Ignorantsmith12 said:
TL;DR Summary: I've heard three different explanations for how the strong force gives nucleons their mass.
1. The force is incredibly strong therefore much energy and E=MC^2
2. The glueon field has particles bumbling in and out of existence.
3. The glueon field is like a Higgs field.
Which, if any, of these explanations if any is true?
As for the Higgs field analogy, going into detail about the Higgs field might be for another thread. Suffice it to say that I have heard that the Higgs field is not like mud, and that is a lazy explanation.
Option 3 is the least true. Option 1 is closer to the truth than Option 2. None of them are perfect (and by the way, the carrier boson of the strong force is spelled "gluon").
The Higgs field imparts mass to quarks, charged leptons (i.e. electrons, muons, and tau leptons), weak force bosons (the W and Z bosons), and the Higgs boson. The mass of these fundamental particles influences the mass that is created by the strong force and its constituent fundamental particles, but this effect is only indirect.
Photons and gluons don't have any rest mass (at least in theory) and are never "at rest" but the energy of these particles can be substituted for mass when evaluating the mass of a particle using the E = mc
2 formula.
Neutrinos have tiny but non-zero mass, but we aren't really sure where it comes from and there are competing theories about that at this point.
PeterDonis said:
However, for a baryon or meson, it is impossible to separate it into its constituents;
I would also take issue with this statement.
A hadron is a system made up of quarks and gluons bound together by the strong force.
While you can't physically measure the mass of free quarks or use the same mass definition that you do for binding energy in an atom, that doesn't mean that there aren't sensible ways to separate out the mass of the constituent parts of a hadron analytically.
You have to be clear about the definition of quark mass that you are using, because there are several different competing definitions of it, each of which has subtle pros and cons.
But, the most widely used definitions do assign well-defined masses to each kind of quark with a value that is the same at any given energy scale, no matter what hadron the quark is a part of (indeed, these are experimentally measured physical constants of the Standard Model and match up also to the strength of that particle's coupling to the Higgs field called a Yukawa, which can be independently determined from Higgs boson decay frequencies). The mass of the top quark can also be measured much more directly, because it decays via the weak force before it can be bound into a hadron and has a mass of about 173 GeV plus or minus. The very reasonable definitions of the quark masses are discussed, for example, by the Particle Data Group in
this review article.
For example, one can look at hadrons that are identical except one valence quark, and then use the difference between the masses of the two hadrons to provide insight into the differences in the masses of the quark that is different. It's more complicated than that, but that's the gist of the idea.
The total "invariant" mass of a hadron with particular quantum numbers and particular valence quarks is a well-defined number, that isn't really a function of the virtual particles in the "particle sea" of that hadron at any particular time.
But, experimentally, for any given hadron, what you really end up with as the output of your measurements of the hadron's mass is really a curve over a range of masses derived from many individual data points, with a peak and gradual fall offs higher and lower, which is called a "resonance", and not just a single data point. A generic example of what the output of your experiment measuring the mass of a resonance looks something like this:
You really need both the mass of the peak of that resonance M(Z) which is the "invariant" mass and what you are most likely to measure experimentally, and the width of the resonance, Γ(Z) which indicates the extent to which a measurement is off that peak (and is also related to the mean lifetime of the particle), to understand a particle's mass (in this case, a Z boson) fully.
The way that you interpret the mass of the particular components, and the definitions of the quark masses that you use, is to some extent a function of why you need to know those values.
But, for most purposes, it is most useful to think of the mass of a hadron as made up of the mass of the valence quarks of the hadron (defined according to one of the typical definitions of that, such as the MS Bar definition, and once scientists measuring quark masses work them out, determinable from a reference source like the Particle Data Group) and then to use that one definition that you choose to use consistently. Then, the balance of the mass of the hadron is generally attributed to its strong force field made up of gluons being exchanged by quarks.
This is what someone is doing when they say, for example, that about 1% of the mass of the proton is made up of its valence quarks (two up quarks and one down quark, with a combined mass in the most common definition of light quark masses of about 9-10 MeV, with significant relative measurement uncertainties) and the balance attributed to the strong force field of the proton.
When you use this approach, all hadrons are more massive than the sum of their valence quark masses. But, proportionately, hadrons with lighter valence quarks tend to have a small proportion of their total mass attributed to their valence quarks, while hadrons with heavier valence quarks tend to have a larger proportion of their total mass attributed to their valence quarks.
This makes sense because the strong force couples to a quark's strong force color charge, and every quark has a strong force color charge of the same magnitude.
But, the relationship between total hadron mass and its component sources is also not as simple as the sum of the valence quark masses plus a strong force field mass equal to the number of quarks in the hadron adjusted for their spin. There is some feedback between the two quantities, which can be calculated using approximations of the Standard Model theory of the strong force known as QCD. Predominantly, this is done using an approach known as Lattice QCD.
