A study of neutral particle decay in magnetic field with the "Worldline Instanton" approach

We study the process of neutrino decay to electron and $W$-boson in the external magnetic field using the semiclassical “worldline instanton” approach. Being interested only in the leading exponential factor, we make calculations in a toy model, treating all particles as scalars. This calculation determines the effective threshold energy of the reaction as a function of the magnetic field. Possible astrophysical applications are discussed. It is emphasized that the method is general and is applicable to a decay of an arbitrary neutral particle into charged ones in the external electromagnetic field.