Chiral Magnetic Effect and evolution of electromagnetic field

V. Toneev and V.Voronyuk, JINR, Dubna

Three Days on Quarqyonic Island, May 19-21, Wroclaw, 2011

♥ Introductory remarks♥ A CME estimate (arXiv:1011.5589; 1012.0991; 1012.1508 )♥ Nuclear kinetics in electromagnetic field (arXiv:1103.3239arXiv:1103.3239)♥ 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 Dynamics is a random walk between states with different between states with different topological charges. topological charges.

NCS = -2 -1 0 1

2

Energy of gluonic field is periodic in NCS 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

Dynamics is a random walk between states with different topological Dynamics is a random walk between states with different topological charges. In this states charges. In this states a balancea balance between left-handed and right-handed between left-handed and right-handed quarks quarks is destroyedis destroyed, N, NRR-N-NLL=Q=QTT → → violation violation of P-, CP- symmetryof P-, CP- symmetry. .

AverageAverage total topological charge total topological charge vanishesvanishes < <nnww>=0 but >=0 but variancevariance is equal is equal

to the total number of transitions <nto the total number of transitions <nww22>=N>=Ntt

Fluctuation of topological charges Fluctuation of topological charges in the presencein the presence of magnetic field of magnetic field induces electric current which will separate different chargesinduces electric current which will separate different charges

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

Charge separation in HIC

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) 057901.

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) 057901.

STAR Collaboration, PRL 103, 251601 (2009)

200 GeV

62 GeV

Combination of intense B and deconfinement is needed for a spontaneous parity violation signal

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; V.T. and V.Voronyuk, arXiv:1011.5589; 1012.0991; 1012.1508 1012.0991; 1012.1508

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

[~2π/Sd ] Bcrit ≈ (10. — 0.2) m

π2 [~(αST)2] and ε

crit ≈ 1 GeV/fm3

retardation condition retardation condition

ε

L-W potenL-W poten..

Magnetic field and energy density evolution in Au+Au collisions at b=10 fm

UrQMDeBy

Characteristic parameters for the CME

The lifetimes are estimated at eBcrit

=0.2mπ

2 and εcrit

=1 GeV/fm3

for Au+Au collisions with b=10 fm (KAu=2.52 10-2 ) For all energies of interest For all energies of interest ττBB << ττεε

The CME increases with energy decrease till the top SPS/NICA energyThe CME increases with energy decrease till the top SPS/NICA energy If compare If compare √s√s

NNNN = 200 and 62 GeV = 200 and 62 GeV tthis increase is his increase is too strong !too strong !

Ways to remove the discrepancy

The correlator ratio at two measured energies for b=10 fm

Uncertainity in Uncertainity in √s√s NN NN dependence does not help; dependence does not help; β<0 ?!β<0 ?!

Should be Should be ττBB(62) =1.2 τ(62) =1.2 τBB(200) (instead of ~3); (200) (instead of ~3); lifetimeslifetimes

Uncertainty in impact parameterUncertainty in impact parameter; not essential; not essential Inclusion of participant contribution to eB; Inclusion of participant contribution to eB; very small effectvery small effect■■ To decrease To decrease eBeB

critcrit till 0.01m till 0.01mππ

22 to reach regime to reach regime ττB B == ττε ε ; ; <62 <62

■ ■ If If eBeBcritcrit increases the lifetime ratio is correct for eincreases the lifetime ratio is correct for eBBcrit crit ≈ 1.05 m≈ 1.05 m

ππ2 2 very very

close to the maximal eclose to the maximal eBBcrit crit ==1.2 m1.2 mππ

2 2 ; ; questionable, no CME for Cu questionable, no CME for Cu

■ ■ To introduce the initial time when equilibrium of quark-gluon matterTo introduce the initial time when equilibrium of quark-gluon matter is achieved, tis achieved, t

i,ε i,ε >0, associated with a maximum in ε-distribution, >0, associated with a maximum in ε-distribution,

ττBB(62) / τ(62) / τBB(200)≈(0.62-0.32)/(0.24-0.08)≈2.0; (200)≈(0.62-0.32)/(0.24-0.08)≈2.0; not enoughnot enough

■ ■ To combine the last two scenarios; To combine the last two scenarios; success ! success !

