Helicity of spin-extended chiral particles

The helicity of a free massless relativistic particle, $\chi^o={\bf s}.{\bf p}/|{\bf p}|$, is generalized, for a particle in an electromagnetic field, to $\chi={\bf s}.{\bf p}/{\cal E}$, where ${\cal E}$ is the modified kinetic energy. Both $\chi^o$ and $\chi$ coincide and are conserved for minimal coupling (gyromagnetic ratio $g=0$) but are different and neither of them is conserved when the coupling is non-minimal, $g\neq0$, generating non-zero effective mass. For a chiral particle with $g=2$ in a constant electric field both helicities converge asymptotically to the same value. Helicity is also conserved for minimal gravitational coupling.