Study of a mixed quark-hadron phase in heavy-ion collisions (NICA project)

1
Chiral Magnetic Effect and evolution of
electromagnetic field
V. Toneev and V.Voronyuk, JINR, Dubna
? Introductory remarks ? A CME estimate
(arXiv1011.5589 1012.0991 1012.1508 ) ?
Nuclear kinetics in electromagnetic field
(arXiv1103.3239) ? Conclusions
Three Days on Quarqyonic Island, May 19-21,
Wroclaw, 2011
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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)
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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-NLQT ? violation of
P-, CP- symmetry. Average total topological
charge vanishes ltnwgt0 but variance is equal to
the total number of transitions
ltnw2gtNt Fluctuation of topological charges in
the presence of magnetic field induces electric
current which will separate different charges
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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 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.
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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
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Qualitative estimate of the CME
QS -- saturation momentum,
The generated topological charge
Gs ?2 T4 (SUSY Y-M)?
Sphaleron transition occurs only in the
deconfined phase, the lifetime is
V.T. and V.Voronyuk, arXiv1011.5589 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
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Magnetic field and energy density evolution in
AuAu collisions at b10 fm
UrQMD
eBy
L-W poten.
retardation condition
e
2p/Sd Bcrit (10. 0.2) mp2 (aST)2
and ecrit 1 GeV/fm3
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Characteristic parameters for the CME
The lifetimes are estimated at eBcrit0.2mp2 and
ecrit1 GeV/fm3 for AuAu collisions with b10
fm (KAu2.52 10-2 )

• For all energies of interest tB lt te
• The CME increases with energy decrease till the
  top SPS/NICA energy
• If compare vsNN 200 and 62 GeV this
  increase is too strong !

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Ways to remove the discrepancy
The correlator ratio at two measured energies for
b10 fm
(exp)?

• Uncertainity in vs NN dependence does not help
  ßlt0 ?!
• Should be tB(62) 1.2 tB(200) (instead of 3)
  lifetimes
• Uncertainty in impact parameter not essential
• Inclusion of participant contribution to eB
  very small effect
• To decrease eBcrit till 0.01mp2 to reach
  regime tB te lt62
• If eBcrit increases the lifetime ratio is
  correct for eBcrit 1.05 mp2 very
• close to the maximal eBcrit 1.2 mp2
  questionable, no CME for Cu
• To introduce the initial time when
  equilibrium of quark-gluon matter
• is achieved, ti,e gt0, associated with a
  maximum in e-distribution,
• tB(62) / tB(200)(0.62-0.32)/(0.24-0.08)2.0
  not enough
• To combine the last two scenarios success !

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The calculated CME for AuAu collisions
Calculated correlators for AuAu (b10 fm)
collisions at vsNN200 and 62 GeV agree with
experimental values for eBcrit 0.7 mp2 ,
K6.05 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) )
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System-size dependence
The CME should be proportional to the nuclear
overlap area SSA(b)
Centrality e0 Npart
Correlation between centrality and impact
parameter
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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
is as follows
For point-like particles
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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 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
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Magnetic field evolution
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Magnetic field evolution
V.Voronyuk, V.T. et al., arXiv1103.4239 
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Magnetic field and energy density correlation
AuAu(200) b10 fm
V.Voronyuk, V.T. et al., arXiv1103.4239 
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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., arXiv1103.4239 
? Until t1 fm/c the induced magnetic field is
defined by spectators only. ? Maximal magnetic
field is reached during nuclear overlapping time
?t0.2 fm/c, then the field goes down
exponentially.
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Electric field evolution
Electric field of a single moving charge has a
hedgehog shape
V.Voronyk, V.T. et al., arXiv1103.4239 
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Observable
No electromagnetic field effects on observable !
V.Voronyk, V.T. et al., arXiv1103.4239 
21
Average momentum increment
?p dp
Transverse momentum increments ?p due to
electric and magnetic fields compensate each
other ! (worring hope)
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Conclusions

• The magnetic field and energy density of
  the deconfined matter reach very high values in
  HIC for vsNN11 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 lt
  vsNN lt20 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.

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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