vectorlike fermion

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.

haushofer

It would help if you give some references where they talk about this. Without context it is hard to answer your question.

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

http://deepblue.lib.umich.edu/bitstr.../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 :)

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.

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 [itex]\Psi[/itex], the current [itex]\bar{\Psi}\gamma^\mu\Psi[/itex] is a vector, while [itex]\bar{\Psi}\gamma^\mu\gamma^5\Psi[/itex] is an axial vector. The left-chiral current of the weak interaction is [itex]\bar{\Psi}\gamma^\mu(1-\gamma^5)\Psi[/itex], hence the name of the "V-A theory."

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,
c_Vγ^μ - c_Aγ^μγ⁵
where c_V = T³ - 2 sin²θ_W Q and c_A = 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.

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 [itex]\gamma^5[/itex] term. There's no connection between [itex]c_A[/itex] and [itex]T^3[/itex], 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 [itex]\bar{N}\gamma^\mu E[/itex].