# Vectorlike fermion

by wphysics
Tags: fermion, vectorlike
 Sci Advisor HW Helper PF Gold P: 2,603 Vectorlike fermion The notion of vector-like originates in the property of the current that couples to the gauge field in question. With a Dirac fermion $\Psi$, the current $\bar{\Psi}\gamma^\mu\Psi$ is a vector, while $\bar{\Psi}\gamma^\mu\gamma^5\Psi$ is an axial vector. The left-chiral current of the weak interaction is $\bar{\Psi}\gamma^\mu(1-\gamma^5)\Psi$, hence the name of the "V-A theory."
 Sci Advisor HW Helper PF Gold P: 2,603 If by "they," you mean del Aguila et al, the vector-like couplings are listed in Table 1. A vector-like coupling to the Z does not include the $\gamma^5$ term. There's no connection between $c_A$ and $T^3$, as the former is identically zero for the new particles. They also allow for the possibility of weak isospin doublet, in which case the W couples to a charged vector current like $\bar{N}\gamma^\mu E$.