Electromagnetic moments of quasi-stable particle

TL;DR

This paper investigates the challenges of defining electromagnetic moments for quasi-stable particles, demonstrating non-analytic behavior at decay thresholds and proposing conditions under which conventional definitions are valid.

Contribution

It reveals the limitations of traditional electromagnetic moment definitions for quasi-stable particles and provides criteria for their valid application near decay thresholds.

Findings

Conventional magnetic dipole moment diverges at the decay threshold.

Valid definition requires magnetic field strength to be much smaller than the energy difference.

Implications for electroweak theory, chiral EFT, and lattice QCD studies.

Abstract

We deal with the problem of assigning electromagnetic moments to a quasi-stable particle (i.e., a particle with mass located at particle's decay threshold). In this case, an application of a small external electromagnetic field changes the energy in a non-analytic way, which makes it difficult to assign definitive moments. On the example of a spin-1/2 field with mass $M_{*}$ interacting with two fields of masses $M$ and $m$, we show how a conventionally defined magnetic dipole moment diverges at $M_{*}=M+m$. We then show that the conventional definition makes sense only when the values of the applied magnetic field $B$ satisfy $|eB|/2M_{*}\ll|M_{*}-M-m|$. We discuss implications of these results to existing studies in electroweak theory, chiral effective-field theory, and lattice QCD.