QED cross sections in strong magnetic fields

Abstract

The magnetospheres of magnetars, a class of highly magnetized neutron stars, host magnetic fields exceeding the Schwinger limit, where Quantum Electrodynamics (QED) becomes nonlinear. In such environments, QED scattering processes are strongly modified, which may affect plasma dynamics. In this work, we apply a formalism originally developed for the study of magnetic-field effects in hot quark-gluon plasma to strong-field QED. The method resums interactions between virtual electrons and the external magnetic field, consistently incorporating the finite decay widths of excited Landau levels derived from the fermion self-energy. Using this framework, we perform the first systematic analysis of tree-level QED scattering processes in strong magnetic fields, concentrating on the processes of highest relevance for the plasma dynamics of magnetars. All resulting cross sections are provided in an open-source Python package.

Figures (7)

• Figure 1: a) In the Furry expansion, the fermion propagator includes all possible interactions with $\mathcal{A}^\mu$, denoted here by squiggly lines that end with $\cross$fedotov_advances_2023. b) In a background magnetic field, the 3-photon fermion loop is non-zero and yields an effective 3-photon vertex. Together with the Furry expansion, this photon self-interaction gives rise to the nonlinear effects of SFQED. c) The fermion self-energy $\Sigma$ regulates some divergences present in SFQED cross sections.
• Figure 2: Total Compton cross section for a photon moving in a direction perpendicular to the magnetic field, with $b=0.1$. The blue and orange solid lines stand for our results for the X- and O-modes, respectively, while the corresponding results of Ref. mushtukov_compton_2016 are denoted by red and violet dashed lines.
• Figure 3: Differential cross section for Compton scattering, with both (O-mode) photons moving perpendicular to the magnetic field ($\theta=\flatfrac{\pi}{2}=\theta'$), $n_i=0$, and $b=10$. The solid blue line stands for the full result, while the other lines denote various approximations as explained in the main text.
• Figure 4: Two-photon-pair-creation cross section for a head-on collision of photons moving perpendicular to the magnetic field with $\omega=\omega'$ and $b=1$. The dash-dotted lines correspond to the production of specific spin states as indicated in the legend, with the left arrow always standing for the electron and the right one for the positron. The solid blue line shows the sum of the four combinations.
• Figure 5: Cross section of one-photon pair annihilation as a function of the electron longitudinal momentum $p^z$ at $b=10$, averaged over incoming spin states and summed over outgoing polarization states. The color coding refers to the shared Landau levels of the electron and positron, which we vary from 0 to 100.