Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Signatures of chiral magnetic wave in heavy ion collisions
H. -U. Yee,∗1∗2Chiral magnetic wave1) is a collective hydrodynamic
mode of chiral charge densities in the presence of background magnetic field, as a consequence of underlying
triangle anomaly of QCD. It has a longitudinal dispersion relation along the direction of the magnetic fieldω = ±vχ k − iDL k 2 + · · · ,(1)where the chiral magnetic velocity vχ is completely
fixed by the thermodynamic charge susceptibility χ asvχ =eNc B,
4π 2 χ(2)whereas the sign in front of the first term in the dispersion relation depends on the chirality, that is, lefthanded charge fluctuations propagate in the opposite
direction to that of the right-handed charge fluctuations. Since off-central heavy ion collisions can create
magnetic fields as large as eB ∼ m2π at RHIC andabout ten times larger at LHC, they provide an interesting environment where one can potentially test possible experimental signatures of chiral magnetic wave.
One observable that might be affected by the chiralmagnetic wave is the elliptic flows of early photons anddileptons, for which the recent experimental data fromRHIC indicate a value larger than the current theory
estimate without taking into account the presence ofmagnetic fields. Earlier studies have suggested possible enhancement of the elliptic flows of photons dueto the magnetic field, but a proper account of possible effects coming from chiral magnetic wave was firstexamined in Ref.2) in the framework of AdS/CFT correspondence. We observed that the chiral magneticwave can significantly modify the elliptic flows for themomentum p < 1 GeV. Also, the quadrupole to theelliptic flow square ratio, v4 /v22 , is largely different
from a constant, violating a typical scaling v4 ∼ v22 forcharged hadrons. We also predicted a distinctive signature in the polarization of photons originating fromchiral magnetic wave. Future experiments probing themomentum range p < 1 GeV will be interesting topotentially see such behaviors due to chiral magneticwave.
Another observable of interest is the charge dependent elliptic flows of pions, ∆v2 ≡ v2 (π − ) − v2 (π + ),which was recently measured at RHIC. The QCD
plasma formed by heavy ion collisions naturally has asmall average positive vector charge density as a remnant of the colliding two positively charged nuclei, but
one can also select events with any sign of the net
charge that exist via statistical fluctuations. Recalling that QV = QL + QR and QA = −QL + QR where∗1∗2QV,A are vector (axial) charge densities and QL,R areleft (right)-handed chiral charge densities, the initial
vector charge density with average zero axial charge
corresponds to having equal amounts of chiral charges
QL and QR . Chiral magnetic wave acting on thesechiral charges will move them apart in opposite directions along the magnetic field, which leads to a net
vector charge quadrupole moment that is proportional
to the initial vector charge density. Based on this, wepredicted in Ref.3) that this quadrupole moment, inconjunction with the radial flow developed by hydrodynamic evolution, will eventually result in ∆v2 proportional to the initial vector charge density,∆v2 = rA± ,A± =(N+ − N− ),(N+ + N− )(3)with a positive slope parameter r, which has been confirmed by the experimental analysis of RHIC. The simulation in Ref.3) for r to compare with experimental
value was crude, neglecting many realistic elements
in heavy ion collisions, and in Ref.4) we significantly
improved the simulation by implementing a realistic
2+1 dimensional hydrodynamic code with isothermal
Cooper-Frye freeze out condition, as well as chiralphase transition effect on the chiral magnetic wave.
Our result for r and its dependence on the impact parameter compare well with experiments, although ouranalysis does not exclude other contributions unrelated
to triangle anomaly.
In Ref.5) we systematically classified possible P andCP odd observables in photon and dilepton emission
rates. Since axial charge is P and CP odd, which isa unique characterization of it, these observables must
be proportional to event-by-event fluctuations of axial charges in the QCD plasma formed in heavy ion
collisions. Our observables are related to spin (helicity) alignments of the photons and dileptons, and wehave shown that they probe the imaginary part of thechiral magnetic conductivity of the plasma at finite
momenta, which ultimately arises from the underlying
triangle anomaly of QCD.
References
1) D. E. Kharzeev and H. -U. Yee: Phys. Rev. D 83,085007 (2011).
2) H. -U. Yee: Phys. Rev. D 88, 026001 (2013).
3) Y. Burnier, D. E. Kharzeev, J. Liao and H. -U. Yee:Phys. Rev. Lett. 107, 052303 (2011).
4) H. -U. Yee and Y. Yin, Phys. Rev. C 89, 044909 (2014).
5) K. A. Mamo and H. -U. Yee: Phys. Rev. D 88, 114029(2013).

Department of Physics, University of Illinois, Chicago
RIKEN Nishina Center- 104 -