1. Charge-dependent correlations from event-by-event anomalous hydrodynamics [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

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. 16

17. 17

18. 18

19. 19

20. : # of pairs : # of ( ) Axial charges from color flux tubes 20

21. Axial charges from color flux tubes 21

22. Axial charges from color flux tubes 22 Sign of

23. Axial charges from color flux tubes 23 Sign of

24. estimated by anomaly equation 24

25. 25 - RHIC energy - b=7.2fm(20-30%) - B

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

27. 27 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013] □Event-by-event anomalous hydro □Initial random ✓ ✓

28. Correlations:, 28 - b=7.2(20-30%) - RHIC energy - 100k events -

29. Why fluctuation also become larger? 29

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

31. (same) vs centrality 31

32. (opposite) vs centrality 32

33. Background effects Transverse momentum conservation Local charge conservation Cluster particle correlations 33 [ 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] ]

34. 34 Anomalous transport in heavy-ion collisions? [STAR, PRL2009, PRC2010] [ALICE, PRL2013] □Event-by-event anomalous hydro □Initial random ✓ ✓ Outlook pt & eta dependence Better experimental observables Dissipations/back reaction/CVE/2-particle correlation/…

35. Possible improvements 35 Anomalous hydro evolution Freeze-out Correlations Initial state - n5 profile based on CGC - Charge separation in glasma - More realistic EOS with mu & mu5 dep. - CVE - Backreaction to EM fields - Dissipational effects - viscosity - conductivity - Multi-particle corr. - Differential analysis - eta, pt - Parameter dep. - Cmu5, B, √s - New obs. insensitive to background

36. Backup slides 36

37. Background magnetic fields 37

38. vs centrality 38

39. Electromagnetic fields 39