Celebrating the Standard Model: The Twins We're Made Of (2024)

At the core of every atom lies its nucleus, where protons and neutrons are found. As their names suggest, these two subatomic particles are profoundly different.

• Protons carry positive electric charge, and can attract negatively-charged electrons, making atoms possible.
• Neutrons have no electric charge and are thus electrically neutral, hence their name; they have no impact on the electrons in atoms.

The distinctions extend to their magnetic effects. Both protons and neutrons have a “magnetic moment,” meaning that in a magnetic field, they will point like compasses. But neutrons point in the opposite direction from protons, and less agressively.

Nevertheless, the proton and neutron have almost identical masses, differing by less than two tenths of a percent! If we ignored their electric and magnetic effects, they’d almost be twins. Why are they so different in some ways and so similar in others? What does it reflect about nature?

To resolve this puzzle required three stages of enlightenment…

Step 1: The Nuclear Force is Strong in These Ones

Atomic nuclei were a puzzle for several decades. The proton was discovered, and identified as the nucleus of hydrogen, before 1920. But other nuclei had larger electric charge and mass; for instance, the helium nucleus has double the charge and about four times the mass of a proton. Only in 1932 was the neutron discovered, after which point it soon became clear that nuclei are made of protons and neutrons combined together. Physicists then realized that to prevent the protons’ mutual electric repulsion from blowing a nucleus apart, there must exist an additional attractive force between the protons and neutrons, now known to be an effect of the “strong nuclear force”, that pulls harder and holds the nucleus together.

Almost immediately following the discovery of the neutron, and noting its similar mass to that of the proton, Heisenberg proposed that perhaps they were the same particle in two different manifestations, despite their different electric charges. Soon it was learned that small atomic nuclei that differ only in the replacing of one proton with one neutron often have remarkably similar masses. For example,

Thus, not only are protons and neutrons in isolation almost interchangable (excepting electromagnetism), they remain so when bound together by the strong nuclear force. This is a clue that the strong nuclear force treats them identically, or nearly so. Meanwhile, although their different electromagnetic properties seem of great importance to us at first, they are actually little more than a shiny but irrelevant detail, akin to two different paint colors on cars of exactly the same make.

It turns out the proton and neutron are not quite the same object. But their similarities can still be attributed to similarities in their contents.

Step 2: Bags of Three

Based on the properties of many other particles discovered in the 1940s and 1950s, both Murray Gell-Mann and George Zweig (see also work by A. Petermann) proposed an idea that I’ll refer to as “kuarqs”, in which

• the proton involves two up kuarqs and one down kuarq;
• the neutron involves two down kuarqs and one up kuarq;
• the reason that the proton and neutron are twins is that the up kuarq and down kuarq are twins, differing only in their electric and magnetic effects.

You should note, in addition to my odd spelling, that I did not say “the proton is made of two up kuarqs and one down kuarq”. That’s for a very good reason.

Some physicists, including Zweig, considered that these kuarqs might truly be particles inside a proton. In this view, much as a helium nucleus is a bag made of two protons and two neutrons, each carrying about a quarter of the nucleus’s mass, a proton would be a bag made of three kuarqs, each kuarq carrying a third of the proton’s mass. The neutron would be the same except with one up kuarq replaced with one down kuarq.

These physicists were able to make quite a lot of successful predictions using this viewpoint, in which:

But Gell-Mann (and to some extent Zweig also) emphasized that it would be a mistake to literally view the proton as a simple bag of three objects. The strong nuclear force is too strong for this; such a simplistic view would make the picture inconsistent. Most importantly, other types of related particles, especially pions, would be impossible to explain in a simple way using this method; so how could one expect protons and neutrons to be so simple?

