♥ Introductory remarks ♥ Fluctuating sources of CME background ♥ Analysis of CME experiments

1. Fluctuating Background in Estimates of the Chiral Magnetic Effect V. Toneev In collaboration withE. Bratkovskaya, W. Cassing, V. Konchakovski,V. Voronyuk ♥ Introductory remarks ♥Fluctuating sources of CME background ♥Analysis of CME experiments ( Phys. Rev. C84, 035202 (2011); Phys. Rev. C85, 034910 (2012);arXiv:1112.2519) ♥Conclusions Workshop on Particle Correlations and Femtoscopy, Frankfurt, September 10 -14, 2012

2. Chiral magnetic effect (reminding) Gauge field transitions with changing the topological charge involve configurations which may violateP and CP invariance of strong interactions. Fermions can interact with a gauge field configurations, transforming left- into right-handed quarks and vice-versa via the axial chiral anomaly and thus resulting in generated asymmetry between left- and right-handed fermions. In this states a balance between left-handed and right-handed chiral quarks is destroyed. In the presence of inbalanced chirality a magnetic field induces a chiral electric current along the the magnetic field. D.Kharzeev et al., NP A803, 227 (2008); Ann.Phys. 325, 205 ( 2010);PR D78, 074033 (2008)

3. L or B Charge separation in HIC: CP violation signal Magnetic field through the axial anomaly induces a parallel electric field which will separate different charges Non-zero angular momentum (or equivalently magnetic field) in heavy-ion collisions make it possible for P- and CP-odd domains to induce charge separation (D.Kharzeev, PL B633 (2006) 260). Electric dipole moment of QCD matter ! Measuring the charge separation with respect to the reaction plane was proposed by S.Voloshin, Phys. Rev. C70 (2004) 057901.

4. Charge separation in RHIC experiments STAR Collaboration, PRL103, 251601 (2009) 200 GeV 62 GeV Combination of intense B and deconfinement is needed for a spontaneous parity violation signal

5. Parton-Hadron String Dynamics W.Cassing, Е.Bratkovskya, PR C78, 054919 (2008); NP A834, 215 (2009); W.Cassing, EPJ ST 168, 3 (2009); V.Voronyuk et al., PR C84, 035202 (2011)

6. Transport model with electromagnetic field The Boltzmann equation is the basis of QMD like models: Generalized on-shell transport equations in the presence of electromagnetic fields can be obtainedformally by the substitution: A general solution of the wave equations is as follows Lienard-Wiehert potential For point-like particles

7. Sources of fluctuation in an initial state ●Fluctuation in the position of spectator protons results in electromagnetic field fluctuation ●Event fluctuation in space geometry of participant nucleons is converted into flow fluctuation ●In the later (transient) time, fluctuation in temperature, baryon and chargedensity can result in some substructure (dipole-, quadropule-like) in a parton or/and hadron excited matter

8. An estimate of the created magnetic field UrQMD V. Skokov, V.T., A. Illarionov, Int. J. Mod. Phys. A 24, 5923 (2009) V. Voronyuk et al., Phys. Rev. C84, 035302 (2011)

9. Fluctuation of electromagnetic field Full width is about 2/mπ2 for all transverse field components “Thin disk” overestimates the width by factor about 3 <|EX|> ≈ <|EY|> ≈ <|BX|> V.Voronyuk et al., Phys.Rev. C84, 035202 (2011) restrictedA.Bzdak, V.Skokov, Phys.Lett. B710, 171 (2012) thin disk W.Dend, X.Huang, Phys.Rev. C85, 044907 (2012) HIJING V.T. et al., arXiv:1208.2519 PHSD A

10. Compensation effect Δp= δp Transverse momentum increments Δp due to electric and magnetic fields compensate each other !

