# How interact makes mass ?

1. Feb 3, 2013

### big_bounce

Hello all .

We know about 95 percent to 98 percent of proton mass is not contributed by quark mass. In truth, most proton mass is derived from interaction energy between the quarks .

MY question is how interact makes mass ?
the mass means inertial mass or relative mass ?

Last edited: Feb 3, 2013
2. Feb 3, 2013

### tom.stoer

It's standard rest mass; w/o using a particle collider or something like that you can't see that the mass is caused by interaction.

In quantum field theory you can in principle do the following: find an eigenstate |E,p=0> of the Hamiltonian H and the momentum operator P such that
H|E,p> = E|E,p>
P|E,p> = 0

b/c p=0, whenever E>0 this is due to interaction (kin. energy is zero)

3. Feb 3, 2013

### geoduck

Can E<0?

Also I thought bound state energies are always negative, so if anything, shouldn't the proton mass be less than the sum of the quark masses?

4. Feb 4, 2013

### tom.stoer

E<0 is not reasonable for a particle mass, but E=0 is.

The idea of bound states which are lighter as their constituents makes some implicit assumptions which are no longer valid in QCD
- it means that one can identify a fixed, finite number of constituents (quarks, gluons)
- it means that one can add rest masses to get the mass of the bound state (- mass defect i.e. binding energy)
- it often starts with a potential and its energy levels

In QCD
- the number of constituents is not fixed; it has to be derived from the theory; and it turns out that it becomes scale dependent
- the kinetic energy of quarks and gluons dominates the total mass; so the quarks and gluons are highly relativistic

So having relativistic quarks and gluons it becomes clear the the proton rest mass is due to the energy of it's 'constituents'

Last edited: Feb 4, 2013
5. Feb 4, 2013

### Bill_K

Not in this case. The QCD potential rises indefinitely at infinity, and approximates a harmonic oscillator potential (positive).

6. Feb 4, 2013

### geoduck

There has to be a potential or else wouldn't the high kinetic energy of the quarks and gluons fly apart? You can estimate it with Δp ~ 1/Δx where Δx is the nuclear size?

Also, if the number of constituents is not fixed and depends on scale, but the mass of a proton is always the same, does this mean that the constituents always conspire to change their masses at each scale so that their total mass equals the proton mass?

Also, can you find the mass of a bound state via the propagator? Take the photon propagator. Technically, shouldn't there be an isolated pole at the bound state of an electron and positron? I don't ever recall seeing this though in the photon propagator.

7. Feb 4, 2013

### geoduck

O okay. The harmonic oscillator potential has positive energy. Actually, I don't ever recall a quantum system that has negative energy. Classically two particles attracted to each other can be very close and have negative energy.

So the QCD potential is a harmonic oscillator at large distances. But at short distances, isn't it free (asymptotic freedom)? Is there a transition zone?

8. Feb 4, 2013

### Bill_K

"Not fixed" does not mean "changing in time." The proton wavefunction is an eigenfunction of H. It means "not sharply determined." The proton wavefunction is a superposition of parts which contain different number of partons.

9. Feb 4, 2013

### D H

Staff Emeritus
Chemical compounds such as a molecule of water, atomic nuclei such as 56Fe. A molecule of water has slightly less mass than the masses of its constituent parts (two atoms of hydrogen and an atom of oxygen), and a 56Fe nucleus weighs slightly less than the sum of the masses of 30 neutrons and 26 protons. Note the stark contrast to the situation where the mass of a proton vastly exceeds the sums of the masses of two up quarks and one down quark.

10. Feb 4, 2013

### Khashishi

There's no way to free a quark from a bound state, so the definition of a quark's mass comes from the idea of asymptotic freedom, which is to say that the strong force goes away at short distances. This is totally opposite of the electric force, which goes away at long distances.
If you could somehow get a lone quark, it's mass would be something like infinite, so the proton does indeed have less mass.

11. Feb 4, 2013

### tom.stoer

Please be careful; there is no potential U(x) in QCD!

The linear potential is a derived quantity, a result, and expectation value, not an input like in Standard QM.

In QCD the interaction is due to a Coulomb gauge Hamiltonian (plus other terms); for a reference you may have a look at slide 4ff of http://www.ectstar.eu/meetings/ConfsWksAndCollMeetings/ConfWksDocument/2011/Talks/Binosi/Reinhardt.pdf [Broken]

Last edited by a moderator: May 6, 2017
12. Feb 5, 2013

### Bill_K

No one said the QCD potential was an input.

13. Feb 6, 2013

### tom.stoer

And no one said it isn't; we should be clear about that