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Di-lepton production from a single photon in strong magnetic fields: Vacuum dichroism

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.