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Vectorlike fermion

by wphysics
Tags: fermion, vectorlike
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wphysics
#1
Dec6-12, 12:09 AM
P: 23
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.
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haushofer
#2
Dec6-12, 03:26 AM
Sci Advisor
P: 913
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
#3
Dec7-12, 02:47 AM
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P: 4,160
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
#4
Dec7-12, 04:51 AM
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PF Gold
P: 2,602
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 [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
#5
Dec7-12, 05:58 AM
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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.
fzero
#6
Dec7-12, 02:12 PM
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PF Gold
P: 2,602
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].


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