Chiral magnetic effect in 2+1 flavor QCD+QED

TL;DR

This work investigates the chiral magnetic effect (CME) in 2+1 flavor QCD+QED at finite temperature using domain-wall fermions on a fixed-topology lattice. The authors probe CME via the electric charge density derived from low-lying Dirac modes in an external magnetic field, and examine topological structures through G-tilde G. They find a clear CME signal in a discretized continuum instanton background, evidenced by charge separation that grows roughly linearly with the field strength, while simulations in a realistic 2+1 flavor configuration above Tc show suggestive but not yet conclusive CME signals due to current nonconservation and finite-L_s effects. The results demonstrate the feasibility of first-principles CME studies in lattice QCD+QED and point to necessary refinements and parameter scans (temperature, field strength, and QED-QCD field correlations) to achieve robust conclusions.

Abstract

The exciting possibility of direct observation of QCD instantons in heavy-ion collisions has recently been proposed by Kharzeev. The underlying phenomenon, known as the chiral magnetic effect, may have been observed recently at RHIC, and a first principles calculation is needed to confirm and understand the results. The chiral magnetic effect is thought to be visible in the symmetric phase, at temperatures above the QCD critical temperature, and in the presence of an external magnetic field. We report on first 2+1 flavor, domain wall fermion, QCD+QED dynamical simulations above the critical temperature, in a fixed topological sector(s), which are used to study the electric charge separation produced by the effect.

Figures (4)

• Figure 1: Chirality $\langle\psi_i|\Gamma_5|\psi_j\rangle$ of the low-modes of the DWF Dirac operator for the QCD configuration 420 discussed in the text, with $B_z=0$. There are 10 zero-modes in this configuration, so the topological charge is $Q=10$ by the Atiyah-Singer index theorem.
• Figure 2: Left panel: Charge separation computed from a single near-zero-mode for a continuum instanton discretized on an $8^4$ lattice. $B_z=0.098175$. Translational invariance is broken in the $x-y$ plane by the Landau states of the quarks. Right panel: total amount of charge separated to the lower half of the lattice in the $z$ direction for the same configuration. All modes with chirality close to one are included in the total. The same amount, but with opposite sign resides in the top half.
• Figure 3: Top left panel: Topological charge density. Top right: right-handed zero-mode, eigenvector 0. Bottom: right-handed zero-mode, eigenvector 7 (right panel) and eigenvector 11 (left). The eigenmodes are all localized around the "instantons". $B_z=0$.
• Figure 4: Charge density from (near) zero-modes. Top left panel: eigenvector 0, $B_z=0$ (left) and $B_z=0.0490874$ (right); bottom: eigenvector 7, $B_z=0.0490874$ (left) and $B_z=0.0736311$ (right).