Electromagnetic moments of quasi-stable particle

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 $M_{\ast }$ interacting with two fields of masses $M$ and $m$, we show how a conventionally defined magnetic dipole moment diverges at $M_{\ast }=M+m$. We then show that the conventional definition makes sense only when the values of the applied magnetic field $B$ satisfy $\mathrm{\mid }eB\mathrm{\mid }\mathrm{/}2M_{\ast }\ll \mathrm{\mid }{M}_{\ast }-M-m\mathrm{\mid }$. We discuss implications of these results to existing studies in electroweak theory, chiral effective-field theory, and lattice QCD.