Relative Minus Sign for u d -> u d Process?

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relative minus sign??

Hi, I have one question for you...
to compute the matrix element for the process u d -> u d I want to use full SM, but I have one problem I'll give you the maths.


process with W:
<ud|(\bar{Ψ}u Ψd)(\bar{Ψ}dΨu)|ud>
process with γ:
<ud|(\bar{Ψ}u Ψu)(\bar{Ψ}dΨd)|ud>
Z and g are the same with γ (i don't write the propagators and the Lorentz parts for simplicity).
Is there a minus sign between W and the others??
I say yes ... but i am not sure.
 
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I just posted this for another post... I SAY YES also.
here's the information I found that explains why there is a minus sign.

rel min sign.jpg
 

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