# Pion and nucleon masses

1. Oct 10, 2005

### kryshen

I have one stupid question:

Is it true that the difference of proton and nucleon mass is due to the electromagnetic self-energy of the proton?

The same question about pi^0 and pi^- mass difference.

2. Oct 10, 2005

### Astronuc

Staff Emeritus
It's not a stupid question.

I believe you mean neutron when you mention "nucleon". Both protons and neutrons are nucleons - they are both found in the nucleus.

One has to look at the quark structure.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/meson.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/baryon.html#c1

3. Oct 10, 2005

### kryshen

To Astronuc,
Thank you for the references, you provided.
Indeed, I meant neutron when mentioned "nucleon". Still, I have a question. If the difference of nucleon masses is explained by the difference of quark structure, how the difference of u and d quark masses is explained?

4. Oct 10, 2005

### Astronuc

Staff Emeritus
Well, I am not sure since I have not really looked into the details. I would hope someone like marlon or others might be able to answer.

However, consider the following equations where u = up quark rest mass, and d = down quark mass.

P (uud) = 2u + d = 938.3 MeV rest energy (mass)

n (udd) = u + 2d = 939.6 MeV rest energy (mass)

but now consider

$\pi^+$ (ud) = 139.6 MeV energy (mass),

and one can look at other particles.

Presumably there are other particles, gluons, which interact with quarks to bind them.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/expar.html#c1

and perhaps these make the differences.

I am still troubled by the pion mass vs the nucleon mass.

5. Oct 10, 2005

### Norman

There are some tricky situations here.

Firstly, the mass of a composite particle is not just the mass of the quarks. The gluons contribute to the mass also.

In addition here is a great article that talks about breaking of charge symmetry which accounts for the difference between the masses of the up and down quarks. QCD should be invariant under the change of an up quark to a down quark, but it is not.

Here is the article:
http://physicsweb.org/articles/world/16/6/3

The issues of the pion masses are exactly the same as the issues of the different masses of the nucleons (atleast it should be...)
Cheers,
Ryan

6. Oct 10, 2005

### mathman

I claim no expertise on the subject, but I understand that nucleon (proton and neutron) masses mostly come from the energy of the gluons holding the quarks together. The bare quark masses are much too small.

7. Oct 10, 2005

### Norman

The mass difference between the up and down quark (and thus the mass difference between the nucleons) is related to the charge symmetry breaking of the up and down quarks.

http://physicsweb.org/article/world/16/6/3

8. Oct 11, 2005

### kryshen

Thank your very much for this reference. Now I get the picture:
if up and down quarks had equal masses, electrostatic repulsion between quarks should make the proton heavier, since it contains two up quarks with charges of +2/3. But the mass difference between the quarks wins over their electrostatic repulsion by a factor of about two, making it the dominant cause of charge-symmetry breaking.

9. Oct 12, 2005

### Astronuc

Staff Emeritus
But apparently according the article on Physicsweb, quark mass is still a mystery and challenge in QCD.

I am not sure if articles on gluon mass are any help either.

10. Oct 12, 2005

### Norman

The mystery of quark mass, in fact the mass of any particle is truly a profound question. Why the particles have the mass they do is one of the most fundamental questions in physics. It is going to take a lot of work in QCD or calculational techniques to get this under wraps soon. There seems to be some interesting experiments going on around it though so maybe someday we will be able to calculate these quantities. Who knows.

11. Oct 12, 2005

### Astronuc

Staff Emeritus
I think the same can be said for charge. No one can say really what charge is, except that we use to explain electro-static and electro-dymanic phenomenon.

We can certainly construct abstract models for mass and charge on the subatomic/subnuclear level though.