♥ Introductory remarks ♥ Fluctuating sources of CME background ♥ Analysis of CME experiments ( Phys. Rev. ( Phys. Rev. C84C84, 035202 (2011); , 035202 (2011); Phys. Rev. CPhys. Rev. C8585, 034910 (2012);, 034910 (2012); arXiv:1112.2519arXiv:1112.2519) ♥ ConclusionsConclusions

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 10 -14, 2012

Gauge field transitions with changing the topological charge involve Gauge field transitions with changing the topological charge involve configurations which configurations which may violatemay violate PP and and CPCP invariance of strong invariance of strong interactions. interactions.

Fermions can interact with a gauge field configurations, transforming Fermions can interact with a gauge field configurations, transforming left- into right-handed quarks and vice-versa via left- into right-handed quarks and vice-versa via the axial chiral the axial chiral anomalyanomaly and thus resulting in generated asymmetry between left- and and thus resulting in generated asymmetry between left- and right-handed fermions. In this states right-handed fermions. In this states a balancea balance between left-handed between left-handed and right-handed chiral quarks and right-handed chiral quarks is destroyedis destroyed. .

In the presence of inbalanced chirality a magnetic field induces In the presence of inbalanced chirality a magnetic field induces a chiral electric current along the the magnetic fielda 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, 074033 (2008)

Charge separation in HIC: CP violation signal

L or BNon-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.

Magnetic field through the axial anomaly induces a parallel electric field which will Magnetic field through the axial anomaly induces a parallel electric field which will separate different chargesseparate different charges

Charge separation in RHIC experimentsSTAR Collaboration, PRL 103, 251601 (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, 054919 (2008); NP A834, 215 (2009); W.Cassing, EPJ ST 168, 3 (2009); V.Voronyuk et al., PR C84, 035202 (2011)

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

Lienard-Wiehert potentialLienard-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, 035302 (2011)

Fluctuation of electromagnetic field

A

V.Voronyuk et al., Phys.Rev. C84, 035202 (2011) restricted A.Bzdak, V.Skokov, Phys.Lett. B710, 171 (2012) thin disk W.Dend, X.Huang, Phys.Rev. C85, 044907 (2012) HIJING V.T. et al., arXiv:1208.2519 PHSD

Full width is about 2/mπ2 for all transverse field components

“Thin disk” overestimates the width by factor about 3

<|EX|> ≈ <|EY|> ≈ <|BX|>

Compensation effect

Δp= δpTransverse momentum increments Δp due to

electric and magnetic fields compensate each

other !

Flow angle fluctuation

Event plane angle Ѱn does not tilted by the created magnetic field fluctuation (grey histograms are PHSD results without fields)

V.T. et al., arXiv:1207.2519

Transverse Momentum Conservation

V.T. et al., arXiv:1208.2518

For TMC source (A.Bzdak et al., Phys.Rev. C83, 014905 (2011) ) describing pions thermodynamically and making use of the central limiting theorem,

For the same-sign correlator

and

The correlator γij ~ v2 !

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:1208.2519

Chiral magnetic wave

(Y.Burnier et al., PRL

107, 052303 (2012)

J.Xu et al., PR C85,

041901 (2012)

Prediction v2(π-)>v2(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

- Qc1 , Qc2 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,δw) counts pairs

with opposite charge sign satisfying condition that δη=(η+ - η- ) € ηw

The same charge pairs are subtracted

V.T. et al., arXiv:1208.2519

central semi-peripheralCharge 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 ~ δϕ ~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 ση and σϕ

which are fitted at every centrality Assumed local equilibrium ??!

V.T. et al., arXiv:1208.2519

To results of the RHIC BES programSTAR Collaboration, J. Phys. G38, 124165 (2011) (√sNN =7.7, 11.5, 39 GeV)

Compensation

HSD background for BES experiments on CMEV.Toneev et al., Phys.Rev. C85, 034910 (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:1208.2519

Parton energy density

●The transverse “electric” Ec and “magnetic” Bc components almost compensate each other. ●The final action of partonic forces is dominated by the non-compensated scalar one.

CME observable cos(ψi+ψj) in PHSDG.Gangadharn, J.Phys.G:Nucl.Part.Phys. 38, 124166 (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:1208.2519

PR C86, 014963 (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

δij

●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 v2 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 √sNN = 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