Electromagnetic moments of quasistable particle

We deal with the problem of assigning electromagnetic moments to a quasistable particle (i.e., a particle with mass located at the particle's decay threshold). In this case, an application of a small external electromagnetic field changes the energy in a nonanalytic 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 vertical bar eB vertical bar/2M(*) << vertical bar M-* - M - m vertical bar. We discuss implications of these results to existing studies in electroweak theory, chiral effective-field theory, and lattice QCD.