(exp)

The calculated CME for Au+Au collisions

Calculated correlators for Au+Au (b=10 fm) collisions at √s

NN=200 and 62 GeV agree with experimental values for

eeBBcrit crit ≈ 0.7 m≈ 0.7 mππ

2 2 , K=, K=6.056.05 10 10-2-2.. No effect for the top SPS energy No effect for the top SPS energy!!

In In aa first approximation, the CME may be considered as linear in b/R first approximation, the CME may be considered as linear in b/R (D.Kharzeev et al., Nucl. Phys.(D.Kharzeev et al., Nucl. Phys. A803 A803, 203 (2008) ), 203 (2008) )

Normalized at b=10 fm (centrality 0.4-0.5) for Au+Au collisions

System-size dependence

Correlation between centrality and impact parameter

The CME should be proportional to the nuclear overlap area S≡SA(b)

Centrality e0 N

part

Ca+Ca

Pb+Pb

Au+Au

Cu+Cu

I+I

Transport model with electromagnetic fieldThe 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 W. Cassing et al., NPA 665665 (2000) 377; (2000) 377; 672672 (2000) 417; (2000) 417; 677677 (2000) 445 (2000) 445

E. Bratkovskaya, NPA E. Bratkovskaya, NPA 686686 (2001), (2001), E. Bratkovskaya & W. Cassing, NPAE. Bratkovskaya & W. Cassing, NPA 807 807 (2008) 214 (2008) 214

Generalized transport equationsGeneralized transport equations on the basis of the Kadanoff-on the basis of the Kadanoff-Baym equations for Greens functionsBaym equations for Greens functions - - accounting for the first accounting for the first order gradient expansion of the Wigner transformed Kadanoff-order gradient expansion of the Wigner transformed Kadanoff-Baym equations beyond the quasiparticle approximation (i.e. Baym equations beyond the quasiparticle approximation (i.e. beyond standard on-shell models) – are incorporated in HSD.beyond standard on-shell models) – are incorporated in HSD.

0.00.5

1.01.5

1

2

0.0

0.5

1.0

1.5

-Im D (M,q,B,T) (GeV-2)

T=150 MeV

B=3

0 Accounting for in-medium effects requires Accounting for in-medium effects requires off-shell transport models!off-shell transport models!

HSD off-shell transport approachHSD off-shell transport approach

The off-shell spectral functions change The off-shell spectral functions change their properties dynamically by propagation their properties dynamically by propagation through the medium and become on-shell in through the medium and become on-shell in the vacuumthe vacuum

Magnetic field evolution

For a single moving charge

Magnetic field evolution

Au+Au(200) b=10 fm

V.Voronyuk, V.T. et al., arXiv:1103.4239 

Magnetic field and energy density correlation

V.Voronyuk, V.T. et al., arXiv:1103.4239 

Au+Au(200) b=10 fm

Time dependence of eBy

V. Voronyuk, V. T. et al., arXiv:1103.4239 

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

V.Voronyk, V.T. et al., arXiv:1103.4239 

V.Voronyk, V.T. et al., arXiv:1103.4239 

No electromagnetic field effects on

observable !

Observable

Average momentum increment

Δp= δp

Transverse momentum increments Δp due to

electric and magnetic fields compensate each

other ! (worring & hope)

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 energy density, 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.

Conclusions

Thanks to

Elena Bratkovskaya Wolfgang Cassing Dmitrii Kharzeev Volodya Konchakovski Vladimir Skokov Sergei Voloshin

and the organizers of the Three Days on Quarkyonic Island, Wroclaw, May 19-21, 2011