Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics

Abstract

We provide a resolution of an old issue in weak coupling computation of the Chiral Magnetic Effect (CME) current, where a free chiral fermion theory gives two different results depending on the order of the two limits, $\omega \to 0$ (frequency) and $k\to 0$ (spatial momentum). We first argue based on hydrodynamics that in any reasonable interacting theory of chiral fermions the non-commutativity between the two limits should be absent, and we demonstrate this at weak coupling regime in two different frameworks: kinetic theory in the relaxation time approximation, and diagrammatic computation with resummation of damping rate. In the latter computation, we also show that the "pinch" singularity, which would make the summation of ladder diagrams necessary as in the P-even correlation function, is absent in the relevant P-odd correlation function. The correct value of CME current is reproduced even in the presence of relaxation dynamics in both computations.

26 pages, 3 figures

References in corpus (13)

• The Chiral Magnetic Effect
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Charge separation induced by P-odd bubbles in QCD matter
• Chiral Magnetic Wave
• Quantum Anomalies in Dense Matter
• Chiral Magnetic conductivity
• Lorentz Invariance in Chiral Kinetic Theory
• Notes on chiral hydrodynamics within effective theory approach
• Holographic Anomalous Conductivities and the Chiral Magnetic Effect
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• Chiral magnetic effect in lattice QCD with a chiral chemical potential
• Some Field Theoretic Issues Regarding the Chiral Magnetic Effect
• From the chiral magnetic wave to the charge dependence of elliptic flow

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• Chiral electric separation effect in the quark-gluon plasma
• Chiral Hall Effect and Chiral Electric Waves
• Nonlinear electromagnetic response in quark-gluon plasma
• Collective Modes of Chiral Kinetic Theory in Magnetic Field
• Chiral Magnetic and Vortical Effects in Higher Dimensions at Weak Coupling