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I'm not sure what physical intuition you are after about the coupled components of Dirac spinors, which describe a particle and an antiparticle of both spin directions each. The Dirac Equation with yo …

From (6.38), for ultra relativistic fermions, $\kappa= \frac{p}{m+E}$ goes to 1, so positive helicity ones are almost pure right-chiral, and negative helicity ones are almost pure left-chiral. … For speed v ~1/50, you have $\kappa\approx 0.01$, so, by contrast, positive helicity fermions are almost equal parts right-chiral and left-chiral, and similarly for negative helicity. …

the fact that Helicity is invariant under parity. No such fact. … , so Helicity is odd under parity. Chirality is also odd under parity (L is sent to R). …

Left-chiral ones have negative helicity, and right-chiral ones positive helicity. The numerical magnitude of eigenvalues is irrelevant here: The article focusses on the sign of the helicity. … Note how a fermion reverses chirality, spin and helicity upon charge conjugation. …

Helicity and chirality are associated, but not identical. Left-chirality is associated with negative helicity (-1/2) and right chirality with positive 1/2 helicity, mostly. … Thus, by above, the muon must also have positive helicity, despite its left chirality, the disfavored one from above, enhanced by the muon mass. …

So, top helicity is out of the discussion when it comes to decays. … The Ws produced are thus polarized either with negative helicity, or longitudinal! No positive helicity, W helicity states of the top quark decays. …

You might profit from this old talk by Nichitiu. The "theoretical" ratio of coupling widths to the photon is, in fact, 9 to 1. The respective flavor wavefunctions of light vector mesons are, schematic …

Helicity and chirality coincide for massless particles, whose sense of motion cannot be reversed by a Lorentz transformation. … Hence the correlation your see in the picture: you may associate positive helicity massless particles with right-chirality, and negative-helicity massless particles with left-handed chirality. …

Note its right and left chiral components are different than those of the above positive helicity given, even though they have the same eigenvalues, (and mismatched with your text's (6.32).... … sometimes called "left", and positive helicity is misidentified as "right", to remind you of its connection to chirality seen here. …

All such helicity arguments pick a maximum along a spin axis, and rotations off it introduce diminution of the superposition component involved!) …

a "Left" helicity state. … This mismatch between helicity and chirality will ensure that if f is massless, when helicity coincides with chirality, the decay won't go: helicity wins. …

As the comments indicate, this mix of helicity components is frame-dependent. … Helicity can be positive or negative. Thus, I encourage you to use the term helicity here at your own risk. …

Then boost it to the opposite infinitesimal momentum so it has the opposite helicity. The helicity is then a step function of the momentum. … dictates the charged lepton have positive helicity. …

as "R", as helicity and chirality are identical. … A more apposite title would have been "Helicity with indefinite chirality"! …

Also in this limit, chirality and helicity are the same, and they are good quantum numbers, preserved in the process. … It is easy to use the rotation matrices in your helicity amplitudes, $d^1_{1~1}(\theta)$=$(1+\cos \theta)/2$, etc., to rotate from the initial to the final state, square, and get the cross-sections provided …