fixed by spectator motion For high p , expansion ��� ������ rapid and much ������� affected by spectators ���������� For low p , expansion ������ sluggish and ��������� completes after ������� spectators gone Simulation by Shi (pBUU) � � � � �� �� �� ���� Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions 2 nd -Order or Elliptic Flow Anisotropy studied at midrapidity: v 2 = � cos 2 φ � , where φ is azimuthal angle relative to reaction plane Au+Au v 2 Excitation Function Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Subthreshold Meson (K/ π ) Production 7 7 soft EOS, pot ChPT Ratio of kaons per hard EOS, pot ChPT 6 6 (M K+ /A) Au+Au / (M K+ /A) C+C (M K+ /A) Au+Au / (M K+ /A) C+C soft EOS, IQMD, pot RMF hard EOS, IQMD, pot RMF participant nucleon KaoS 5 5 soft EOS, IQMD, Giessen cs in Au+Au collisions to hard EOS, IQMD, Giessen cs kaons in C+C collisions 4 4 vs beam energy 3 3 filled diamonds: KaoS data 2 2 open symbols: theory 1 1 Fuchs et al 0.8 0.8 1.0 1.0 1.2 1.2 1.4 1.4 1.6 1.6 E lab [GeV] E lab [GeV] Kaon yield sensitive to EOS because multiple interactions needed for production, testing density The data suggest a relatively soft EOS Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Constraints from Flow on EOS Au+Au flow anisotropies: 100 ρ ≃ ( 2 − 4 . 6 ) ρ 0 . pressure (MeV/fm 3 ) No one EOS yields both flows right. Discrepancies: 10 Kaon Yields inaccuracy of theory Flow: F & v 2 π + v 2 , K=240MeV Most extreme models for π + v 2 , K=300MeV GMR EOS can be eliminated Fermi Gas RMF: NL3 1 1 1.5 2 2.5 3 3.5 4 4.5 ρ/ρ 0 PD, Lacey & Lynch + Fuchs + Le Fevre + Hong + . . . Neutron Matter: Uncertainty in symmetry energy Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Charged π Probing High- ρ Symmetry Energy B-A Li PRL88(02)192701: S ( ρ > ρ 0 ) ⇒ n / p ρ>ρ 0 ⇒ π − /π + a 80 E sym (MeV) m E y s 60 40 b E Pions originate 20 sym from high ρ 0 ρ/ρ 0 1 2 3 1.6 2.3 132 Sn+ 124 Sn, b=1 fm E/A=200 MeV (n/p) ρ / ρ 0>1 1.5 2.1 ( π / π ) like + 1.4 1.9 - 1.3 1.7 1.2 1.5 0 10 20 30 0 10 20 3 0 t (fm/c) Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Dedicated Experimental Efforts SAMURAI-TPC Collaboration (data taken; 8 countries and 43 researchers): comparisons of near-threshold π − and π + and also n - p spectra and flows at RIKEN, Japan. NSCL/MSU, Texas A&M U Western Michigan U, U of Notre Dame GSI, Daresbury Lab, INFN/LNS U of Budapest, SUBATECH, GANIL China IAE, Brazil, RIKEN, Rikkyo U Tohoku U, Kyoto U LAMPS TPC at RAON (S Korea): triple GEM, 3 π sr Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions FOPI Au+Au π − /π + Data? Reisdorf et al. (FOPI) NPA781(07)459 data: black symbols theory: colored symbols Opposing sensitivity to S ( ρ ) claimed in transport & used to explain data! Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions FOPI π − /π + Reproduced by pBUU . . . irrespectively of S int ( ρ ) = S 0 ( ρ/ρ 0 ) γ : Jun Hong & PD PRC90(14)024605 . . . Other probes possible, but general problem of model ambiguity remains! Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Chronology • Motivation: Discrepancies Impediment to Conclusions • Workshops at ECT* Trento in 2004 & 2009 – Jorg Aichelin, Christopher Hartnack, Evgeni Kolomeitsev – similar physics, naive full-run comparisons • Second Phase ≥ 2014 – Isospin physics, δ = ( ρ n − ρ p ) /ρ ∼ 0 . 2 needs more precision/consistency – Betty Tsang, Jun Xu, Yingxun Zhang, Akira Ono, Maria Colonna – similar/identical physics, naive restart – breaking problem into pieces: initial state, collisions, Pauli pcple, detailed balance, mean field. . . • Impact on Everyday Practices Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Papers & Participants – E. E. Kolomeitsev et al. , J. Phys. G 31 (2005) S741 – Jun Xu et al. (31 authors), Phys. Rev. C 93 (2016) 044609 – Yingxun Zhang et al. (30 authors), Phys. Rev. C 97 (2018) 034625 – . . . Transport Comparison Danielewicz
Introduction Successes & Failures Comparison Project Impacts: TuQMD Example Conclusions Premise – Specify the same physics inputs for different transport codes – Compare outputs – Full-run comparisons * elastic collisions only * constant isotropic cross section σ = 40 mb * soft EOS + momentum-independent mean-field * Next: π & K production – Controlled simplified conditions * isolated nucleus * collisions in a box ← approach to equilibrium * mean field in a box * Next: ∆ + π production in a box. . . Transport Comparison Danielewicz
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