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How to determine quantum numbers for beta functions?

  1. Jun 18, 2013 #1
    I'm trying to understand the notation (3, 1, 2/3) for the up quark and (3, 2, 1/6) for the left-handed up and down quarks.... Is the first number related to SU(3), the second SU(2) and the third I believe is the hyper charge... Not sure what the significance is of the first two numbers...

    I think the 1 in (3, 1, 2/3) means the up quark doesn't interact with the weak force. But what would the 3 mean? A triplet in SU(3)? If so, how would I find it?

    Possible equations:

    Q = I3 + Y
    Q = I3 - Y
    Q = T3 + Y
     
  2. jcsd
  3. Jun 18, 2013 #2

    Bill_K

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    Science Advisor

    The 3 means the quarks are members of a color triplet. Otherwise they are characterized by weak isospin T and weak hypercharge Y. The relationship connecting T and Y to Q is Q = T3 + Y/2.

    Left-handed fermions are weak isodoublets. Right-handed ones are weak isosinglets. This means they don't interact with the W boson, but they still do interact with the Z. Quark values:

    uL: T = 1/2, T3 = +1/2, Y = 1/3, Q = 2/3
    dL: T = 1/2, T3 = -1/2, Y = 1/3, Q = -1/3
    uR: T = 0, T3 = 0, Y = 4/3, Q = 2/3
    dR: T = 0. T3 = 0, Y = -2/3, Q = -1/3
     
  4. Jun 18, 2013 #3
    OK, that makes sense. Thank you, Bill K!

    ...Do right-handed quarks couple to the W or Z bosons? My guess is no, which might be why there is not a right-handed quark doublet? Is this because their weak isospin is 0?
     
  5. Jun 18, 2013 #4
    Can anyone tell me what this process is called, so maybe I can read a bit more about it? Any suggestions would be great
     
  6. Jun 18, 2013 #5

    Avodyne

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    Science Advisor

    Some authors (e.g., Srednicki) normalize hypercharge so that Q = T3 + Y. In the OP's notation of (3,1,2/3) for the right-handed up quark, this is the normalization that is used.

    For the basics of how the various fields interact, see "After electroweak symmetry breaking" in
    http://en.wikipedia.org/wiki/Electroweak_interaction

    For more details, see any good book on particle physics or QFT of the Standard Model.
     
  7. Jun 18, 2013 #6
    Thank you, Avodyne... Helpful!!! Thanks for pointing out it's normalized... I don't think I could have figured that out on my own :)
     
    Last edited: Jun 18, 2013
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