References - Bogoliubov Laboratory of Theoretical Physics - JINR

3. Vector current of strange quarks and Chiral Magnetic Effect in Heavy
Ions Collisions. The calculation of vector rather than axial current of heavy (and
strange) quarks appears to be even easier. The answer is actually contained in the classical
Heisenberg-Euler effective lagrangian for light-by light scattering. Calculating its variation
with respect to the electromagnetic potential one immediately get the expression for the
current. The transition from QED to QCD is performed by the substitution of three
of quark-photon vertices by the quark-gluon ones. The C-parity ensures that the result
contains only the symmetric SU(3) structure d abc and is proportional to Abelian one which
was explored earlier [8]. The notion of this current allows to determine the strangeness
contribution to the anomalous magnetic moment of the nucleon and to the mean square
radius of the pion.
Another interesting manifestation of strange quark vector current emerges if one substitutes
[7] the two rather than three quark-photon vertices by quark-gluon ones. The
results describes the vector current induced by cooperative action of (two) gluonic and
electromagnetic fields. Its physical realization corresponds, in particular, to heavy ions
collisions where extremely strong magnetic fields are generated. The most interesting
contributions comes from the term (F ˜ F ) 2 in Heisenberg-Euler lagrangian, leading to the
current
j s μ
= 7πααs
45m 4 s
˜Fμν∂ ν (G ˜ G) (6)
One may easily recognize here the analog of the famous Chiral Magnetic Effect (CME) (see
[9] and Ref. therein). The correspondence is manifested by the substitution 1
m4 ∂
s
ν (G ˜ G) →
∂ν � d4z(G ˜ G) → ∂νθ The latter requires the appearance of two scales, now in multiscale medium, (the ones
corresponding to integration and taking the derivative) and leads to the derivative of
topological field θ. The later property makes the interpretation of lattice simulations
[10, 11] ambiguous. Note also that the calculated effect for heavy quarks is not directly
related neither to topology nor to chirality. In particular, it is present also when all the
three fields are electromagnetic ones, which may be of physical interest, as soon as the
electromagnetic and chromodynamical fields are of the same order in heavy ions collisions.
Acknowledgments I am indebted to P. Buividovich, D. Kharzeev, A. Moiseeva, M.
Polyakov, M. Polikarpov and V.I. Zakharrov for discussions. This work was supported in
part by the Russian Foundation for Basic Research (grants No. 09-02-01149, 09-02-00732-
�), and the Russian Federation Ministry of Education and Science (grant No. MIREA
2.2.2.2.6546).
References
[1] A.V. Efremov and O.V. Teryaev, Report JINR-E2-88-287, Czech.Hadron Symp.1988,
p.302.
[2] A.V. Efremov, J. Soffer and O.V. Teryaev, Nucl.Phys. B346 (1990) 97
[3] M. V. Polyakov, A. Schafer and O. V. Teryaev, Phys. Rev. D 60, 051502 (1999)
[arXiv:hep-ph/9812393].
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