Evolution of electromagnetic field in HIC and chiral magnetic effect V. Toneev In collaboration with V. Voronyuk, E. Bratkovskaya, W.Cassing, V. Konchakovski, S. Voloshin ♥ Introductory remarks (what is the CME ?) ♥ Nuclear kinetics in electromagnetic field created by HIC Phys. Rev. C84, (2011) (Phys. Rev. C84, (2011)) arXiv: ♥ Analysis of CME experiments (arXiv: ) Conclusions ♥ Conclusions

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 generates 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

Lienard-Wiehert potential First estimate of the created magnetic field UrQMD retardation condition Au+Au (200 GeV) b=10 fm V. Skokov, V.Toneev, A. Illarionov, Int. J. Mod. Phys. A 24, 5923 (2009),

From Kharzeev

Qualitative estimate of the CME For a r.w. the variance is equal to the total number of transitions =N t The generated topological charge the lifetime is V.T. and V.Voronyuk, arXiv: ; ; Average correlators are related to the topological charge Normalized at b=10 fm (centrality ) for Au+Au collisions eB crit ≈ 0.7 m π 2 CME disappears somewhere near √s NN ~ 20 GeV !

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

W. Cassing et al., NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445 E. Bratkovskaya, NPA 686 (2001), E. Bratkovskaya & W. Cassing, NPA 807 (2008) 214 E. Bratkovskaya, NPA 686 (2001), E. Bratkovskaya & W. Cassing, NPA 807 (2008) 214 Generalized transport equations on the basis of the Kadanoff-Baym equations for Greens functions - accounting for the first order gradient expansion of the Wigner transformed Kadanoff-Baym equations beyond the quasiparticle approximation (i.e. beyond standard on-shell models) – are incorporated in HSD. Accounting for in-medium effects requires off-shell transport models! Accounting for in-medium effects requires off-shell transport models! HSD off-shell transport approach The off-shell spectral functions change their properties dynamically by propagation through the medium and become on-shell in the vacuum The off-shell spectral functions change their properties dynamically by propagation through the medium and become on-shell in the vacuum

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

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.

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 model

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 D.Gangadharan (STAR Collaboration), talk at QM11 (√s NN =7.7, 11.5, 39 GeV) Compensation

HSD background for BES experiments on CME V.Toneev et al., arXiv: Experiments at 7.7 and 11.5 GeV are explained by HSD, the CME is not seen

The HSD transport model with retarded electromagnetic fields has been developed. The magnetic field and energy density of the deconfined matter reach very high values. 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 hadronic scenario without reference to the spontaneous local CP violation. Direct inclusion of quarks and gluons in evolution is needed (PHSD model) for exploring the CME at √s NN above the top SPS energy as well as in future to consider spin d.o.f., to mimic directly the CME. Conclusions