Abstract
We study di-lepton production from a single photon in the presence of a strong constant magnetic field. By the use of the Ritus-basis formalism, we analytically evaluate the photon-to-di-lepton conversion vertex with fully taking into account the non-perturbative interactions between the produced fermions and the strong magnetic field. We show that the di-lepton spectrum becomes anisotropic with respect to the magnetic-field direction and depends on the photon polarization as a manifestation of the vacuum dichroism in a strong magnetic field. According to the energy conservation in the presence of the Landau quantization, not only the transverse momentum of the produced fermions but also the longitudinal momentum is discretized, and the di-lepton spectrum exhibits spike structures as functions of the incident photon energy and the magnetic field strength. We also show that the di-lepton production is strictly prohibited for massless fermions in the lowest Landau levels as an analogue of the so-called helicity suppression.
Highlights
Fields, an on-shell real photon travels at the speed of light in vacuum without modification of the refractive index or conversion to di-lepton, even when the vacuum polarization effect is included
We show that the di-lepton spectrum becomes anisotropic with respect to the magneticfield direction and depends on the photon polarization as a manifestation of the vacuum dichroism in a strong magnetic field
We emphasize that the differential cross section for the di-lepton production computed in this paper provides more information than the aforementioned imaginary part of the refractive index, which corresponds to the integrated cross section
Summary
To provide a self-contained construction, we first review the Ritus-basis formalism [41, 42].1 In case of a constant external magnetic field, the energy spectrum of charged fermions is subjected to the Landau quantization and the Zeeman shift. In case of a constant external magnetic field, the energy spectrum of charged fermions is subjected to the Landau quantization and the Zeeman shift. We discuss the energy level of a charged fermion in the presence of a constant magnetic field. To this end, it is convenient to rewrite the Dirac equation (2.1). We impose the canonical commutation relations on the Dirac field operator ψ (see appendix A.2 for details) and normalize the transverse wave function φn,py , which fixes the normalization of the Ritus basis Rn,py , as d2x⊥φ∗n,py (x⊥)φn ,py (x⊥) = 2πδ(py − py)δn,n.
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