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Please clarify

  1. Feb 6, 2008 #1
    I am asking this question because I did not get it clarified in any of the books I have read.
    What is the rule for having the quark structure of an antiparticle given the structure of the particle?Is it always OK to put bar on the quark symbols of the corresponding particle?

    Specifically,I know proton is represented as [tex]\ u \ u \ d [/tex] and antiproton as
    [tex]\bar{u}\bar{u}\bar{d}[/tex]

    Is it true that since neutron is [tex]\ u \ d \ d [/tex], we must have anti neutron:
    [tex]\bar{u}\bar{d}\bar{d}[/tex]?

    Another thing: Is there any rule for the order of letters while writing the symbol for a particle?In other words, uud or udu or duu---do they mean the same?
     
    Last edited: Feb 6, 2008
  2. jcsd
  3. Feb 6, 2008 #2

    malawi_glenn

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    In a hadron, all quarks in the anti hadron shall be anti, just as you did with the neutron.

    Another example, the anti-particle to the [tex] \pi ^+ [/tex], Quark content: [tex] u \bar{d} [/tex], Is [tex] \pi ^+ [/tex], Quark content: [tex] d\bar{u} [/tex]. Since [tex] \bar{\bar{u}} = u [/tex] etc.

    The "rule" is to start with all quarks in the same generation, e.g (u and d) then (c and s) then (b and t). Then in the same gruop you start with the positive charged quark. Then you have the anti-quarks in the end.

    For example, the D meson: [tex] D^+ = c\bar{d} [/tex]

    But I think different conventions exists, the important things are the total quark content, Mass, Spin etc. Those are the quantities that determines the physics.
     
    Last edited: Feb 6, 2008
  4. Feb 6, 2008 #3
    I see.Thanks.
     
  5. Feb 6, 2008 #4

    clem

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    The order has to be correlated with the other degrees of freedom.
    For instance, in the proton, the two u quarks must be in the symmetric spin one state.
    If you change uud to udu, then the spin wave function has to be similarly permuted.
     
  6. Feb 6, 2008 #5

    malawi_glenn

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    That does not make sense. It is a difference of writing the representation of the hadron by its quark content as uud , and by writing its state as: |p> = 1/sqrt(18){2|uud> + 2|udu> + ... etc.
     
  7. Feb 11, 2008 #6

    clem

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    The quark order must be consistent with the spin order. For instance, for the proton
    (using a for spin up and b for spin down), a suitable wave function is
    |p>=uud(2aab-aba-baa)/\sqrt{6}.
    If the quark order is changed to udu, then the last two spins must also be interchanged to give |p>=udu(2aba-aab-baa)/\sqrt{6}.
     
  8. Feb 11, 2008 #7

    malawi_glenn

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    but as I said, you are talking about the wave function. The OP asked about the "REPRESENTATION". In the representation, you dont write the whole wave function, you write the quark content, spin, mass etc.

    And if you want the whole wave function, |p>=uud(2aab-aba-baa)/\sqrt{6} is not good enough, it has 9 terms
     
  9. Feb 13, 2008 #8

    clem

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    Only Neelakash knows what he asked.
    I don't know what Malawi means by "representation"
    If you just mean the number of each type of quark, the order doesn't matter.
    If you mean something more, then the quark order must be correlated with the spin order in each term.
    You could write the wave function I gave three permuted times, but then would you do every calculation three times? What I wrote is all you need.
     
  10. Feb 13, 2008 #9

    malawi_glenn

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    Neelakash meant : "Specifically,I know proton is represented as [tex]\ u \ u \ d [/tex]
    and antiproton as
    [tex]\bar{u}\bar{u}\bar{d}[/tex]"

    So what both him and me means with representation is that when looking in particle tables etc, you often only finds the quark content. So what he aksed is "uud and udu" the same particle? And my answer indicated that there are more things than just the quark content that matters, spin etc also plays role. For example the delta+ baryon has the same quark representation (uud) as p, but has a different wave function. So neither him or me was originally talking about wave function, we only disscussed the representation. And the representation follows the convention that I posted..
     
  11. Feb 13, 2008 #10
    My suggestion is to read on Fonda-Ghirardi what is the tensor-Representations for SU(3).
    After manypulating this object you'll get your answer.

    regards
    Marco.

    Opps I'm sorry i meant Huang Kerson's Book, if i remeber righ... chapter 2 and the book was: Quark and leptons..
     
    Last edited: Feb 13, 2008
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