Charge-dependent correlations from event-by-event anomalous hydrodynamics [arXiv:1412.0311] Yuji Hirono [Stony Brook Univ.] Collaborators: T. Hirano [Sophia.

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Charge-dependent correlations from event-by-event anomalous hydrodynamics [arXiv: ] Yuji Hirono [Stony Brook Univ.] Collaborators: T. Hirano [Sophia U], D. E. Kharzeev [SBU/BNL] 1

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

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

Charge dependent correlations [STAR] 4

5

6 B

7 B

8

9

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

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

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

Equation of state - conformal massless quarks & gluons Anomalous hydrodynamics equations 13 Constitutive equations CME CSE

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

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

16

17

18

19

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

Axial charges from color flux tubes 21

Axial charges from color flux tubes 22 Sign of

Axial charges from color flux tubes 23 Sign of

estimated by anomaly equation 24

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

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

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

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

Why fluctuation also become larger? 29

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

(same) vs centrality 31

(opposite) vs centrality 32

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 [ ] ]

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/…

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

Backup slides 36

Background magnetic fields 37

vs centrality 38

Electromagnetic fields 39