Amplitude for $q\bar{q} \to Z$

Asked Jun 20 '23 at 17:50

Active Jun 20 '23 at 17:50

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In ELectroweak theory, the amplitude for the incoming quark and anti quark to $Z$ boson production in the following diagram is given zero. The outgoing particle $Z$ is given here as blue boson.

I am confused what is the reason behind it. One reason maybe the $Tr(T^a)$ which is connected with the external particle may give zero, but here the color factor seems to be $T^aT^b\delta^{ab}$, so this is not possible.

asked Jun 20 '23 at 17:50

Tanmoy Pati

1

Look at the triangle loop: a color octet and two colorless Z's go into it! – Cosmas Zachos Jun 20 '23 at 18:33
can you elaborate a bit? – Tanmoy Pati Jun 20 '23 at 18:44
2

Write down the amplitude: you will see that a colored object enters the triangle and doesn't leave. So its trace vanishes. – Cosmas Zachos Jun 20 '23 at 19:03

Amplitude for $q\bar{q} \to Z$

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