# Gluon Contribution to Baryon Mass

1. Jul 30, 2010

### cbd1

I am confused as to how the mass equivalence of the the 3 gluons in at nucleon can give rise to an increase in the baryon's rest mass.

I can see how the mass equivalence of the energy contained in the gluons interaction can be added to the the amount of gravitational field generated by the particle, but not how it can add to it's inertial mass.

Last edited: Jul 30, 2010
2. Jul 30, 2010

### humanino

Why not ? It's sure is tiny, but can be calculated.

3. Jul 30, 2010

Staff Emeritus
It's not tiny. Most of the mass of a proton is in the glue field.

An electric field E has a mass ~VE2/c2, right? (Because E2 is an energy density) The same thing happens with the strong force.

4. Jul 30, 2010

### cbd1

But an electric field cannot be gravitationally attracted. And it also does not have inertia..

Like I was asking, where and how does the energy equivalence of the gluons become inertial mass? Sure, gluons have a mass equivalence, but they do not have mass like the quarks do. What gives them mass all of a sudden when they tie quarks together?

5. Jul 30, 2010

### humanino

Yes ! Of course, I meant "in the case of heat, it's tiny".

6. Jul 30, 2010

### humanino

Yes, it can. A photon is indeed trapped in a black hole (whence the name).

7. Jul 30, 2010

### cbd1

A photon is trapped in a black hole due to no paths leading out, not due to its having gravitational mass.

8. Jul 31, 2010

### humanino

Yes that is correct. It remains that a photon will be deviated by a BH. If I decide to put a BH nearby the path of a photon, the BH will deflect the photon. The metric field couples to the energy-momentum tensor, which the photon carries as well.

9. Jul 31, 2010

### cbd1

Photons have no inertial or gravitational mass. They are deviated by geodesics, or the "curvature" of spacetime, not pulled on by gravity. Besides, this is not my question.

Once again, what is it that makes the massless gluon add mass to baryons? They have not inertial mass, yet they (are theorized) to add most of the inertial mass to the baryons they help form. How?

Please, someone with an understanding of this specific question, reply.

10. Jul 31, 2010

### sheaf

explained the sources of mass in the proton. The main contribution is the energy due to the quark/gluon field binding the baryon together.

Last edited by a moderator: Apr 25, 2017
11. Jul 31, 2010

### tom.stoer

The only difference between photons and gluons is that photons do not interact (at least not in leading order), whereas gluons do strongly interact. That's the reason why gluons do contribute so much to the baryon masses.

Last edited: Jul 31, 2010
12. Jul 31, 2010

### Tomsk

Sorry if this is off topic, but what's the difference?

13. Jul 31, 2010

Staff Emeritus
Why do you say that?

Which has more mass, a charged or uncharged capacitor? And where is the energy stored?

14. Jul 31, 2010

### cbd1

Thanks Tom,
I see that gluons interact with the strong force as well as mediate it. But I am still at a loss of how the gluon interacting with the strong interaction field gives it mass all of a sudden. You would think there would have to be some kind of mechanism. I know physicists have calculated equations that say the quarks make mass somehow, but could you expand on how "interacting" gives the quarks mass, in words?

Last edited: Jul 31, 2010
15. Jul 31, 2010

### cbd1

I don't know. Are there experiments that have proven this? Does a charged battery weigh more on a scale than an uncharged battery?

16. Jul 31, 2010

You are confusing quarks and gluons.
Quarks are particles of matter. Three quarks make a nucleon. They do not mediate the strong force. Gluons are force carrying particles.
It is similar to electromagnetism. Electrons (matter particles) interact with other electrons by exchange of photons (force carriers). However gluon, unlike photon, can also interact directly with another gluon.

17. Jul 31, 2010

### cbd1

Sorry, I accidentally put 'quarks' where I meant 'gluons'. Fixed that in the post.

18. Jul 31, 2010

### Parlyne

It's not the fact of the interaction, per se, that creates mass. Let me see if I can clarify this. In relativity, when we speak of mass, we're usually talking about the invariant mass. This is what we would measure directly by putting an object on a scale, since it's rather hard to weigh anything that isn't sitting still. An object's invariant mass is given by the length of its 4-momentum vector:
$$m = \sqrt{p^\mu p_\mu} = \sqrt{E^2-|\vec{p}|^2},$$
where I'm implicitly using units in which c = 1.

For a single photon or gluon, this will be 0. However, for a system of multiple particles, we have to sum the 4-momenta before squaring. Thus, the mass of a composite system looks like
$$m = \sqrt{\left(\sum_i E_i\right)^2-\left|\sum_i \vec{p}_i\right|^2}.$$
Because of the vector sum of 3-momenta, a system of multiple massless particles can actually have a net non-zero rest mass.

This is where the interaction comes in. The nature of the strong force means that quarks and gluons only exist in bound states; and, the mass of the bound state must be determined as I showed above. If the bound state is at rest, the momentum sum will be 0; but, the energy sum will depend on the strength of the binding force, leading to a prediction for the mass of the bound state.

Does this clarify anything?

19. Jul 31, 2010

Staff Emeritus
It must, although by an immeasurably tiny amount. The Principle of Equivalence mandates this.

20. Jul 31, 2010

### cbd1

Yes. This helps me to see that when the components are counted individually, it seems that the gluons will have no mass, but when the quantum system of quarks and gluons are calculated together, we see that there is a much different result for mass.

In this case, it does seem that the equations help in understanding. So, in words, it is not so much that the gluons themselves gain mass when binding quarks, but that the system of quarks and gluons results in the total particle having mass.