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How is the Theta angle of $SU(5)$ grand unified theory related to the three Theta angles in the $U(1) times SU(2) times SU(3)$ standard model?

Physics Asked by ann marie cœur on June 2, 2021

There are three Theta angles in the $U(1) times SU(2) times SU(3)$ standard model:

call them
$$U(1): theta’ F tilde{F}$$
$$SU(2):theta” F tilde{F}$$
$$SU(3):theta”’ F tilde{F}$$

But there is a single Theta angle of $SU(5)$ grand unified theory
$$SU(5):Theta F tilde{F}$$

Question

How is the single Theta angle of $SU(5)$ grand unified theory related to the three Theta angles in the $U(1) times SU(2) times SU(3)$ standard model? How can the three parameters $theta’,theta”,theta”’$ be related to a single $Theta$ of $SU(5)$?

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