Gell-Mann therefore argued that his kuarqs were mainly a mathematical trick, an organizing device, and were unlikely to actually exist as actual particles. Even if they did exist, he reasoned, they should have very large masses, with the proton mass reduced by the strong nuclear force (due to binding energy, which makes an atom’s mass slightly less than the combined mass of its electrons, protons and neutrons, and similarly reduces the mass of a nucleus below that of its protons and neutrons.)

Step 3: Bags of Plenty

The full story only began to become clear ten years later, in the early 1970s. It turned out that Gell-Mann was right: his kuarqs do not exist. And yet they reflect something that does: a subset of the elementary particles that we call “quarks”.

There are indeed up and down quarks, just as there are up and down kuarqs. But in contrast to kuarqs,

• quarks are real particles, not mere mathematical tools;
• the up and down quarks are not twins;
• protons and neutrons are not made from three quarks.

Now perhaps you can understand why I used different spelling for the two things that are pronounced “cworks”. Physicists call Gell-Mann’s kuarqs by the name “constituent quarks”, and elementary quarks by the name “current quarks.” The terms are confusing and very hard to remember; even as a professional, I have to think for a moment to make sure I don’t say one when meaning the other… So I find the different spellings (in a written article) much clearer. [NOTE: I am the only one who does this! Use only with caution.]

As you see, quarks are very different from kuarqs; their masses are very small compared to a proton’s mass, and the down quark mass is more than double that of the up quark. (Actually it took several decades for the table shown above to stabilize, because quarks are never seen individually and their masses must be inferred indirectly.)

The picture of a proton and neutron is then also very different. Instead of imagining three kuarqs moving slowly around a proton, one finds large numbers of fast-moving particles inside. The proton and neutron have almost identical interiors; they contain essentially the same combinations of quarks, anti-quarks and gluons. Their only difference is that a single up quark of the former is exchanged for a single down quark in the latter. More about this viewpoint is explained here or, more carefully, in my book chapter 6.3.

What this means is that the proton and neutron are twins not because the up and down quarks are twins, but rather in spite of the fact that the up and down quarks are not twins. If we convert a proton to a neutron by trading an up quark for a down quark, the neutron’s mass remains the same as the proton’s because the difference between the up and down quark masses is much smaller than that of the proton’s mass, and is thus almost irrelevant.

Essentially, the strong nuclear force brings about the proton and neutron as bags of many fast-moving particles. So strong is that force that any differences in the quarks’ electric effects, magnetic effects, and even their masses are minor details, all of which combine together to explain the very small difference between the proton and neutron masses, as well as their electric and magnetic differences.

With protons and neutrons so complicated, you might well wonder why all protons are the same, all neutrons are the same, and why protons and neutrons are so similar inside. Some discussion of this quantum-physics effect is given in my book’s final chapters.

Kuarqs and Quarks

When quarks of very low mass were discovered in experiments and confirmed in theory, Gell-Mann was quick to insist that he’d known his kuarqs were real particles all along. Clearly this is revisionist history,. Not to take much away from the great man, who deserved his Nobel prize, but he was right the first time. His kuarqs were mathematical objects, and the reason that his kuarq approach (and that of Zweig) worked so well for protons, neutrons and other similar particles is indeed due to the existence of somewhat obscure mathematical symmetries, as pointed out in a wonderful 1994 paper of Dashen, Jenkins and Manohar. This paper does not settle all the issues (specifically it does not address pions and other “mesons”), but it does help make clear the senses in which kuarqs differ from quarks. It also explains why models of protons and neutrons that have no kuarqs in them at all (cf. the “Skyrme model”) can make just as good predictions as those that do, as long as they contain the same obscure mathematical symmetries. Kuarqs, in short, are useful but not necessary concepts.

This is in contrast to quarks, which are elementary particles appearing directly and explicitly in the equations of the Standard Model of particle physics. There are six types, only three of which are reflected in Gell-Mann and Zweig’s kuarqs. They are fundamental ingredients to modern computer simulations that can directly compute the difference between the proton and neutron masses. We can’t do particle physics without them.