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Fluctuating Background in Estimates
of the Chiral Magnetic Effect
V. Toneev
In collaboration with E. Bratkovskaya, W. Cassing,
V. Konchakovski, V. Voronyuk
♥ Introductory remarks
♥ Fluctuating sources of CME background
♥ Analysis of CME experiments
( Phys. Rev. C84, 035202 (2011);
Phys. Rev. C85, 034910 (2012); arXiv:1112.2519)
♥ Conclusions
Workshop on Particle Correlations and Femtoscopy, Frankfurt, September 10 -14, 2012
Chiral magnetic effect (reminding)
Gauge field 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 chiral
anomaly and thus resulting in generated asymmetry between left- and
right-handed fermions. In this states a balance between left-handed
and right-handed chiral quarks is destroyed.
In the presence of inbalanced chirality a magnetic field induces
a chiral electric current along the the magnetic field.
D.Kharzeev et al., NP A803, 227 (2008); Ann.Phys. 325, 205 ( 2010); PR D78, 074033 (2008)
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 in RHIC experiments
STAR 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 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
Lienard-Wiehert potential
For point-like particles
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
Full width is about 2/mπ2 for all transverse field components
“Thin disk” overestimates 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:1208.2519
PHSD
Compensation effect
Δp= δp
Transverse 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
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
Electric charge fluctuations in the
transient stage I
A charged dipole is defined as
V.T. et al., arXiv:1208.2519
Electric charge fluctuations in the
transient stage II
A charged quadrupole is defined as
- Qc1 , Qc2 magnitude
Prediction
v2(π-)>v2(πis+)small,
Chiral magnetic wave
(Y.Burnier et al., PRL
-30%
its orientation
for √s=11 GeV
is almost uniform,
107, 052303 (2012)
- main axis is changed from
event to event
Hadron models and exp. J.Xu et al., PR C85,
041901 (2012)
give ~10%
There
is not much room for CMW
Charge balance function (time evolution)
central
semi-peripheral
Charge balancing partners
Conditional probability
N+-(δη,δw) counts pairs
with opposite charge sign
satisfying condition that
δη=(η+ - η- ) € ηw
The same charge pairs
are subtracted
B-distribution formed in the quark phase is not
changed (for η) or changed a little (for ϕ) in time
V.T. et al., arXiv:1208.2519
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 program
STAR Collaboration, J. Phys. G38, 124165 (2011) (√sNN =7.7, 11.5, 39 GeV)
Compensation
HSD background for BES experiments on CME
V.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
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 noncompensated scalar one.
V.T. et al., arXiv:1208.2519
CME observable cos(ψi+ψj) in PHSD
G.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
δ
V.Toneev et al., arXiv:1208.2519
PR C86, 014963 (2011)
δij
The partonic scalar potential is
overestimated in PHSD getting
comparable the charge separation
with experiment but 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
●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.