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Lecture 2. Evolution of
electromagnetic field in HIC and
the Chiral Magnetic Effect
♥ Introductory remarks (what is the CME ?)
♥ Electromagnetic field created by HIC
(Phys. Rev. C84,
035202 (2011))
♥ Analysis of CME experiments
(Phys. Rev. C 85, 034910 (2012),
arXiv:1208.2518)
♥ Conclusions
Hot quark soup produced at RHIC
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)
Energy of gluonic field is periodic in NCS
direction (~ a generalized coordinate)
Dynamics is a random walk
between states with different
topological charges.
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
Chiral magnetic effect
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 lefthanded and right-handed quarks is destroyed, NL-NR=2NFQw →
violation of P-, CP- symmetry.
Dynamics is a random walk between states with different topological
charges. Average total topological charge vanishes <nw>=0 but
variance is equal to the total number of transitions <nw2>=Nt
In the presence of inbalanced chirality a magnetic field induces
a current along the the magnetic field.
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).
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)
Charge separation in HIC: CP violation signal
Magnetic field through the axial anomaly induces a parallel electric field which will
separate different charges
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).
Measuring the charge
separation with respect to the
reaction plane was proposed
by S.Voloshin, Phys. Rev. C
70 (2004) 057901.
Electric dipole moment of QCD matter !
Charge separation: lattice results
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, 054503 (2009)
Charge separation in RHIC experiments
STAR Collaboration,
PRL 103, 251601 (2009)
Measuring the charge separation with respect
to the reaction plane was proposed by
S.Voloshin, Phys. Rev. C 70 (2004) 057901.
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
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
Magnetic field calculation
The Lienart-Wiechard potential is applied to the time
evolution of heavy-ion collisions within the UrQMD model
Retardation condition
with the retardation condition
 Field will have only By 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
■
V.Skokov, A.Illarionov, V.T, IJMP A24, 5925 (2009)
Magnetic field and energy density
evolution in Au+Au collisions at b=10 fm
UrQMD
eBy
ε
[~2π/Sd ] Bcrit ≈ (10. — 0.2) mπ2 [~(αST)2]
and
εcrit ≈ 1 GeV/fm3
From Kharzeev
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, the increase is too strong !
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) )
Normalized at b=10 fm
(centrality 0.4-0.5) 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)
A two neutron star collision
For two-nuclei collisions,
artist’s view: arXiv:1109.5849
Magnetic field evolution
Au+Au(200)
b=10 fm
V.Voronyuk, V.T. et al., Phys. Rev. C84, 035202 (2011)
Magnetic field and energy density correlation
Au+Au(200)
b=10 fm
V.Voronyuk, V.T. et al., Phys. Rev. C84, 035202 (2011)
Time dependence of eBy
D.E. Kharzeev et
al., Nucl. Phys.
A803, 227 (2008)
Collision of two
infinitely thin
layers (pancakelike)
V. Voronyuk, V. T.
et al., PR C84,
035202 (2011)
● 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
Full width is about 2/mπ2 for all transverse field components
“Thin disk” overestimated the width by factor about 3
<|EX|> ≈ <|EY|> ≈ <|BX|>
V.Voronyuk et al., Phys.Rev. C84, 035202 (2011) restricted
A.Bzdak, V.Skokov, Phys.Lett. B710, 171 (2012) thin disk
A
W.Dend, X.Huang, Phys.Rev. C85, 044907 (2012) HIJING
V.T. et al., arXiv:1208.2518
PHSD
Electric field evolution
Electric field of a single
moving charge has a
“hedgehog” shape
V.Voronyuk, V.T. et al., Phys. Rev. C84, 035202 (2011)
Observable
No electromagnetic
field effects on
observable !
V.Voronyuk, V.T. et al., Phys. Rev. C84, 035202 (2011)
CME – charge separation
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)
STAR Collaboration,
PRL 103, 251601 (2009)
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, 064902 (2010).
■ A.Bzdak, V.Koch and J.Liao, Remarks on possible local parity violation in heavy ion collisions,
Phys. Rev. C81, 031901 (2010).
■ S.Pratt, Alternative contributions to the angular correlations observed at RHIC associated with
parity fluctuations, arXiv:1002.1758.
■ S.Schlichting and S.Pratt, Explaining angular correlations observed at RHIC with flow and
local charge conservation, arXiv:1005.5341.
■ 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,
014913 (2011).
■ S.Pratt, S.Schlichting and S.Gavin, Effects of momentun conservation and flow on angular
correlations, Phys. Rev. C84, 024909 (2011).
■ M.Asakawa, A.Majumder and B.Müller, Electric charge separation in strong transient magnetic
fields, Phys. Rev. C81, 064912 (2010).
■ A.Bzdak, V.Koch and J.Liao, Azimuthal correlations from transverse momentum correlations
and possible local parity violation, Phys. Rev. C83, 014905 (2011).
Really all these hadronic effects are accounted for in the
HSD/PHSD model
Transverse Momentum Conservation
For TMC source (A.Bzdak et al., Phys.Rev.
C83, 014905 (2011) ) describing pions
thermodynamically and making use of the
central limiting theorem,
correlator is
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.
V.T. et al., arXiv:1208.2518
In-plane and out-of-plane correlatons
STAR, PR C81, 054908 (2010)
The observed correlations are inplane, contrary to CME expectations !
(A.Bzdac, V.Koch, J.Liao, arXiv:0912.5050)
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, 124165 (2011) (√sNN =7.7, 11.5, 39 GeV)
Compensation
HSD background for BES experiments on CME
V.T. et al., Phys.Rev., C85, 034910 (2012)
Experiments at 7.7 and 11.5 GeV are explained by HSD, the CME is not seen
CME observables in PHSD
Partonic scalar part
Partonic vector part
The action of the
partonic scalar field
on quarks is NOT
compensated !
V.T. et al., arXiv:1208.2518
CME observable cos(ψi+ψj) in PHSD
G.Gangadharn, J.Phys.G:Nucl.Part.Phys. 38, 124166 (2011)
Charge separation in PHSD
V.T. et al., arXiv:1208.2518
PR C86, 014963 (2011)
The partonic scalar potential is
overestimated in PHSD getting
comparable the charge separation
with those at LHC
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
Conclusions
●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 √sNN
= 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.