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Beta decay of neutron gives a quark mass of Proton (uud) and e- much less than udd

  1. Dec 5, 2008 #1
    Here is a beta decay related question:
    Masses are from Particle Data Group (http://pdg.lbl.gov/2008/listings/contents_listings.html)

    Neutron has udd quarks. Mass is approximately 2.5, 5, 5 MeV. Total 12.5 MeV

    Products are:
    1. Proton. uud quarks. Mass approx 2.5, 2.5, 5 MeV
    2. Electron. mass about 0.5 Mev
    3. Neutrino, mass trivial.

    Neutron's quark mass of 12.5 MeV gives about 10.5 MeV.

    Or to look at it differently, down quark converts to up quark and electron. 5 MeV of the down quark gives 3 MeV (2.5 for u quark and .5 for e-)

    Why the difference?

    --------- Clarification of my question:

    My question or puzzle can be more specifically stated as "where is the missing mass?" In a beta decay, (where a down quark decays to an up quark, electron and neutrino) we have an approximate 5.0 MeV particle producing particles of mass 2.55 and 0.511. There is a loss of about 2 MeV, based on the accepted masses of the particles. Where did the lost energy go?
     
    Last edited: Dec 5, 2008
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  3. Dec 5, 2008 #2

    malawi_glenn

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    What is the question? What difference?
     
  4. Dec 5, 2008 #3
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Most of the mass of the neucleon doesn't come from the up and down quark content. A proton and a neutron both weigh about 940 MeV.
     
  5. Dec 5, 2008 #4

    clem

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    The n-p mass difference comes from different quark-quark interactions as well as just the d-u mass difference.
     
  6. Dec 5, 2008 #5
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Which different interactions ?
     
  7. Dec 5, 2008 #6

    clem

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    The n-p mass difference is affected by:
    1. The d-u mass difference.
    2. The Coulomb interaction between quarks.
    3. The magnetic moment-magnetic moment interaction between quarks.
    4. The different QCD spin-spin interaction between quarks.
    Each of these four effects are of the same order of magnitude.
     
  8. Dec 5, 2008 #7

    malawi_glenn

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    hehe I couldn't even understand the question!
     
  9. Dec 5, 2008 #8
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Thanks for the clarification.
     
  10. Dec 5, 2008 #9
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    My question or puzzle can be more specifically stated as "where is the missing mass?" In a beta decay, (where a down quark decays to an up quark, electron and neutrino) we have an approximate 5.0 MeV particle producing particles of mass 2.55 and 0.511. There is a loss of about 2 MeV, based on the accepted masses of the particles. Where did the lost energy go?
     
  11. Dec 5, 2008 #10
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Binding energy. These are QCD effects that are very difficult to calculate.
     
  12. Dec 5, 2008 #11
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    It seems to me, clem pointed out not only QCD must be taken into account. But I essentially agree if you mean that QCD makes it most difficult.
     
  13. Dec 5, 2008 #12

    malawi_glenn

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    The correct answer for you is kinetic energy of electron + neutrino.
     
  14. Dec 5, 2008 #13
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Yeah---those other things we can calculate. Do you (or clem) know the other contributions to the n-p mass difference? I'd venture a guess that they're pretty small, and it's the QCD contribution which dominates. (Don't ask me to put money on it!)
     
  15. Dec 6, 2008 #14
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    From the quark masses, the proton is already supposed to be lighter. But it is not that simple, because the lighter u and different charges make it a very difficult dynamical problem, and we know the charge and mass distributions are different. It's all model dependent actually, I don't think there is any agreement, I believe the electromagnetic contribution is not small, but I'm open to any good reference.
     
  16. Dec 6, 2008 #15

    clem

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    This is right for any decay. Beyond that the energy differences on the quark level come from the four sources I mentioned. No one of them dominates.
    Just adding and subtracting masses is too simplistic.
    I will look for a reference, but it will probably be a bit technical. I haven't seen this in a textbook.
     
  17. Dec 7, 2008 #16
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    I found the following calculation :
    Strong-Isospin Breaking in the Neutron-Proton Mass Difference
     
  18. Dec 9, 2008 #17
    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Yes, the kinetic energy. After I posted and thought more, I realized the value of 0.511 is for the RESTING mass of the electron. The electron is ejected and so the rest mass gives a low end value for the mass. We have to consider the kinetic energy of the electron and neutrino.
     
  19. Dec 9, 2008 #18

    clem

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    Re: beta decay of neutron gives a quark mass of Proton (uud) and e- much less than ud

    Phys. Rev. 25 (1982) 1997 is a phenomenological determination of the contributions of the d-u mass difference and the magnetic and QCD spin-spin energies on the n-p mass difference.
    Eq. (1) applied to the p and n gives those contributions. The Coulomb energy
    Q_iQ_j<1/r_ij> can then be determined as the difference between those three effects and the value n-p=1.29 MeV. They are all of the same order of magnitude.
     
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