Chirality is defined through the ±1 eigenvalue under action of γ^5 on ψ, a Dirac field thus projected into its left- or right-handed component by the projection operators (1−γ^5)/2 or (1+γ^5)/2 on ψ. For massless particles (only!) chirality coincides with [helicity], a notion which is frame-dependent, and hence ambiguous for massive particles. Avoid using the [helicity] tag instead: the projectors must be implied.
Chirality is a formal quantification of a Dirac fermion's $\psi$ difference from its parity image. It is defined through the ±1 eigenvalue under action of the operator $\gamma^5$ on $\psi$. Any Dirac field can thus be projected into its left- or right-handed component by acting with the projection operators $(1−\gamma^5)/2$ or $(1+\gamma^5)/2$ on $\psi$. For massless particles (only!) chirality coincides with helicity, a notion which is frame-dependent, and hence ambiguous for massive particles.
