# Vectorlike fermion

1. Dec 6, 2012

### wphysics

In many papers about hep theory, I can find the concept, vectorlike fermion.

But, I cannot get the exact meaning of vectorlike fermion.

I would like you guys to explain vectorlike fermion.

Thank you.

2. Dec 6, 2012

### haushofer

If I do the googling for you, I come across this paper,

http://deepblue.lib.umich.edu/bitstream/2027.42/28619/1/0000431.pdf

where they seem to explain the term in the introduction very clearly. If you still don't grasp the idea, you should be a bit more specific :)

3. Dec 7, 2012

### Bill_K

The definition is clear enough. In the Standard Model, the left-handed fermions form isospin doublets, while the right-handed ones form isospin singlets. So the usual mass term, being a product of the two, requires the help of the Higgs field to be gauge invariant. But for these vectorlike fermions, the left- and right-handed components are supposed to transform the same way, making the mass term invariant independently of the Higgs.

The question I have is, why do they refer to them as vector-like.

4. Dec 7, 2012

### fzero

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."

5. Dec 7, 2012

### Bill_K

Ok, for a normal fermion, the interaction with the W is V-A. They make no mention of that. But the interaction with the Z, which they do discuss, is a different mixture,
cVγμ - cAγμγ5
where cV = T3 - 2 sin2θW Q and cA = T3.
For the vector-like fermion are they assuming it's an isosinglet?? (So that T3 = 0.) The intro only said the left- and right-handed components were supposed to transform the same way.

6. Dec 7, 2012

### fzero

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 $\bar{N}\gamma^\mu E$.