Transcript Study of a mixed quark-hadron phase in heavy

Evolution of electromagnetic field in
HIC and chiral magnetic effect
V. Toneev
In collaboration with V. Voronyuk, E. Bratkovskaya,
W.Cassing, V. Konchakovski, S. Voloshin
♥ Introductory remarks (what is the CME ?)
♥ Nuclear kinetics in electromagnetic field created by HIC
(Phys. Rev. C84, 035202 (2011))
♥ Analysis of CME experiments (arXiv:1112.2595)
♥ Conclusions
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 generates 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
First estimate of the created magnetic field
V. Skokov, V.Toneev, A. Illarionov, Int. J. Mod. Phys. A 24, 5923 (2009),
Lienard-Wiehert potential
UrQMD
Au+Au (200 GeV)
b=10 fm
retardation condition
From Kharzeev
Qualitative estimate of the CME
For a r.w. the variance is equal to the total number of transitions <nw2>=Nt
The generated topological charge
the lifetime is
Average correlators are related to the topological charge
eBcrit ≈ 0.7 mπ2
CME disappears
somewhere near
√sNN ~ 20 GeV !
V.T. and V.Voronyuk, arXiv:1011.5589;
1012.0991; 1012.1508
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
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
(HSD calculation result)
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.
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 model
In-plane and out-of-plane correlatons
The observed correlations are in-plane,
contrary to CME expectations ! (A.Bzdac,
STAR, PR C81, 054908 (2010)
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
D.Gangadharan (STAR Collaboration), talk at QM11 (√sNN =7.7, 11.5, 39 GeV)
Compensation
HSD background for BES experiments on CME
V.Toneev et al., arXiv:1112.2595
Experiments at 7.7 and 11.5 GeV are explained by HSD, the CME is not seen
Conclusions
The HSD transport model with retarded electromagnetic fields has
been developed.
The magnetic field and energy density of the deconfined matter reach
very high values.
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 hadronic scenario without
reference to the spontaneous local CP violation.
Direct inclusion of quarks and gluons in evolution is needed (PHSD
model) for exploring the CME at √sNN above the top SPS energy as
well as in future to consider spin d.o.f., to mimic directly the CME.