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

1. Dec 5, 2008

### liometopum

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
2. Dec 5, 2008

### malawi_glenn

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

What is the question? What difference?

3. Dec 5, 2008

### BenTheMan

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.

4. Dec 5, 2008

### clem

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.

5. Dec 5, 2008

### humanino

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

Which different interactions ?

6. Dec 5, 2008

### clem

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.

7. Dec 5, 2008

### malawi_glenn

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!

8. Dec 5, 2008

### humanino

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

Thanks for the clarification.

9. Dec 5, 2008

### liometopum

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?

10. Dec 5, 2008

### BenTheMan

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.

11. Dec 5, 2008

### humanino

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.

12. Dec 5, 2008

### malawi_glenn

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.

13. Dec 5, 2008

### BenTheMan

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!)

14. Dec 6, 2008

### humanino

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.

15. Dec 6, 2008

### clem

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.

16. Dec 7, 2008

### humanino

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

17. Dec 9, 2008

### liometopum

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.

18. Dec 9, 2008

### clem

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.