1. Several clouds when constraining the stiffness of the symmetry energy Qingfeng Li 1

2. Outline On the theoretical side: Theory/Model richness Observable systematicness and puzzles On the experimental side: Existing flow data from FOPI/LAND at GSI Background Model dependence transport of  (1232) resonance and  mesons mass-splitting spin-orbit interactions afterburner (coalescence) Clouds New experiments More consistent models Forthcoming 2

3. Background: on the theoretical side Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-Consistent Green’s Function (SCGF) Theory Variational Many-Body (VMB) approach Green’s Function Monte Carlo Calculation V lowk + Renormalization Group Effective Field Theories Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) QCD-based theory Phenomenological Approaches Relativistic mean-field (RMF) theory Quark Meson Coupling (QMC) Model Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations Self-consistent Relativistic Boltzmann Uehling-Uhlenbeck (SC-RBUU) 3 Go with: Successes, Uncertainties Improvements Need: Successors …

4. Background: on the theoretical side  Transport Models for HIC’s at intermediate energies:  N-body approaches  QMD  AMD, BQMD, CMD  IDQMD, ImQMD, IQMD  FMD, LQMD, UrQMD  One-body approaches  BUU  (I)BUU/VUU, GiBUU  BNV, LV, IBL  Relativistic covariant approaches  RBUU/RVUU  RQMD 4 QMD-like BUU-like

5. Probes of DDSE especially at high densities from the HICs  The (double) ratio of multiplicities of nucleons,  s,  s, pions, kaons and hard photons as functions of Eb, b, N/Z; pt, y, Ekin, etc.  The (double) flow, flow difference, differential flow of nucleons, pions as functions of Eb,b,N/Z,pt, y, Ekin, etc.  Keep ongoing … 5

6. Puzzles related to SE at high-densities (During 2009-2011) 6 ZQF, PL B683 (2010) 140 ZGX, Phys. Rev. Lett. 102, 062502, 2009 Super-soft Stiff Moderate soft Physics Letters B 697 (2011) 471

7. In the year 2013… 7 W. J. Xie, … F.S. Zhang, PLB 718 (2013) 1510 Super-soft, again

8. In the year 2014… 8 Medium modifications on threshold energy is essential, which will be discussed later. See, TS&CK, PRC91, 014901(2015) for more details It does not matter? It DOES matter!

9. Background: on the experimental side Quite a few facilities working (partly) for this field: o FRIB (or FRIB/China?) at MSU in USA o NUSTAR at FAIR/GSI in Germany o RIBF at RIKEN in Japan o CSR at HIRFL/Lanzhou in China o … 9

10. ALADIN/FOPI/LAND existing flow data ~ UrQMD analysis List of Publications (Year 2009-2015): o Prog. in Part. and Nucl. Phys. 62 (2009) 425; o Int. J. of Mod. Phys. E 19 (2010) 1653; o Phys. Lett. B 697 (2011) 471; o Phys. Rev. C 83 (2011) 044617; o SCIENCE CHINA Physics, 55 (2012) 252 ; o Phys. Rev. C 88 (2013) 044912 ; o Eur. Phys. J. A 50 (2014) 38; o Phys. Rev. C 89 (2014), 034606; o Phys. Rev. C 89 (2014), 044603; o Eur. Phys. J. A 51 (2015) 37 10

11. 11

12. Model dependence ModelersModelsReferences A. OnoAMD PRC66(02)014603 C. HartnackIQMD EPJA1(98)151 P. NapolitaniBQMD PR202(91)233 Y.X. ZhangImQMD PLB664(08)145; PRC71 (05)024604; PRC74(06)014602 P. DanielewiczBUU A lot! Q.-F. LiUrQMD/M PRC73(06)051601; 83(11)044617; 89(14)034606;89(14)044603;JPG32(06)151 P. GiordanoBNV (CT) NPA732(04)202; PRC72(05)064609 M. PfabeBNV NPA703 (2002) 603 T. GaitanosRBUU(Munich) NPA714(03)643;NPA741 (04) 209 GiBUU (SK)BUU-Giessen gibuu.physik.uni-giessen.de GiBUU (RMF)RBUU-Giessen PLB663(08)197; arXiv:0904.2106v1; PRC76(07)044909 B.-A. LiIBUU PR160(88)189; PRC44(91)450 & 2095. H. SchadeBUU PLB 695 (2011)74 12

13. Initial density profiles 13 From J. Xu

14. Elliptic flow 14 From J. Xu

15. Model dependence in the comparsion work UrQMD & Tuebingen-QMD PRC 88, 044912 (2013) UrQMD & IBUU PLB 726 (2013) 211 15 Good news! qualitatively bad news? quantitatively

