Abstract
In this paper, we consider vacuum polarization effects in the model of charged fermions with anomalous magnetic moment and axial-vector interaction term in a uniform magnetic field. Nontrivial orrections to the effective Lagrangian from the anomalous moment and axial-vector term are calculated with account for various configurations of parameters of the model.
Highlights
As is known a charged particle described by the Dirac equation should possess an intrinsic moment, i.e., spin, and a kinematic Dirac magnetic moment whose value is equal to the Bohr magneton μ0 = e 2mcIn the lowest order with respect to the fine-structure constant αe2 c (Schwinger [1]), the total value of the electron magnetic moment with account fot the vacuum contribution becomes μS ch = μ0 + ΔμS ch, ΔμS ch α 2π · μ0, (1)where ΔμS ch is the Schwinger vacuum magnetic moment of the electron, which was shown [2] to depend on the electron energy and the strength of the external magnetic field
In the lowest order with respect to the fine-structure constant α e2 c (Schwinger [1]), the total value of the electron magnetic moment with account fot the vacuum contribution becomes μS ch = μ0 + ΔμS ch, ΔμS ch where ΔμS ch is the Schwinger vacuum magnetic moment of the electron, which was shown [2] to depend on the electron energy and the strength of the external magnetic field
Modern experiments give the following estimates: |b0| 10−14GeV, | b | 10−31GeV. This calculation of the effective Lagrangian is motivated by the study of the so called chiral magnetic effect [17] with the vacuum current induced by an external magnetic field in the presence of the chiral chemical potential, which is similar to the above mentioned Lorentz-violating term
Summary
As is known a charged particle described by the Dirac equation should possess an intrinsic moment, i.e., spin, and a kinematic Dirac magnetic moment whose value is equal to the Bohr magneton μ0. A Dirac particle can obtain an anomalous magnetic moment (AMM) Δμ not necessarily equal to its vacuum value ΔμS ch ([3]). We calculate a one-loop effective Lagrangian of electromagnetic field in the framework of the SME, generalized by introducing the Pauli–Schwinger AMM term in the Dirac Lagrangian for a fermion in a constant and uniform magnetic field. [16]): |b0| 10−14GeV, | b | 10−31GeV This calculation of the effective Lagrangian is motivated by the study of the so called chiral magnetic effect [17] with the vacuum current induced by an external magnetic field in the presence of the chiral chemical potential, which is similar to the above mentioned Lorentz-violating term. Background interaction of the form of the Pauli–Schwinger term can occur in the framework of the SME and in parity-violating interactions of cosmic fields with atoms, molecules, and nuclei [3]1
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