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Published online 20 November 2008 | Nature | doi:10.1038/news.2008.1246
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Nuclear masses calculated from scratch
An exhaustive calculation of proton and neutron masses vindicates the Standard Model.
Atoms are much heavier than the fundamental particles from which they are made. European scientists have now shown that this oddity can be fully understood using the conventional Standard Model of particle physics.
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I must admit to being a little stunned by this article, since binding energy is a negative quantity and therefore reduces the masses of bound particles. For example, the Sun's energy comes from the release of binding energy as protons are fused into Helium-4 nuclei, which weigh less than the protons and neutrons of which it is composed would weigh as free particles. This is not to say that the article is wrong. I gather that the real issue is the quark-antiquark pairs which are constantly present in the hadrons and act to bind the whole together are themselves contributing positive mass to the assemblage. I am not sure how this should be described, but for me at least the term "binding energy" does not do that effect justice.
Edward Schaefer raises an interesting point. I've asked Christine Davies if she can shed light on this, as she was sure to have a clearer picture than I do. This is what she says: " 'Binding energy' is a somewhat tricky concept What you really mean is energy relative to particles separated from each other and free from interactions. Then it is normal to think of binding energy as being negative because the bound state has less energy than the free particles and this is why it is energetically favourable to make it. "Such a free state is not possible for quarks. It would require infinite energy to separate quarks so in a sense their free case has infinite energy. So really when you talk about 'binding energy' for quarks in a hadron you just mean the mass of the hadron - the mass of the quarks (and there ambiguities in how you define this mass because you can't 'weigh' free quarks). Then the binding energy in a nucleon is large and positive, i.e. accounts for most of its mass." I think that clarifies the situation nicely. The key, I guess, is the curious aspect of quarks that their interaction increases in strength as they get further apart.
As a complete outsider, I cannot see why the explanation above would clarify the situation. If, as is stated, 'it would require infinite energy to separate quarks so in a sense their free case has infinite energy', the quarks' energy would still be lower in the bound state than in the (impossible) free state, wouldn't it?
I am going to retain my objections, but between these comments, another aticle, and the Science article (reference 1 of this article), I now have a better understanding of the issues. First of all, in the Science article, Durr et al refer to the overall energy of the baryons as "contained energy" of which only 5% is the "quark mass". I must admit to being a bit uncertain as to what this quark "mass" is. I suspect that it is a bound rest mass, but in any case for each flavor it is a value derived from the masses of certain baryons. Added to those quark masses are the kinetic energy of the system, and also the energy of the "sea quarks" and anti-quarks that the system is emersed in. The kinetic energy of the quarks and also the mass-energy and kinetic energy of the continuously present (but virtual) sea quarks are legitimate positive contributors to the mass of the baryon. Even so, it also seems that the classical concept of "binding energy", being the amount of energy that a free quark loses as it joins the bound system, is rendered moot if infinite energy is truly needed to free a quark. Given that, the term "binding energy" should not be used at all. OTOH, if in principle a finite amound of energy could in principle separate a quark from the rest of a hadron (if a quark-antiguark pair creation did not instead split the hadron in two), then I still would call for binding energy to be a negative quantity, and the other types of energy in the system (kinetic, sea quark and gluon energies) to be appropriately assigned and treated as part of the contained energy of the overall system.
When theoretical physicists talk about the mass of a quark, they are referring to a parameter that appears in the Lagrangian with the dimensions of mass. In the standrd model this parameter occurs due to the interaction between the quark field and the higgs particle and its roughly 2-5 MeV. A proton is 3 quarks so youd expect something like 15 MeV (give or take) and instead you get 1 GeV. The point is that you shouldnt think of mass (when it comes to sub atomic particles) the same way you would talk about mass of say an orange.
Dr. Miller - Your comment is most appreciated and sheds some more light on this topic. Even so the end result of this calculation is something that contributes to the mass of an orange. The mass of a quark may be an abstract concept. The mass of a proton is not. Furthermore, how one describes the energy difference between what the Langrarian provides and the final baryon mass remains an issue for me. A silly suggestion: Call it the "glue energy".
I wonder whether "mass of a quark" can be interpreted as the theoretical mass a quark would have when extremely close to another quark, so that the work done against the strong force would be negligible. If that definition is correct, then separating the quarks (as they are separated in the proton) would require energy, and the whole system would have a larger mass than the sum of the quark masses; the difference might be called "binding energy" (even though I would call it "separating energy").
This is all predicated on the assumption that there are such things as gluons in the first place and that quarks have colour but there are still reasons for doubting this. The motivation for believing that quarks have colur started with the fact there are four Delta baryons - including a doubly-charged one made of three up quarks with parallel spins and a negatively charged one containing three sin-parallel down quarks. In order to explain how these two particles can have three identical particles without violating the Exclusion principle it was suggested that they must have another property - colour - in which they do differ. But flip one of the quark spins and you get spin 1/2 versions - a doubly charged proton and a negatively charged neutron which we have never seen.