A Difference between generations of quarks

[bilzebor]

TL;DR Summary

why is the isospin different then the other flavors

hello,
in the model of quarks, each of them is described by a flavor, but the quantum number for the first generation of quarks is the same (the isospin) for the up (1/2) and down (-1/2) quark.
For the other generation though it is a distinct number (s,charm,...) for each quark.

From what I understand, since the SU(2) symetry is only slightly broken for the up and down quark and for historical reason, people use the isospin for both, but they use different quantum numbers for the other quarks because then SU(3,4,...) is more broken.

Does than mean that technically we could use 2 different numbers for the up and down quark? or am I missing something?

thanks

 

[Vanadium 50]

technically we could use 2 different numbers for the up and down quark

I don't know what that means.

 

[bilzebor]

I don't know what that means.

I meant the quantum number that characterizes up and down quarks, so the isospin
I don't really understand why there is only one for the first generation, and two for the other generations

sorry if I'm not clear

 

[Vanadium 50]

Are you asking why weak isospin for quarks is a doublet? Or are you asking if eigenvalues of isospin should be different?

What is your background? You've tagged this as requesting a graduate-level answer.

 

[bilzebor]

yes I'm wondering why we use isospin doublet only for the first generation of quark

I thought it was because for the 2nd and 3rd generations the masses of the quarks are different, but up and down quarks also have different masses

(I'm a graduate student)

 

[Vanadium 50]

All three quark generations are weak isospin doublets. Regular ("strong") isospin is an approximate symmetry that arises because the u and d quarks have low masses with respect to the QCD scale.

 

[mfb]

We could have introduced upness and downness instead of using isospin. If we would have learned about all 6 quarks at the same time I assume that's what would have been done, but for historic reasons we got isospin. But, as V50 mentioned, the very similar (and small) mass of the first generation makes isospin special.

 

[Vanadium 50]

We could have introduced upness and downness instead of using isospin. If we would have learned about all 6 quarks at the same time I assume that's what would have been done

Maybe, but it would be hard to understand the difference between the π0 and η. Or why you have ρ→ππ but ω→πππ. I suspect someone would invent it. Probably Dave Jackson.