11. Flow angle fluctuation Event plane angle Ѱndoes not tilted by the created magnetic field fluctuation (grey histograms are PHSD results without fields) V.T. et al., arXiv:1207.2519

12. Transverse Momentum Conservation For TMC source (A.Bzdak et al., Phys.Rev. C83, 014905 (2011) )describing pions thermodynamically andmaking use of the central limiting theorem, correlator is For the same-sign correlator and The correlator γij ~ v2!TMC source is not able to explain the observed asymmetry. It is blind to the particle charge. V.T. et al., arXiv:1208.2518

13. Electric charge fluctuations in the transient stage I A charged dipole is defined as V.T. et al., arXiv:1208.2519

14. Electric charge fluctuations in the transient stage II A charged quadrupole is defined as Prediction v2(π-)>v2(π+) 30% for √s=11 GeV Hadron models and exp. give ~10% - Qc1 , Qc2 magnitude is small, - its orientation is almost uniform, - main axis is changed from event to event There is not much room for CMW Chiral magnetic wave (Y.Burnier et al., PRL 107, 052303 (2012) J.Xu et al., PR C85, 041901 (2012)

15. Charge balance function (time evolution) central semi-peripheral Charge balancing partners ConditionalprobabilityN+-(δη,δw)counts pairs with opposite charge sign satisfying condition that δη=(η+ - η- ) € ηw The same charge pairs are subtracted B-distribution formed in the quark phase is not changed (forη) or changed a little (for ϕ) in time V.T. et al., arXiv:1208.2519

16. Charge balance function (comparison with experiment) PHSD does not reproduce an enhancement at δη ~ δϕ ~0 in central collisions w.r.t. peripheral ones (like UrQMD) Blast wave model do that under two additional assumptions: ●electric charge is exactly conserved; ●pairs in ensemble are distributed in Gaussian way in rapidity andtransverseangle withση and σϕwhich are fitted at every centrality Assumed local equilibrium ??! V.T. et al., arXiv:1208.2519

17. To results of the RHIC BES program STAR Collaboration, J. Phys. G38, 124165 (2011) (√sNN =7.7, 11.5, 39 GeV) Compensation

18. HSD background for BES experiments on CME V.Toneev et al., Phys.Rev. C85, 034910 (2012) Experiments at 7.7 and 11.5 GeV are explained by HSD, the CME is not seen

19. Scalar parton potential Parton energy density ●The transverse “electric” Ec and “magnetic” Bc components almost compensate each other. ●The final action of partonic forces is dominated by the non-compensated scalar one. V.T. et al., arXiv:1208.2519

20. CME observable cos(ψi+ψj) in PHSD G.Gangadharn, J.Phys.G:Nucl.Part.Phys. 38, 124166 (2011) PHSD overestimates results for √s=39 and 200 GeV being in agreement with experiment at lower energies

21. Both in-plane and out-of-plane components needs an additional sizable source of asymmetry rather than only out-of-plane component as expected from CME Charge separation in PHSD V.Toneev et al., arXiv:1208.2519 δ PR C86, 014963 (2011) δij The partonic scalar potential is overestimated in PHSD getting comparable the charge separation with experiment butat LHC

22. Conclusions • ●Fluctuation in the spectator proton position results in noticeable fluctuation in e.m. field but not so large as predicted in the “thin disc” approximation. • ● Fluctuation in the position of participant baryons is the source of the impact parameter fluctuation. It leads to an increase of the magnitude of v2 and generates odd flow harmonics. Does not influenced by retarded e.m. field. • ● Actual calculations show no noticeable influence of the created electromagnetic fields and their fluctuation on observables. It is due to a compensation effect in action of transverse components of electric and magnetic fields on the quasiparticle transport. • ●In intermediate stage of HIC the statistical fluctuations of charged particles in momentum space can generate charge dipole or even quadrupole. However these fluctuations are small, their orientation uniform and direction of the main axis is changed from event to event. • ● First low-energy experiments within the RHIC BES program at √sNN = 7.7 and 11.5 GeV can be explained within hadronic scenario without reference to the spontaneous local CP violation. • ● Direct inclusion of quarks and gluons in evolution (PHSD model) shows that the partonic scalar potential overestimates data and a new source is needed . This new source does not dominate in out-of-plane direction as could be expected for the CME but both in-plane and out-of-plane components contribute with a comparable strength (explicit color d.o.f. ?). • ●Interpretation of the CME measurements is still puzzling.