How is the property of chirality used? I was studying the book "Scattering and Structure" by Bogdan Povh;  it mentions that this property is used as a criterion to decide whether one is dealing with a massless or a massive particle.
I didn't understand this, can someone please elaborate on it?
 A: The mass term transitions a propagating particle into one of the opposite chirality, whereas in  the  absence of this mass term,  chirality is preserved.
Specifically, a mass term connects fermions of two chiralities. Consider
$$
i(\overline{\psi_L}\partial \!\! / ~\psi_L + \overline{\psi_R}\partial \!\! / ~\psi_R) +m (\overline{\psi_L}  \psi_R +\overline{\psi_R}  \psi_L).    
$$
The kinetic term has an L-chiral fermion preserve its chirality, L→L,  R→R, as it propagates, in the absence of the mass term. But the mass term
connects the two chiralities, L→R,   R→L, so chirality may switch as the fermion travels along.
Originally, neutrinos were thought to be massless, so R neutrinos were not thought to exist, and would be stricken off the above lagrangian retaining only the first of the 4 terms (only antineutrinos were R). But, nowadays, with the confirmation of neutrino masses through neutrino flavor oscillations, R neutrinos ("sterile" ones, as they do not couple to Ws) must exist, and the SM accommodates them just fine as inactive bystanders (gauge singlets).
A: I can't remember the reference, but I have read something along these lines which helps make the distinction:
Imagine a particle that always travels with its "handedness direction" pointing in its direction of travel. If it is massive, then it cannot travel at the speed of light and it is then possible for you to approach it "from behind" and note which way its handedness is pointing, and if you approached it "from in front" then its handedness vector would be pointing in the opposite direction. In this sense, its handedness is not a unique attribute, since the apparent handedness of the particle depends on your state of motion relative to it.
On the other hand, if the particle is massless then it will travel at c and it is then impossible for you to catch up to it from behind and observe its handedness "from behind", and then observe its handedness from "in front" and note a discrepancy. To me this means that if the particle is traveling at c, then its handedness will not be frame-dependent.
Having said all that, I do not know which term (helicity or chirality) refers to which case as described above! I ask the experts here to weigh in and set me straight about this. Does the distinction between chirality and helicity have anything to do with the frame-dependence of "handedness"?
