NQMA-THEORY-06
GSI SCIENTIFIC REPORT 2009
Estimate of the magnetic field strength in heavy-ion collisions∗
V. Skokov† 1 , Yu. Illarionov2, and V. Toneev3
GSI, Darmstadt, Germany; 2 University of Trento, Italy; 3 JINR, Dubna, Russia
∗ Work
supported by Frankfurt Institute for Advanced Studies
† V.Skokov@gsi.de
260
0.2
b = 4 fm
eBy/mπ
2
0.15
Elab=10A GeV
Elab=60 A GeV
Elab=160A GeV
0.1
0.05
00
2.5
2
4
6
t, fm/c
b = 4 fm
8
10
1/2
sNN =130 GeV
2
2
One of the most exciting signals of the deconfinement
and the chiral phase transitions in heavy-ion collisions, the
chiral magnetic effect, suggested in Ref. [1], predicts the
preferential emission of charged particles along the direction of angular momentum in the case of the noncentral
heavy-ion collisions due to the presence of nonzero chirality. This effect is because the strong magnetic field in the
presence of imbalanced chirality induces a current along
the magnetic field. As it was stressed in Refs. [1, 2], both
the deconfinement and the chiral phase transitions are essential for the chiral magnetic effect to take place.
The effects caused by a strong magnetic field are not
limited by the chiral magnetic effect [2]. They include
also the induced chiral symmetry breaking, modification
of the nature of the chiral phase transition (e.g. turning the
crossover phase transition to the first-order one through influence on the chiral condensate), influence on the possible
color-conducting phases and the pion condensate, spontaneous creation of the axial currents, and formation of the
π0 -domain walls. Recently, the effect of a large magnetic
field on the sound velocity of a propagating plane wave was
studied.
The key quantity of these effects is a magnitude of the
background magnetic field strength created in heavy-ion
collisions. Early estimates of the magnetic field for RHIC
energies was made in Ref. [1]. It was shown that the field
may reach very high values eB ∼ 3·m2π ∼ 3×1018 Gauss.
In Ref. [3] we improved the previous qualitative estimate
by making the quantitative calculation of the magnetic field
for heavy-ion collisions at different impact parameters and
different energies and studying its characteristics. The calculations were carried out within the microscopic transport model, namely the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD), and were complemented
by analytical considerations.
In Fig. 1, the time evolution of the magnetic field
strength for SPS and RHIC energies is shown. The magnetic field is created in the noncentral Au–Au collision with
the impact parameter b = 4 fm. The resulting field strength
is averaged over 100 events to reduce statistical fluctuations.
Note that this magnetic field strength is higher by about
4 orders of magnitude than that in the surface of magnetar.
The calculated dependence of the magnetic field strength
on the coordinate y parallel to the direction of angular momentum demonstrates that the field stays approximately
constant up to y ∼ 5 fm, showing the high degree of homogeneity in the central region.
eBy/mπ
1
1/2
sNN =200 GeV
1.5
1
0.5
00
0.1
0.2
0.3
t, fm/c
0.4
0.5
Figure 1: The time evolution of the magnetic field strength
eBy at the central point of colliding ions in Au–Au collisions with impact parameter, b = 4 fm, in the UrQMD
model, for different bombarding energies. The magnetic
field obtained by modelling the gold ions as two Lorenz
contracted non-interacting uniformly charged spheres with
radius R = 7 fm are shown by dashed lines.
We estimated the lowest bound of the maximal magnetic
√
field strength at the LHC energy sN N = 4.5 TeV to be
about 15 · m2π in collisions of Pb–Pb ions with the impact
parameter b = 4 fm.
References
[1] D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl.
Phys. A 803, 227 (2008) [arXiv:0711.0950].
[2] K. Fukushima, D. E. Kharzeev and H. J. Warringa, Phys. Rev.
D 78, 074033 (2008) [arXiv:0808.3382].
[3] V. Skokov, A. Y. Illarionov and V. Toneev, Int. J. Mod. Phys.
A 24 (2009) 5925 [arXiv:0907.1396].