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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
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
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 charge vanishes <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
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 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
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
V.T. and V.Voronyuk, arXiv:1011.5589;
1012.0991; 1012.1508
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 and energy density evolution
in 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
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 !
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
2
■ To decrease eB
crit till 0.01mπ to reach regime τB = τε ; <62
2 very
■ If eB
increases
the
lifetime
ratio
is
correct
for
eB
≈
1.05
m
crit
π
crit
2
close to the maximal eBcrit =1.2 mπ ; 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 !
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
System-size dependence
The CME should be proportional to the nuclear overlap area S≡SA(b)
Centrality
e0 Npart
Au+Au
Pb+Pb
I+
I
Cu+Cu
Ca+Ca
Correlation between centrality and impact parameter
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
HSD off-shell transport approach
-2
-Im D (M,q,B,T) (GeV )
T=150 MeV
Accounting for in-medium effects requires
off-shell transport models!
B=30
2
0.5
0.0
V/c)
1.0
1
q (Ge
The off-shell spectral functions change their
properties dynamically by propagation
through the medium and become on-shell in
the vacuum
1.5
0.5
1.0
M (G
eV/c 2)
1.5
0.0
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.
W. Cassing et al., NPA 665 (2000) 377;
672 (2000) 417; 677 (2000) 445
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
Au+Au(200)
b=10 fm
V.Voronyuk, V.T. et al., arXiv:1103.4239
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.,
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.
Electric field evolution
Electric field of a single
moving charge has a
“hedgehog” shape
V.Voronyk, V.T. et al., arXiv:1103.4239
Observable
No electromagnetic
field effects on
observable !
V.Voronyk, V.T. et al., arXiv:1103.4239
Average momentum increment
Δp= δp
Transverse momentum
increments Δp due to
electric and magnetic fields
compensate each other !
(worring & hope)
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 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.
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