I Helicity and chirality

1. Jul 10, 2017

Silviu

Hello! I have some questions about helicity and chirality: So I understand how is helicity defined and that it has eigenvalues of 1 or -1. But can a particle (massless) have mixed helicity? Like the spin not to be along the direction of motion? (I assume it can but I want to make sure, because in all the articles I read they talk only about 1 and -1 values for it). I understand (I hope) the meaning of chirality but I am not really sure how does it affects the weak interaction. From what I understand, an electron is a superposition of left and right chirality electrons and when you measure the chirality, you pick one of them. So when an electron interacts with a W boson (let's say) does it pick a chirality and something happens only if the left chirality is chosen? Or if an electron gets out of a weak interaction, you are sure it is left handed? And in general, if you have an electron in lab, how can you find out it's chirality? Thank you!

2. Jul 11, 2017

vanhees71

Sure, if you have a proper superposition of the two helicity eigenvectors the helicity becomes undetermined,
$$|\psi \rangle=c_1 |h=1 \rangle + c_2 |h=-1 \rangle.$$
If we normalize it such that $|c_1|^2+|c_2|^2=1$ the probability to find a particle with helicity $1$ when measuring helicity, is $|c_1|^2$ and to find it with helicity $-1$ is $|c_2|^2$. If not either $c_1$ or $c_2$ are 0, the particle's helicity is indetermined.