Helicity of spin-extended chiral particles

TL;DR

This paper extends the concept of helicity for massless particles to particles in electromagnetic fields, analyzing how different couplings affect helicity conservation and behavior, especially for chiral particles with specific gyromagnetic ratios.

Contribution

It introduces a generalized helicity definition for particles in electromagnetic fields and explores its conservation properties under various coupling scenarios, including non-minimal coupling.

Findings

Helicity coincides and is conserved for minimal coupling (g=0).

Helicity differs and is not conserved for non-minimal coupling (g≠0).

In a constant electric field, chiral particles with g=2 have helicities converging asymptotically.

Abstract

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.