Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 49 (2016)

Axial current generation by P-odd domain in QCD matter†
I. Iatrakis,∗1 S. Lin,∗2 and Y. Yin∗3
It is believed that parity-odd domains are produced in heavy ion collisions. The effect of parity odd domains can be modeled by an external θfield, which couples to topological charge density q =g 2 µνρσtrGµν Gρσ , where g is the strong coupling
32π 2 ǫconstant and G is the gluon field strength. An external θ field can induce nonvanishing q. According to
the axial anomaly equationµ= −2q,∂ µ JA(1)a nonvanishing q can generate chiral imbalance, which
can be characterized by axial chemical potential µA .
The µA is a key component of the chiral magnetic effect(CME). The CME predicts the generation of electric
current along an external magnetic field in deconfined
quark-gluon plasma with chiral imbalance1)
Nc e2
µA B.
jV =2π 2(2)The CME is currently being intensvely researchedthrough heavy ion collision experiments at relativistic heavy ion collider (RHIC) and large hadron collider(LHC). The goal of this paper is to explore the responseof the axial current to the θ field and the backreactionof the axial charge to the θ field.
We can write the response of q to θ as q(ω, k) =−GR (ω, k)θ(ω, k), with the response function in thehydrodynamic limit given by
GR (ω, k) = −χ −iΓCS ω κCS 2−
k + ···.
2T2(3)

Here, the first term represents the topological susceptibility, which is highly suppressed in deconfined quarkgluon plasma. The second term is the Chern-Simon(CS) diffusion, where ΓCS is the diffusion rate. Thisterm is known to be responsible for axial charge generation. The third term is present when the externalθ field is spatially inhomogeneous. We note that thecorresponding transport coefficient κCS is measurable
on the lattice in the static limit ω → 0. It measures theresponse of q to spatial inhomogeneity of the θ field.
More interestingly, we found in a model-independent
way that it leads to the generation of axial current
along the gradient of θjA = κCS ∇θ.

(4)We also confirmed the current through a holographic†∗1∗2∗3model calculation.2) It is worth noting that the holographic calculation also considers the contribution of
the conventional diffusive current. We argued that thiscurrent could be phenomenologically important in thecontext of heavy ion collisions as compared to the chiral separation effect and the chiral electric separation
effect. A schematic view of axial current generation isshown in Fig.1.

Condensed from the article in Phys. Rev. Lett. 114, 25(2015)
Department of Physics and Astronomy, Stony Brook UniversityRIKEN Nishina Center
Department of Physics, Brookhaven National Laboratory- 118 -Fig. 1. A schematic view of axial current generation along
the gradient of the θ field.

We also considered the backreaction of the axial
charge to the effective θ field. In the homogeneous
limit k = 0, the θ field generates an axial charge density
nA =ΓCSθT(5)through the diffusion of the topological charge and axial anomaly. Using axial charge susceptibility χA (notto be confused with topological susceptibility), it gives
rise to an axial chemical potentialΓCSθ.
(6)
µA =
χA T
Following Ref.3) , we identify µA with ∂t θ. By comparing this with Eq. 6, we obtain an exponential decay
for the effective θ field with the decay time scale set
χA T. The physical reason for the backas τsph = 2ΓCSreaction is that the presence of axial charge modifies
the gluon potential such that the topological charge
density is changed to partially balance out the axialcharge. This results in a damping of the topologicalnontrivial configurations like sphaleron. Thus, we refer to τsph as the sphaleron damping rate. In termsof the θ field, it is realized as the exponential decayof the field. We also confirmed the backreaction in aholographic model calculation.2)
References
1) D. Kharzeev, L. McLerran and H. Warringa, Nucl.
Phys. A 803, 227 (2008).
2) I. Iatrakis, S. Lin and Y. Yin, J. of High Energy Phys.
030, 09 (2015).
3) D. Kharzeev, Annals. Phys. 325, 205 (2010).