Chiral Magnetic Effect and evolution of electromagnetic field

1. Chiral Magnetic Effect and evolution of electromagnetic field V. Toneev and V.Voronyuk, JINR, Dubna ♥ Introductory remarks ♥ A CME estimate (arXiv:1011.5589; 1012.0991; 1012.1508) ♥ Nuclear kinetics in electromagnetic field (arXiv:1103.3239) ♥ Conclusions Three Days on Quarqyonic Island, May 19-21, Wroclaw, 2011

2. Energy of gluonic field is periodic in NCSdirection (~ a generalized coordinate)‏ NCS= -2 -1 0 1 2 Instantons and sphalerons are localized (in space and time) solutions describing transitions between different vacua via tunneling or go-over-barrier Dynamics is a random walk between states with different topological charges. Parity violation in strong interactions 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. 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)

3. 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, 054503 (2009) Charge separation:CP violation signal Dynamics is a random walk between states with different topological charges. In this states a balance between left-handed and right-handed quarks is destroyed, NR-NL=QT→ violation of P-, CP- symmetry. Average total topological chargevanishes <nw>=0 but variance is equal to the total number of transitions <nw2>=Nt Fluctuation of topological charges in the presence of magnetic field induces electric current which will separate different charges

4. L or B Charge separation in HIC 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.

5. Charge separation in RHIC experiments Measuring the charge separation with respect to the reaction plane was proposed by S.Voloshin, Phys. Rev. C70 (2004) 057901. STAR Collaboration, PRL103, 251601 (2009) 200 GeV 62 GeV Combination of intense B and deconfinement is needed for a spontaneous parity violation signal

6. Qualitative estimate of the CME QS -- saturation momentum, The generated topological charge Γs ~ λ2 T4 (SUSY Y-M)‏ Sphaleron transition occurs only in the deconfined phase, the lifetime is V.T. and V.Voronyuk, arXiv:1011.5589; 1012.0991; 1012.1508

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

8. Magnetic field and energy density evolutionin Au+Au collisions at b=10 fm UrQMD eBy L-W poten. retardation condition ε [~2π/Sd ] Bcrit ≈ (10. — 0.2) mπ2 [~(αST)2] and εcrit ≈ 1 GeV/fm3

9. Characteristic parameters for the CME The lifetimes are estimated at eBcrit=0.2mπ2 and εcrit=1 GeV/fm3 for Au+Au collisions with b=10 fm (KAu=2.52 10-2 ) • For all energies of interest τB<τε • The CME increases with energy decrease till the top SPS/NICA energy • If compare √sNN = 200 and 62 GeV this increase is too strong !

10. Ways to remove the discrepancy The correlator ratio at two measured energies for b=10 fm (exp)‏ • Uncertainity in √s NN dependence does not help; β<0 ?! • Should be τB(62) =1.2 τB(200) (instead of ~3); lifetimes • Uncertainty in impact parameter; not essential • Inclusion of participant contribution to eB; very small effect ■To decrease eBcrit till 0.01mπ2 to reach regime τB =τε ; <62 ■ If eBcritincreases the lifetime ratio is correct for eBcrit ≈ 1.05 mπ2 very close to the maximal eBcrit =1.2 mπ2 ; questionable, no CME for Cu ■ To introduce the initial time when equilibrium of quark-gluon matter is achieved, ti,ε >0, associated with a maximum in ε-distribution, τB(62) / τB(200)≈(0.62-0.32)/(0.24-0.08)≈2.0; not enough ■ To combine the last two scenarios; success !

11. Normalized at b=10 fm (centrality 0.4-0.5)for Au+Au collisions The calculated CME for Au+Au collisions Calculated correlators for Au+Au (b=10 fm) collisions at √sNN=200 and 62 GeV agree with experimental values for eBcrit ≈ 0.7 mπ2 , K=6.05 10-2. 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) )

12. Au+Au Pb+Pb I+I Cu+Cu Ca+Ca System-size dependence The CME should be proportional to the nuclear overlap area S≡SA(b) Centrality e0 Npart Correlation between centrality and impact parameter

13. 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 For point-like particles

14. HSD off-shell transport approach Accounting for in-medium effects requires off-shell transport models! The off-shell spectral functions change their properties dynamically by propagation through the medium and become on-shell in the vacuum E. Bratkovskaya, NPA 686 (2001), E. Bratkovskaya & W. Cassing, NPA 807 (2008) 214 Generalized transport equationson 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. W. Cassing et al., NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

15. For a single moving charge Magnetic field evolution

16. Au+Au(200) b=10 fm Magnetic field evolution V.Voronyuk, V.T. et al., arXiv:1103.4239

17. Magnetic field and energy density correlation Au+Au(200) b=10 fm V.Voronyuk, V.T. et al., arXiv:1103.4239

18. Time dependence of eBy D.E. Kharzeev et al., Nucl. Phys. A803, 227 (2008)Collision of two infinitely thin layers (pancake-like) V. Voronyuk, V. T. et al., arXiv:1103.4239 ● 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.

19. Electric field evolution Electric field of a single moving charge has a “hedgehog” shape V.Voronyk, V.T.et al., arXiv:1103.4239

20. Observable No electromagnetic field effects onobservable! V.Voronyk, V.T.et al., arXiv:1103.4239

21. Average momentum increment Δp= δp Transverse momentum increments Δp due to electric and magnetic fields compensate each other !(worring & hope)

22. Conclusions • The magnetic field and energy density of the deconfined matter reach very high values in HIC for √sNN≥11 GeV satisfying necessary conditions for a manifestation of the CME. • Under some restrictions on the magnetic field and energydensity, the model describes the observable CME at two measured energies 200 and 62 GeV. For the chosen parameters, the model predicts that the CME will be ~13 times smaller at LHC energy and disappears somewhere in 60 < √sNN <20 GeV. • The HSD transport model with retarded electromagnetic fields has been developed. Actual calculations show no noticeable influence of the created electromagnetic fields on observables. It is due to a compensating effect between electric and magnetic fields • Direct inclusion of quarks and gluons in evolution is needed (PHSD model). • Experiments on the CME planned at RHIC by the low-energy scan program are of great interest since they hopefully will allow to infer the critical magnetic field eBcrit governing the spontaneous local CP violation.

23. Thanks to Elena Bratkovskaya Wolfgang Cassing Dmitrii KharzeevVolodya Konchakovski Vladimir Skokov Sergei Voloshin and the organizers of the Three Days on Quarkyonic Island, Wroclaw, May 19-21, 2011