2020/08/25 by Bo Feng, Defu Hou, De-fu Hou +2
Mathematics · Physics and Astronomy · #Chiral anomaly #Dark Matter and Cosmic Phenomena #Fermion #High-Energy Particle Collisions Research #Limit (mathematics) #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Propagator #Pseudovector #Quantum electrodynamics #Quantum mechanics #Singularity #Vertex (graph theory) #hep-ph
paper · pdf · doi:10.1103/physrevd.103.056004
published as Phys. Rev. D 103, 056004 (2021) · 16 pages, 4 figures
arxiv created 2020/08/25 · openalex created_date 2020/09/01 · openalex publication_date 2021/03/05 · arxiv updated 2021/03/10 · openalex updated_date 2026/08/05
We study the noncommutativity of different orders of zero energy-momentum limit pertaining to the axial chemical potential in the chiral magnetic effect. While this noncommutativity issue originates from the pinching singularity at one-loop order, it cannot be removed by introducing a damping term to the fermion propagators. The physical reason is that modifying the propagator alone would violate the axial-vector Ward identity and as a result a modification of the longitudinal component of the axial-vector vertex is required, which contributes to chiral magnetic effect (CME). The pinching singularity with free fermion propagators was then taken over by the singularity stemming from the dressed axial-vector vertex. We show this mechanism by a concrete example. Moreover, we proved, in general, the vanishing CME in the limit order that the static limit was taken prior to the homogeneous limit in the light of Coleman-Hill theorem for a static external magnetic field. For the opposite limit that the homogeneous limit is taken first, we show that the nonvanishing CME was a consequence of the nonrenormalization of chiral anomaly for an arbitrary external magnetic field.