# The lifetime of unstable particles in electromagnetic fields

## TL;DR

This paper investigates how external electromagnetic fields influence the lifetime of unstable particles by analyzing their electromagnetic moments, providing calculations for muons, neutrons, and the Δ(1232) resonance, and discussing potential observable effects.

## Contribution

It introduces the concept that electromagnetic moments of unstable particles have an absorptive component affecting their lifetimes, with explicit calculations for specific particles at leading order.

## Key findings

- The imaginary part of the magnetic moment for muons and neutrons is computed.
- External magnetic fields cause a tiny but quantifiable change in particle lifetimes.
- The effect is significant enough to be potentially observable in experiments.

## Abstract

We show that the electromagnetic moments of unstable particles (resonances) have an absorptive contribution which quantifies the change of the particle's lifetime in an external electromagnetic field. To give an example we compute here the imaginary part of the magnetic moment for the cases of the muon and the neutron at leading order in the electroweak coupling. We also consider an analogous effect for the strongly-decaying $\Delta$(1232) resonance. The result for the muon is Im$ \mu = e G_F^2 m^3/768 \pi^3$, with $e$ the charge and $m$ the mass of the muon, $G_F$ the Fermi constant, which in an external magnetic field of $B$ Tesla give rise to the relative change in the muon lifetime of $3\times 10^{-15} B$. For neutron the effect is of a similar magnitude. We speculate on the observable implications of this effect.