 Massive-fermion chiral weight at fixed helicity

For a positive-energy Dirac spinor normalized to unit probability and with positive helicity, the left-chiral component has squared weight $(1-\beta )/2$, where $\beta =|\mathbf{p}|/E$ in natural units. Its right-chiral weight is $(1+\beta )/2$; for negative helicity the two are exchanged. In an ultrarelativistic positive-helicity particle, the left-chiral amplitude is suppressed by a mass-to-energy ratio.