16. Further comparison between UrQMD&IBUU PLB738 (2014) 397 16

17. N-  -  dynamics — in the view of Quantum Transport Theory based on RBUU time evolution of a many-particle quantum system  nonequilibrium field theory—QHD Hartree Mean-Field Fock Momentum-dep. Bonn directed Collisions Bonn exchanged Collisions 2 nd order 4 th order 17

18. Mean-Field Term On-shell: And: For simplicity, for simplicity…   18

19. Mass-splitting PRC 69, 017601 (2004) 19

20. Mass-splitting puzzle “two definitions”: Dirac one: Non-relativistic one: … A more consistent MF is urgently desired. Phys. Rev. Lett. 95, 022302 (2005) 20

21. Effect of mass-splitting on flows 21

22. Collision Term (also complicated) Transition probability     NN  N  22

23. Transition probability W ~ differential cross section d  /d  (s,t,u)  (s,cos(  )) 23

24. differential cross section d  /d  ~integral cross section Threshold: CS: See, PRC69, 017601 (2004), for NN  NN case 24

25. Medium modified threshold-energy and cross section effects on pion production See, TS&CK, PRC91, 014901(2015) 25

26. Medium Modifications on NNECS PHYSICAL REVIEW C, 62, 014606 (2000) PHYSICAL REVIEW C 69, 017601 (2004) J. Phys. G: Nucl. Part. Phys. 32 (2006) 407 PHYSICAL REVIEW C 81, 034913 (2010) PHYSICAL REVIEW C 83, 044617 (2011) PHYSICAL REVIEW C 89, 034606 (2014) PHYSICAL REVIEW C 89, 044603 (2014) Eur. Phys. J. A 51 (2015) 37 Obtained from RBUU Used in UrQMD 26

27. Systematics for proton flows (NNECS*) 27 To be submitted

28. Systematics for  production 28 From J. Phys. G: Nucl. Part. Phys. 32 (2006) 151 Summer School @ Mainz 2005

29. N  rescattering process in medium? 29 To be submitted

30. Angular distributions in UrQMD It is assumed that the angular distributions for all relevant two-body processes are similar and can be described approximately by the differential cross- section of in-medium NN elastic scattering derived from the collision term of the RBUU equation. It only uses free cross sections and free on-shell particles. It is only used for the angular distributions of all elementary two-body processes but not for the corresponding total cross sections. 30

31. NNCS even at higher energies… Flow puzzles submitted 31

32. Spin-orbit interactions 32

33. Coalescence after-burner How to construct clusters?  r? But if too excited?  p? But if gays or lesbins? More polishments on: o Isospin-dependence o Excitation energy (due to strong phase-space correlation, excitation energy has been almost decided by  r&  p ) Coalescence Model (Minimum Spanning Tree) 33

34. Both dynamical transport and afterburner are important in a large beam energy region 34

35. Both dynamical transport and afterburner are important in a large beam energy region Submitted 35 =

36. How to reconstruct  from   N  channel ? “contaminated” one from one-  pt distribution “pure” one from correlated protons and charged pion pairs See MPLA 24 (2009) 41 for more details. 36

37. ASY-EOS(S394) experiment at GSI Au+Au; Zr+Zr; Ru+Ru E b =400 MeV/nucleon Within a large impact parameter range Z  4 (up to Be) nearly 4  coverage Yield, yield ratios, flow parameters v 1,v 2 Especially for neutrons with high precision. With the help of KraTTA from Krakow 37

38. For details, please see talks of Profs. W. Trautmann, H. Wolter, Y. Leifels, … 38

39. Experimental detection efficiency 39 From P. Russotto

40. 40

41. MST: (2.8 fm, 0.25 GeV/c)Iso-MST: p-p: MST; n-x: (3.8fm, 0.25 GeV/c) 41

42. Ability of S  RIT in Japan 132 Sn+ 12 Sn E b up to 350 MeV/nucleon Central collisions Z  3 (up to Li); charged  mesons nearly 4  coverage Yield, yield ratios … It is hoped to have some results before the end of this year! http://dx.doi.org/10.1016/j.nima.2015.01.026 42

43. More consistent models Transport 2003 (Trento I) Transport 2009 (Trento II) Transport 2014 (Shanghai) Transport 2016 (in June?) (Beijing) “collision physics in a box” 1-2 GeV/A mainly 100 MeV/A 43 100, 400 MeV/A

44. Thank you for your attention! liqf@zjhu.edu.cn 44

45. Form Factors at vertices 45

46. 46

47. For NN->N  47