Pion and Nucleon Masses: The Role of Electromagnetic Self-Energy Explained

[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.

 

[Astronuc]

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.

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.

Please refer to these - http://hyperphysics.phy-astr.gsu.edu/hbase/particles/hadron.html

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

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/hadron.html#c6

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

 

[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?

 

[Astronuc]

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.

 

[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

 

[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.

 

[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.

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

 

[kryshen]

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

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.

 

[Astronuc]

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

Charge-symmetry breaking also manifests itself in the interactions of pions with protons and neutrons in a very interesting way that is linked to the neutron-proton (and hence, up and down quark) mass difference. Because the masses of the up and down quarks are almost zero, another approximate symmetry of QCD called "chiral" symmetry comes into play. This symmetry relates to the spin angular momentum of fundamental particles. Quarks can either be "right-handed" or "left-handed", depending on whether their spin is clockwise or anticlockwise with respect to the direction they are moving in. Both of these states are treated approximately the same by QCD.

The origin of the quark masses is not fully understood. In the Standard Model of particle physics, the Higgs mechanism allows the generation of such masses but it cannot predict the actual mass values. This is like having a recipe to make cookies that will work with either chocolate chips or nuts. Why are the masses of the up and down quarks almost the same, and why are the masses of the other four quarks so very different? No fundamental understanding of this mass hierarchy exists. But the TRIUMF and IUCF experiments mean that nature's violation of charge symmetry can now be used to tackle at least the up-down piece of this puzzle.

See also - http://hyperphysics.phy-astr.gsu.edu/hbase/particles/qmass.html

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

 

[Norman]

But apparently according the article on Physicsweb, quark mass is still a mystery and challenge in QCD.
See also - http://hyperphysics.phy-astr.gsu.edu/hbase/particles/qmass.html
I am not sure if articles on gluon mass are any help either.

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.

 

[Astronuc]

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.

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.