The weak-field expansion for processes in a homogeneous background magnetic field

TL;DR

This paper develops a weak-field expansion of the charged fermion propagator in a uniform magnetic field, expressing it as a series in field strength and applying it to particle decay processes to compute magnetic effects.

Contribution

It introduces a systematic weak-field expansion of the fermion propagator based on Landau levels, enabling calculation of magnetic effects in particle processes.

Findings

Leading and subleading magnetic-field effects are computed for specific decay processes.

The expansion provides a practical method to analyze magnetic influences in quantum field theory.

Application demonstrates the approach's utility in particle physics calculations.

Abstract

The weak-field expansion of the charged fermion propagator under a uniform magnetic field is studied. Starting from Schwinger's proper-time representation, we express the charged fermion propagator as an infinite series corresponding to different Landau levels. This infinite series is then reorganized according to the powers of the external field strength $B$. For illustration, we apply this expansion to $\gamma\to \nu\bar{\nu}$ and $\nu\to \nu\gamma$ decays, which involve charged fermions in the internal loop. The leading and subleading magnetic-field effects to the above processes are computed.