# Scattering cross-section under external magnetic field using the optical theorem

## TL;DR

This paper calculates how an external magnetic field alters the scattering cross-section of charged scalars by using the optical theorem and Schwinger propagators, revealing significant modifications compared to vacuum conditions.

## Contribution

It provides the first detailed computation of elastic scattering cross-sections under external magnetic fields in both strong and weak field limits using the optical theorem.

## Key findings

- Cross-sections are significantly modified by magnetic fields.
- Theoretical framework applies Schwinger propagators for charged scalars.
- Results differ notably from vacuum scattering cross-sections.

## Abstract

The cross-section for the lowest order $2\rightarrow2$ elastic scattering between two charged scalars under external magnetic field mediated via a neutral scalar, has been computed in strong as well as weak magnetic field limits. This has been done by applying the optical theorem where the cross-section is expressed in terms of the imaginary parts of different one-loop graphs contributing to the forward scattering amplitudes. The modification in the amplitudes due to the external magnetic field has been done by means of replacing the charged scalar propagators with the Schwinger proper-time ones. Significant modifications of the cross-sections with respect to the vacuum cross-section are observed due to the external magnetic field.