# Nucleon masses

1. Oct 6, 2008

### jimmy.neutron

Hey guys this is my first post on Physics Forums, be gentle.

I've been wondering, what's the current explanation of why protons and neutrons have such very similar masses? Is this due to a difference in the up and down quark masses or is there something else going on here?

Thanks

Last edited: Oct 6, 2008
2. Oct 6, 2008

### hamster143

Proton consists of three quarks - two "up" and one "down". Neutron consists of one "up" and two "down" quarks. Much of the mass of either particle comes from the energy contained within gluons that bind them together. Gluons interact with "up" quarks and "down" quarks in exactly the same way. There are only two differences. Firstly, the "down" quark is slightly heavier than the "up" quark. We don't know exactly by how much, but it's around 2 MeV. Secondly, they have slightly different electromagnetic binding energies. I

3. Oct 6, 2008

### clem

In addition to the d-u mass difference, and EM perturbations, there is a QCD difference due to different energies for different q-q spin states.
All three effects are of the same order of magnitude ~ a few MeV.

4. Oct 7, 2008

5. Oct 8, 2008

### clem

I can't recommend any simple discussion of this, but can warn you that most textbooks oversimplify this calculation.

6. Oct 8, 2008

### jimmy.neutron

dem, could you tell me a little more about the 'QCD difference' please? Is it analogous to http://en.wikipedia.org/wiki/Hund%27s_rule" [Broken]?

I've just read an older thread which suggests that the difference in up and down quark masses is accounted for be some form of symmetry breaking in QCD.

Last edited by a moderator: May 3, 2017
7. Oct 9, 2008

### clem

Most of the posts in that thread are confused. I didn't look at the links they posted.
The QCD difference is not analogous to Hund's rules.
The QCD difference is like the magnetic mass shift in a baryon.
There are four components to the n-p mass difference.
1. A mass difference in the d and u quarks.
2. The Coulombic energies <q_1q_2/r> of quark pairs.
3. The magnetic interaction ~$$<{\vec\hat\mu}_1\cdot {\vec\hat\mu}_2\delta({\vec r})/m_1m_2>$$ of quark pairs. This is like the hyperfine interaction in atoms.
4. There is a QCD analogue of the magnetic interaction. They each come from the relativistic interaction of quarks.
The QCD hyperfine interaction is ~$$\alpha_s<{\vec\hat\sigma}_1\cdot{\vec\hat\sigma}_2\delta({\vec r})/m_1m_2>$$,
where $$\alpha_s$$ is the strong coupling constant. This interaction was first suggested by Sakharov.
If this is too complicated, I'm sorry, but it's the simplest I can make it.

Last edited: Oct 9, 2008
8. Oct 9, 2008

### humanino

What are $\vec\hat\mu$ and $\vec\hat\sigma$ in your equations ? It's not that the topic is too complicated, but your post is not clear. The article lined in the other thread was written by Gerald A Miller, who is a very clear person in his explanations.

http://physicsworld.com/cws/article/print/17566

Last edited by a moderator: Apr 23, 2017
9. Oct 9, 2008

### hamster143

$$\mu$$ is magnetic moment and $$\sigma$$ is spin.

10. Oct 9, 2008

### humanino

So you remove the vector and operator parts, and we are supposed to see a link with fundamental quarks ? All models are "QCD inspired" but I think consider this very remote because of the level of details provided. Are $\sigma$s just the Pauli matrix ?

11. Oct 10, 2008

### clem

I am sorry if I offended anyone by using the standard notations for magnetic moment and the Pauli spin matrix vector. I thought that these were well known to participants in the HE, NP, PP forum. I overestimated some. If you think that Gerry Miller's long published article is clearer than my brief list hoping to help Jimmy Neutron in a forum format, then stick with that. Prof. Miller's clarity was helped by his omission of the magnetic and QCD spin-spin interactions (#3 and #4). This is what I meant by "some texts oversimplify this calculation".