## The Standard Model More Deeply: Lessons on the Strong Nuclear Force from Quark Electric Charges

For readers who want to go a bit deeper into details (though I suggest you read last week’s posts for general readers first [post 1, post 2]):

Last week, using just addition and subtraction of fractions, we saw that the ratio of production rates

• R = Rate (e+ e ⟶ quark anti-quark) / Rate (e+ e ⟶ muon anti-muon)

(where e stands for “electron” and e+ for “positron”) can be used to verify the electric charges of the quarks of nature. [In this post I’ll usually drop the word “electric” from “electric charge”.] Specifically, the ratio R, at different energies, is both sensitive to and consistent with the Standard Model of particle physics, not only confirming the quarks’ charges but also the fact that they come in three “colors”. (About colors, you can read recent posts here, here and here.)

To keep the previous posts short, I didn’t give evidence that the data agrees only with the Standard Model; I’ll start today by doing that. But I did point out that the data doesn’t quite match the simple prediction. You can see that in the figure below, repeated from last time; it shows the data (black dots) lies close to the predictions (the solid lines) but generally lies a few percent above them. Why is this? The answer: we neglected a small but noticeable effect from the strong nuclear force. Not only does accounting for this effect fix the problem, it allows us to get a rough measure of the strength of the strong nuclear force. From these considerations we can learn several immensely important facts about nature, as we’ll see today and in the next post.

## Celebrating the Standard Model: How We Know Quarks Come in Three “Colors”

Within the Standard Model, the quarks (and anti-quarks) are my favorite particles, because they are so interesting and so diverse. Physicists often say, in their whimsical jargon, that quarks come in various “flavors” and “colors”.   But don’t take these words seriously! They’re just labels; neither has anything to do with taste or vision. We might just as well have said the quarks come in “gerflacks” and “sharjees”; or better, we might have said “types” and “versions”.

Today I’ll show you how one can easily see that each of the six flavors of quark comes in three colors (i.e., each gerflack/type of quark comes in three sharjees/versions.)  All we’ll need to do is examine a simple property of the W boson, one of the other particles in the Standard Model.

[Another way to say this is that the Standard Model is often described as having a kind of symmetry named “SU(3)xSU(2)xU(1)”; today we’ll put the “3” in SU(3). ]

### Gerflacks and Sharjees of Quarks

We know there are six types/gerflacks/flavors of quarks because each type of quark has its own unique mass and lifetime, a fact that’s relatively easy to confirm experimentally.  Quarks 1 and 2 are called down and up, quarks 3 and 4 are called strange and charm, and quarks 5 and 6 are called bottom and top; again, the whimsical names don’t have any meaning, and we often just label them d, u, s, c, b, t.

But to understand why each type of quark comes in three versions/sharjees/colors is more subtle, because two quarks of the same “flavor” which differ only by their “color” appear the same in experiments (despite our intuition for what the word “color” usually means.)

What, in fact, is a “color”? Each color/sharjee/version is a kind of strong nuclear charge, analogous to electric charge, which we encounter in daily life through static electricity and other phenomena. Electric charge determines which objects attract and repel each other via electrical forces. Electrons have electric charge, and so do quarks; that’s why electrical forces affect them. But quarks, unlike electrons, have strong nuclear charge too, and those charges determine how quarks attract or repel one another via the the strong nuclear force.

And here’s the interesting point: whereas there is only one version of electric charge (electrons and protons and atomic nuclei have different amounts of it, but it is different amounts of the same thing), there are three different versions/sharjees/colors of strong nuclear charge.  They are often called “red”, “green” and “blue”, or “redness”, “greeness” and “blueness”. (Remember, these are just names for sharjees — for versions of strong nuclear charge. In no sense do they represent actual colors that your eyes would see, any more than the six types/flavors of quarks would taste differently.)

## Celebrating the Standard Model: Atoms, Quarks and the Strong Nuclear Force

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.