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Vectorlike fermion 
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#1
Dec612, 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. 


#2
Dec612, 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 :) 


#3
Dec712, 02:47 AM

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P: 4,160

The definition is clear enough. In the Standard Model, the lefthanded fermions form isospin doublets, while the righthanded 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 righthanded 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 vectorlike. 


#4
Dec712, 04:51 AM

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PF Gold
P: 2,602

Vectorlike fermion
The notion of vectorlike 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 leftchiral current of the weak interaction is [itex]\bar{\Psi}\gamma^\mu(1\gamma^5)\Psi[/itex], hence the name of the "VA theory."



#5
Dec712, 05:58 AM

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P: 4,160

Ok, for a normal fermion, the interaction with the W is VA. They make no mention of that. But the interaction with the Z, which they do discuss, is a different mixture,
c_{V}γ^{μ}  c_{A}γ^{μ}γ^{5} where c_{V} = T^{3}  2 sin^{2}θ_{W} Q and c_{A} = T^{3}. For the vectorlike fermion are they assuming it's an isosinglet?? (So that T^{3} = 0.) The intro only said the left and righthanded components were supposed to transform the same way. 


#6
Dec712, 02:12 PM

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PF Gold
P: 2,602

If by "they," you mean del Aguila et al, the vectorlike couplings are listed in Table 1. A vectorlike 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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