Why do we use "vector-like" to mean "non-chiral", in particle physics?

Question

I've been reading some stuff about searches for vector-like quarks and vector-like leptons, and I'm a little confused about the terminology.

Also, I'm a little new to this, so bear with me.

As far as I can tell, these particles' wave functions are superpositions of right- and left-helicity wavefunctions, where left- or right-helicity is whether the particle's spin is aligned or anti-aligned with its momentum.

And chirality is whether or not the left- and right-helicity components transform identically under gauge transformations or not.

As far as I can tell, vector-like means non-chiral (i.e. the two components do transform identically, which is not the same as for standard model particles which don't transform identically).

What I'm confused about is the use of the word "vector-like" for this... How is this like a vector?

Let me know if I've misunderstood something above too!

Also, basically the same question exists on stackexchange here (from 6 years ago), but the asker didn't provide any background to help their question get answered, so I figured it was worth asking again in more detail.

Answer 1

If the left and right components belong to the same representation of the gauge group, then the gauge field couples to the vector current, \begin{equation} j_\mu^{(V)}=\bar{\psi}\gamma^\mu\psi=\bar{\psi}_L\gamma^\mu\psi_L+\bar{\psi}_R\gamma^\mu\psi_R \end{equation} We can also introduce the axial current, \begin{equation} j_\mu^{(A)}=\bar{\psi}\gamma_5\gamma^\mu\psi=\bar{\psi}_R\gamma^\mu\psi_R-\bar{\psi}_L\gamma^\mu\psi_L \end{equation} For the known leptons and quarks the weak interaction couples to the $V-A$ current, \begin{equation} j_\mu^{(V)}-j_\mu^{(A)}=2\bar{\psi}_L\gamma^\mu\psi_L \end{equation} The name vector-like implies that for those particles the weak interaction couples to the vector current.