♥ Introductory remarks (what is the CME ?) ♥ Electromagnetic field created by HIC Phys. Rev. C84, (2011) (Phys. Rev. C84, (2011)) ♥ Analysis of CME experiments Phys. Rev. C 85, (2012), arXiv: ) (Phys. Rev. C 85, (2012), arXiv: ) Conclusions ♥ Conclusions Lecture 2. Evolution of electromagnetic field in HIC and the Chiral Magnetic Effect

Hot quark soup produced at RHIC

The volume of the box is 2.4 by 2.4 by 3.6 fm. The topological charge density of 4D gluon field configurations. (Lattice-based animation by Derek Leinweber) In QCD, chiral symmetry breaking is due to a non-trivial topological effect; among the best evidence of this physics would be event-by-event strong parity violation. Parity violation in strong interactions Dynamics is a random walk between states with different topological charges. N CS = Energy of gluonic field is periodic in N CS direction (~ a generalized coordinate)‏ Instantons and sphalerons are localized (in space and time) solutions describing transitions between different vacua via tunneling or go-over-barrier In the vicinity of the of the deconfinement phase transition QCD vacuum can posses metastable domain leading to P and PC violation

Topological charge fluctuations in gluodynamical vacuum Buividovich, Kalaijan, Polikarpov

These 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 anomaly and thus resulting in generated asymmetry between left- and right-handed fermions. In this states a balance between left- handed and right-handed quarks is destroyed, N L -N R =2N F Q w → violation of P -, CP - symmetry. Dynamics is a random walk between states with different topological charges. Average total topological charge vanishes =0 but variance is equal to the total number of transitions =N t In the presence of inbalanced chirality a magnetic field induces a current along the the magnetic field. Chiral magnetic effect

Red arrow - momentum; blue arrow - spin; In the absence of topological charge no asymmetry between left and right (fig.1) ;the fluctuation of topological charge (fig.2) in the presence of magnetic field induces electric current (fig.3) Chiral magnetic effect D. Kharzeev, PL B633, 260 (2006); D. Kharzeev. A. Zhitnitsky, NP A797, 67 (2007); D. Kharzeev., L. McLerran, H. Warringa, NP A803, 227 (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 is confirmed by lattice calculations Lattice gauge theory The excess of electric charge density due to the applied magnetic field. Red — positive charges, blue — negative charges. P.V.Buividovich et al., PR D80, (2009) Charge separation: lattice results

Charge separation in RHIC experiments Measuring the charge separation with respect to the reaction plane was proposed by S.Voloshin, Phys. Rev. C 70 (2004) STAR Collaboration, PRL 103, (2009) 200 GeV 62 GeV Combination of intense B and deconfinement is needed for a spontaneous parity violation signal

Qualitative estimate of the CME Q S -- saturation momentum, The generated topological charge Γ s ~ λ 2 T 4 (SUSY Y-M)‏ Sphaleron transition occurs only in the deconfined phase, the lifetime is

Analysis strategy For numerical estimates Average correlators are related to the topological charge (D.Kharzeev, Phys. Lett. B 633 (2006) 260)‏ At the fixing point

Magnetic field calculation  Field will have only B y nonzero component  Field will be negligible for low bombarding energies ■ For ultrarelativstic energies the magnetic field is felt by particles close to the transverse plane  For symmetry reasons the magnetic field is negligible for small b Retardation condition with the retardation condition with the retardation condition The Lienart-Wiechard potential is applied to the time evolution of heavy-ion collisions within the UrQMD model V.Skokov, A.Illarionov, V.T, IJMP A24, 5925 (2009)

Magnetic field and energy density evolution in Au+Au collisions at b=10 fm [~2 π/S d ] B crit ≈ (10. — 0.2) m π 2 [~(α S T) 2 ] and ε crit ≈ 1 GeV/fm 3 eB y ε UrQMD

From Kharzeev

Characteristic parameters for the CME The lifetimes are estimated at eB crit =0.2m π 2 and ε crit =1 GeV/fm 3 for Au+Au collisions with b=10 fm (K Au = )  For all energies of interest τ B < τ ε  The CME increases with energy decrease till the top SPS/NICA energy  If compare √s NN = 200 and 62 GeV, the increase is too strong !

