For the general reader:

Last week I showed you, without any technicalities, how to recognize the elementary forces of nature in the pattern of particle masses and lifetimes. This week we’ll start seeing what we can extract just from the particles’ masses alone… and what we cannot. Today we’ll focus on quarks and the strong nuclear force.

A key factor in nature, which plays an enormous role in everyday life, is the mass of a typical atom. [Note: on this website, “mass” always means “rest mass”, which does not increase with a particle’s speed.] This in turn arises mainly from the masses of protons and neutrons, which are about equal, and tiny: about 0.00000000000000000000000000167 kg (or 0.00000000000000000000000000368 pounds). Since those numbers are crazy-small, physicists use a different measure; we say the mass is about 1 GeV/c², and more precisely, 0.938 GeV/c². In any case, it’s tiny on human scales, but it’s some definite quantity, the same for every proton in nature. Where does this mass come from; what natural processes determine it?

You may have heard the simplistic remark that “a proton is made of three quarks” (two up quarks and a down quark), which would suggest these quarks have mass of about 1/3 of a proton, or about 0.313 GeV/c². But something’s clearly amiss. If you look at websites and other sources about particle physics, they all agree that up and down quark masses are less than 0.01 GeV/c²; these days they usually say the up quark has mass of 0.002 GeV/c² and the down quark has 0.005 GeV/c². So if the proton were simply made of three quarks, it would naively have a mass of less than 1% of its actual mass.

What’s going on? A first little clue is that different sources sometimes quote different numbers for the quark masses. There are six types of quarks; from smallest mass to largest, they are up, down, strange (u,d,s, the three light quarks), charm, bottom (c,b, the two somewhat heavy quarks) and top (t, the super-heavy quark.) [Their names, by the way, are historical accidents and don’t mean anything.] But some websites say the up quark mass is 0.003 instead of 0.002 GeV/c², a 50% discrepancy; the bottom quark’s mass is variously listed as 4.1 GeV/c², 4.5 GeV/c², and so forth. This is in contrast to, say, the electron’s mass; you’ll never see websites that disagree about that.

The origin of all these discrepancies is that quarks (and anti-quarks and gluons) are affected by the strong nuclear force, unlike electrons, Higgs bosons, and all the other known elementary particles. The strong forces that quarks undergo make everything about them less clear and certain. Among numerous manifestations, the most dramatic is that quarks (and anti-quarks and gluons) are never observed in isolation. Instead they’re always found in special combinations, called “hadrons“. A proton is an example, but there are many more. And the strong nuclear force can have a big effect on their masses.

The Modern Proton and the Masses of Quarks

A proton, in fact, is not simply made from three quarks, the way a hydrogen atom is simply made from a proton and an electron. As I described in this article, it’s vastly more complex; it’s made from three quarks plus lots of gluons plus lots of pairs of other quarks and anti-quarks. So the simple intuition we get from atoms does not apply to hadrons like the proton.