Quantum Chromodynamics Binding Energy

[Drakkith]

Binding energy is typically used to talk about the amount of energy needed to separate bound particles. This means that it represents the energy lost when particles enter a bound state.

So, why does this article use the term "binding energy" to talk about the energy/mass content of a proton?

http://en.wikipedia.org/wiki/Proton#Quarks_and_the_mass_of_the_proton

While gluons are inherently massless, they possesses energy—to be more specific, quantum chromodynamics binding energy (QCBE)—and it is this that contributes so greatly to the overall mass of the proton (see mass in special relativity). A proton has a mass of approximately 938 MeV/c2, of which the rest mass of its three valence quarks contributes only about 11 MeV/c2; much of the remainder can be attributed to the gluons' QCBE.

 

[nikkkom]

Good question

 

[Orodruin]

Well, in the QCD setting, separating two color charges would require an infinite amount of energy due to confinement so this definition of binding energy would also be a weird one. I will agree that calling it binding energy may be a bit misleading when it is simply the energy contained in the stuff holding the hadrons together.

 

[RGevo]

I think it still makes sense.

As it refers to composite objects, and since the composite objects have measurable quantum numbers it is correct to call it a binding energy. For example, the valence content of hadrons is measureable.

What is not clear to me is how to model a hadron with point like particles, and what quark masses should be used. Lattice qcd does a good job I guess.

P.s. It doesn't take an infinite amount of energy to separate quarks. It takes a quantifiable energy per unit distance. It takes an infinite amount of energy to separate by an infinite distance. (See lattice qcd results for quark anti quark separation where this is modeled)

 

[Orodruin]

It takes an infinite amount of energy to separate by an infinite distance.

This is typically the definition of the zero-point of the potential energy of both gravity and electric potential.

 

[Drakkith]

I think it still makes sense.

As it refers to composite objects, and since the composite objects have measurable quantum numbers it is correct to call it a binding energy. For example, the valence content of hadrons is measureable.

I still don't see why it's called binding energy.

 

[mfb]

I still don't see why it's called binding energy.

It is a positive energy (visible as mass, and in deep inelastic scattering), and it is related to the QCD bond.

 

[Drakkith]

Can you elaborate on that, MFB?

 

[mfb]

Take a proton, for example: it has 3 valence quarks (two up, one down). Their combined masses (=rest-energy due to special relativity) are about 10 MeV. Without the strong interaction, a collection of those 3 valence quarks at rest would have a mass of 10 MeV.

As we know, a proton is significantly heavier, which also means it has more energy (at rest). This difference comes from the strong interaction. It is so strong that "naked quarks" don't exist in hadrons. You always have to consider the quark, gluons, virtual quarks and the kinetic energy of all those particles together, and this adds up to a much larger energy. That concept is known as constituent quark. If you add those three and compare it to the actual proton mass, you'll note that you get a negative binding energy again.

 

[Drakkith]

If you add those three and compare it to the actual proton mass, you'll note that you get a negative binding energy again.

I understand where the mass of the proton comes from, what I don't understand is why it's commonly said that the mass comes from the binding energy if the usual meaning of the term refers to a negative amount of energy. Am I missing something obvious?

 

[mfb]

Well, the mass comes from "the binding process [and everything else going on related to that]" in QCD.

 

[Vanadium 50]

The gluon field has an energy E^2 + B^2. That's where the mass comes from. It's called binding energy because it takes an infinite amount of energy to separate the constituents, and E^2 + B^2 is less than infinity.

 

[mfb]

What are E and B here?