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

Gauge field transitions with changing the topological charge involve configurations which may violate P 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. Chiral magnetic effect (reminding) D.Kharzeev et al., NP A803, 227 (2008); Ann.Phys. 325, 205 ( 2010); PR D78, (2008)

Charge separation in HIC: CP violation signal L or B 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 B 633 (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. C 70 (2004) Magnetic field through the axial anomaly induces a parallel electric field which will separate different charges

Charge separation in RHIC experiments STAR Collaboration, PRL 103, (2009) 200 GeV 62 GeV Combination of intense B and deconfinement is needed for a spontaneous parity violation signal

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

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 obtained formally by the substitution: A general solution of the wave equations For point-like particles is as follows Lienard-Wiehert potential

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 charge density can result in some substructure (dipole-, quadropule-like) in a parton or/and hadron excited matter

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, (2011)

Fluctuation of electromagnetic field A V.Voronyuk et al., Phys.Rev. C84, (2011) restricted A.Bzdak, V.Skokov, Phys.Lett. B710, 171 (2012) thin disk W.Dend, X.Huang, Phys.Rev. C85, (2012) HIJING V.T. et al., arXiv: PHSD Full width is about 2/m π 2 for all transverse field components “Thin disk” overestimates the width by factor about 3 ≈ ≈

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

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

Transverse Momentum Conservation V.T. et al., arXiv: For TMC source (A.Bzdak et al., Phys.Rev. C83, (2011) ) describing pions thermodynamically and making use of the central limiting theorem, For the same-sign correlator and The correlator γ ij ~ v 2 ! TMC source is not able to explain the observed asymmetry. It is blind to the particle charge. correlator is

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

Chiral magnetic wave (Y.Burnier et al., PRL 107, (2012) J.Xu et al., PR C85, (2012) Prediction v 2 (π - )>v 2 (π + ) 30% for √s=11 GeV Hadron models and exp. give ~10% Electric charge fluctuations in the transient stage II A charged quadrupole is defined as - Q c1, Q c2 magnitude is small, - its orientation is almost uniform, - main axis is changed from event to event There is not much room for CMW

Charge balance function (time evolution) Conditional probability N +- (δη,δ w ) counts pairs with opposite charge sign satisfying condition that δη=(η + - η - ) € η w The same charge pairs are subtracted V.T. et al., arXiv: centralsemi-peripheral Charge balancing partners B-distribution formed in the quark phase is not changed (for η) or changed a little (for ϕ ) in time

Charge balance function (comparison with experiment) PHSD does not reproduce an enhancement at δη ~ δ ϕ ~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 and transverse angle with σ η and σ ϕ which are fitted at every centrality Assumed local equilibrium ??! V.T. et al., arXiv:

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

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

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

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

Charge separation in PHSD The partonic scalar potential is overestimated in PHSD getting comparable the charge separation with experiment but at LHC V.Toneev et al., arXiv: PR C86, (2011) δ 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 δ ij

●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 v 2 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 √s NN = 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. Conclusions