The calculated CME for Au+Au collisions eB crit ≈ 0.7 m π 2, K= No effect for the top SPS energy! Calculated correlators for Au+Au (b=10 fm) collisions at √s NN =200 and 62 GeV agree with experimental values for eB crit ≈ 0.7 m π 2, K= No effect for the top SPS energy! In a first approximation, the CME may be considered as linear in b/R (D.Kharzeev et al., Nucl. Phys. A803, 203 (2008) ) Normalized at b=10 fm (centrality ) for Au+Au collisions

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

Magnetic field evolution For a single moving charge (HSD calculation result) For two-nuclei collisions, artist’s view: arXiv: A two neutron star collision

Magnetic field evolution Au+Au(200) b=10 fm Phys. Rev. C84, (2011) V.Voronyuk, V.T. et al., Phys. Rev. C84, (2011)

Magnetic field and energy density correlation Au+Au(200) b=10 fm Phys. Rev. C84, (2011) V.Voronyuk, V.T. et al., Phys. Rev. C84, (2011)

Time dependence of eB y V. Voronyuk, V. T. et al., PR C84, (2011) D.E. Kharzeev et al., Nucl. Phys. A803, 227 (2008) Collision of two infinitely thin layers (pancake- like) ● Until t~1 fm/c the induced magnetic field is defined by spectators only. ● Maximal magnetic field is reached during nuclear overlapping time Δt~0.2 fm/c, then the field goes down exponentially.

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” overestimated the width by factor about 3 ≈ ≈

Electric field evolution Electric field of a single moving charge has a “hedgehog” shape Phys. Rev. C84, (2011) V.Voronyuk, V.T. et al., Phys. Rev. C84, (2011)

No electromagnetic field effects on observable ! Observable Phys. Rev. C84, (2011) V.Voronyuk, V.T. et al., Phys. Rev. C84, (2011)

CME – charge separation STAR Collaboration, PRL 103, (2009) HSD model with/without electromagnetic fields as a CME background does not reproduce the charged pion separation with respect to the reaction plane => Quark-gluon degrees of freedom ! ? (PHSD model)

Attempts for alternative explanations of a charge separation in relativistic HIC ■ F.Wang, Effects of cluster particle correlations on local parity violation observables, Phys. Rev. C81, (2010). ■ A.Bzdak, V.Koch and J.Liao, Remarks on possible local parity violation in heavy ion collisions, Phys. Rev. C81, (2010). ■ S.Pratt, Alternative contributions to the angular correlations observed at RHIC associated with parity fluctuations, arXiv: ■ S.Schlichting and S.Pratt, Explaining angular correlations observed at RHIC with flow and local charge conservation, arXiv: ■ S.Schlichting and S.Pratt, Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation observables, Phys. Rev. C83, (2011). ■ S.Pratt, S.Schlichting and S.Gavin, Effects of momentun conservation and flow on angular correlations, Phys. Rev. C84, (2011). ■ M.Asakawa, A.Majumder and B.Müller, Electric charge separation in strong transient magnetic fields, Phys. Rev. C81, (2010). ■ A.Bzdak, V.Koch and J.Liao, Azimuthal correlations from transverse momentum correlations and possible local parity violation, Phys. Rev. C83, (2011). Really all these hadronic effects are accounted for in the HSD/PHSD model

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

In-plane and out-of-plane correlatons STAR, PR C81, (2010) The observed correlations are in- plane, contrary to CME expectations ! (A.Bzdac, V.Koch, J.Liao, arXiv: )

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

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.T. et al., Phys.Rev., C85, (2012) Experiments at 7.7 and 11.5 GeV are explained by HSD, the CME is not seen

CME observables in PHSD The action of the partonic scalar field on quarks is NOT compensated ! V.T. et al., arXiv: Partonic vector part Partonic scalar part

CME observable cos(ψ i +ψ j ) in PHSD G.Gangadharn, J.Phys.G:Nucl.Part.Phys. 38, (2011)

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

●The HSD/PHSD transport model with retarded electromagnetic fields has been developed. ●The magnetic field and energy density of the deconfined matter reach very high values. ● Phenomenological analysis predicts disappearance of CME at the energy about the top SPS energy but too small effect at the LHC energy ● Actual calculations show no noticeable influence of the created electromagnetic fields on observables. It is due to a compensating effect in action of transverse components of electric and magnetic fields on the quasiparticle transport. ● First low-energy experiments within the RHIC BES program at √s NN = 7.7 and 11.5 GeV can be explained within (pure) 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 is overestimated. The 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. ?). ● The CME measurements are still puzzling. Conclusions