1. Dynamical modeling of the chiral magnetic effect in heavy-ion collisions [arXiv:1412.0311] Yuji Hirono [Stony Brook Univ.] Collaborators: T. Hirano[Sophia U], D. E. Kharzeev [SBU/BNL] 1

2. 2 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013]

3. [STAR, PRL2009, PRC2010] 3 Anomalous transport in heavy-ion collisions? [ALICE, PRL2013] Outline 1. Physical meaning of obs. 2. EbE anomalous hydro 3. Results

4. Charge dependent correlations [STAR] 4

5. 5

6. 6 B

7. 7 B

8. 8

9. 9

10. 10 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013] □Event-by-event anomalous hydro □Initial random

11. Event-by-event anomalous hydrodynamic model 11 Anomalous hydro evolution Freeze-out Correlations Initial state An initial cond. Particle data for 1 event

12. Non-dissipative anomalous fluid in 3+1D no viscosity/Ohmic conductivity Background electromagnetic fields Anomalous hydrodynamics equations 12

13. Equation of state - conformal massless quarks & gluons Anomalous hydrodynamics equations 13 Constitutive equations CME CSE [Son & Surowka (2009)] [Kalaydzhyan & Kirsch (2011)]

14. MC Sampling of particles Isothermal hypersurface Linux cluster at Sophia Univ. - 128 cores - A few days per 100k events Linux cluster at Sophia Univ. - 128 cores - A few days per 100k events Can be written as 1D integral! [ PPNP70, 108[arxiv:1204.5814] ] K. Murase [U-Tokyo]

15. 15 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013] □Event-by-event anomalous hydro □Initial random ✓

16. Sources of axial charges Color flux tubes Electromagnetic field QCD sphalerons 16 Spatially random Random & Coherent Diffusive & fluctuation

17. 17

18. 18

19. 19

20. 20

21. : # of pairs : # of ( ) Axial charges from color flux tubes 21

22. Axial charges from color flux tubes 22

23. Axial charges from color flux tubes 23 Sign of

24. Axial charges from color flux tubes 24 Sign of

25. estimated by anomaly equation 25

26. 26 - RHIC energy - b=7.2fm(20-30%) - B

27. 27 - RHIC energy - b=7.2fm(20-30%) - 27 B

28. 28 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013] □Event-by-event anomalous hydro □Initial random ✓ ✓

29. Correlations 29 same-charge opposite-charge

30. Correlations:, 30 - b=7.2(20-30%) - RHIC energy - 100k events -

31. Why fluctuation also become larger? 31

32. Correlations:, 32 - b=7.2(20-30%) - RHIC energy - 100k events - Anti-correlation btw. &___

33. (same) vs centrality 33

34. (opposite) vs centrality 34

35. Background effects Transverse momentum conservation Local charge conservation Cluster particle correlations 35 [ S. Pratt, S. Schlichting, S. Gavin, PRC(2011) ] [ S. Schlichting and S. Pratt, PRC(2011) ] [ F. Wang, PRC(2010) ] [ A. Bzdak, V. Koch, J. Liao, PRC(2011) ] In our current simulations, multi-particle correlations are not imposed Cooper-Frye formula → single-particle distributions [ Y. Hori, S. Schlichting, et al [1208.0603] ]

36. 36 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013] □Event-by-event anomalous hydro □Initial random ✓ ✓ Outlook pt & eta dependence / parameter dependence (√s, tau_B, …) Back reaction/Dissipations/CVE/realistic EOS/… Better experimental observables

37. Possible improvements 37 Anomalous hydro evolution Freeze-out Correlations Initial state - n5 profile based on CGC - Charge separation in glasma - More realistic EOS with mu & mu5 dep. - Chiral vortical effect - Backreaction to EM field - Dissipational effects - viscosity - conductivity - Multi-particle corr. - Differential analysis - eta, pt - Parameter dep. - Cmu5, B, √s - New obs. insensitive to background

38. Backup slides 38

39. Background magnetic fields 39

40. vs centrality 40

41. Electromagnetic fields 41

42. Harmonics Azimuthal angle distribution of observed particles Represents the shape the flow 42 “triangle”“elliptic” “directed”

43. Charge dependent correlations [STAR] 43

44. MC-Glauber initial condition 44