Why are SU(3), SU(2) and U(1) groups used in the Standard Model?

[wasi-uz-zaman]

TL;DR

under symmetry SU and U groups are used to confirm invariance of certain quantities.

hi,
i have studied Standard Model for particle physics - at present it is described by three groups -

i have studied - these groups but could not establish what particular feature suggest of these group to be used to describe SM.
Thanks

 

[Vanadium 50]

These describe the equations of the SM. This question is isomorphic to "why are the laws of nature what they are and not something else". Nobody knows. Further, any answer will lead to the same question: if I told you they were subgroups of SU(5) wouldn't that just beg the question "why SU(5)?"

 

[Orodruin]

Because the predictions that come out match observations.

 

[samalkhaiat]

Summary:: under symmetry SU and U groups are used to confirm invariance of certain quantities.

hi,
i have studied Standard Model for particle physics - at present it is described by three groups - View attachment 300525
i have studied - these groups but could not establish what particular feature suggest of these group to be used to describe SM.
Thanks

For historical and mathematical motivations, see my posts in
https://www.physicsforums.com/threads/why-su-2-times-u-1-for-the-sm.846099/