Beta Decay Neutron: Proton, Electron Mass Difference

[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?

 

[malawi_glenn]

What is the question? What difference?

 

[BenTheMan]

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?

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.

 

[Meir Achuz]

The n-p mass difference comes from different quark-quark interactions as well as just the d-u mass difference.

 

[humanino]

The n-p mass difference comes from different quark-quark interactions as well as just the d-u mass difference.

Which different interactions ?

 

[Meir Achuz]

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.

 

[malawi_glenn]

hehe I couldn't even understand the question!

 

[humanino]

Each of these four effects are of the same order of magnitude.

Thanks for the clarification.

 

[liometopum]

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?

 

[BenTheMan]

Binding energy. These are QCD effects that are very difficult to calculate.

 

[humanino]

Binding energy. These are QCD effects that are very difficult to calculate.

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.

 

[malawi_glenn]

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?

The correct answer for you is kinetic energy of electron + neutrino.

 

[BenTheMan]

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.

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!)

 

[humanino]

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.

 

[Meir Achuz]

The correct answer for you is kinetic energy of electron + neutrino.

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.

 

[humanino]

I found the following calculation :
Strong-Isospin Breaking in the Neutron-Proton Mass Difference

We determine the strong-isospin violating component of the neutron-proton mass difference from fully-dynamical lattice QCD and partially-quenched QCD calculations of the nucleon mass, constrained by partially-quenched chiral perturbation theory at one-loop level. The lattice calculations were performed with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b ~ 0.125 fm, lattice spatial size of L~2.5 fm and pion masses ranging from m_pi~290 MeV to ~350 MeV. At the physical value of the pion mass, we predict M_n - M_p |(d-u) = 2.26 +- 0.57 +- 0.42 +- 0.10 MeV where the first error is statistical, the second error is due to the uncertainty in the ratio of light-quark masses, eta=m_u/m_d, determined by MILC, and the third error is an estimate of the systematic due to chiral extrapolation.

 

[liometopum]

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.

 

[Meir Achuz]

I'm open to any good reference.

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.