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Physics + MathPhysics & Math

What is the Shape of a Proton?

A marble, a peanut, a donut—or all of the above? Go inside physicists' quest to understand the nature of the proton.

The Nature of RealityThe Nature of Reality

Picture a proton.

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You’re probably thinking of something small and round, like a subatomic marble. That’s not a bad start, and it’s certainly good enough for most chemistry and physics classes. Maybe you’re imagining what the quarks inside the proton might look like too, and then you might ponder: how can three smaller balls make up a larger sphere? What is actually going on here? You might chalk it all up to quantum weirdness and go think about something else for a while.

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Yet those questions trouble many particle physicists as well. When it comes to protons, even the simplest questions—How big is it? What is its shape?—turn out to have complicated answers. While we’ve known the basics for decades, the details are more elusive. Take size, for example. Measuring the proton isn’t as simple as getting out a really tiny ruler: Any measuring tool we use is made of other particles, and those interact with the proton we’re trying to measure. The solution: “We do it the same way [Ernest] Rutherford discovered the atom has a very small and positively charged nucleus,” said Alberto Accardi , a physicist at Jefferson Lab and Hampton University in Virginia—that is, by firing other particles at the target particle and measuring how they “scatter.” Similarly, to measure the size of a proton, physicists typically bombard it with electrons or muons, a more massive relative of the electron. The spread of the particles after scattering reveals the size and shape, much as you could use the shadow of a tall building to estimate its height. Physicists have performed scattering experiments for a century now, and determined the radius of the proton to be about

0.88 femtometers (0.88 × 10 -15 meters).

However, there are inherent limits to the accuracy of electron bombardment, so researchers double-checked the proton’s size using atoms of muonic hydrogen , a form of hydrogen made up of a proton and muon, rather than a proton and electron. Since muons are 207 times heavier than electrons, muonic hydrogen is a lot smaller than the regular form, so the size of a proton has a measurable effect. (The larger muon mass shrinks the atom by shifting the center of mass, just like you hold a heavier object closer to your body than a lighter one.) Using this method, researchers found the proton is 0.84 femtometers in radius—a tiny but significant difference. Physicists are stumped as to why this might be, leading to some wild speculation about the nature of fundamental forces.

Measuring the proton’s shape has also led to some interesting results. Based on theoretical calculations in nuclear physics and scattering experiments like those used to measure proton size, we know a proton is indeed spherical. Or rather, it’s spherical-ish: the shape fluctuates around the spherical average, and those non-spherical flickers arise from the quarks and other bits inside the proton. While the fluctuations take many forms, the dominant ones are either a “peanut” shape or a “bagel” shape, in the words of physicist Gerald Miller .

To understand the source of those strange shapes, physicists have to look inside the proton. To see that, researchers shoot high-speed electrons and muons at it. These particles carry so much energy that they no longer just bounce off the proton. Instead, they break the proton apart, giving researchers access to the particles that make it up.

We usually say that protons are made of three quarks: two “up” quarks and one “down.” (“Up” and “down” are just names rather than directions, but at least they’re easy to remember.) Accardi and others have found, however, that that’s not entirely correct: as Accardi says, “The proton is made of three ‘valence’ quarks and a bunch of quark-antiquark pairs, as well as gluons that hold all these together.” Just as valence electrons give an atom its basic chemical structure, valence quarks provide a lot of the noticeable properties of a proton.

Instead of a marble, it seems, a proton is a kind of “stew”: the up and down valence quarks are like the biggest chunks, but other ingredients combine to produce the total flavor. Those ingredients include gluons—particles that act as a binding “broth”—along with pairs of quarks and antiquarks. Antiquarks are the antimatter partners to quarks, so they don’t pair stably with their matter counterparts. Nevertheless, in the high-energy environment inside a proton, they are constantly created and destroyed along with their partners, in a process that contributes to the total behavior of a proton.

All of these constituents together are known as partons , and the combination of their properties and interactions makes protons what they are. For example, the two up quarks are positively charged while the down is negative; that means the internal structure of a proton has both positive and negative electric charges that add up to a net positive charge. Similarly, the spins of the quarks aren’t all aligned, but combine in some complicated way to produce the proton spin. The surprising “peanut” shape arises from quarks whose spin is parallel to the overall proton spin; those with opposite spin make a bagel-shaped proton.

Puzzlingly, though, the quarks and gluons together aren’t enough to account for the total spin of a proton; it’s like putting in enough ingredients for a bowl of stew and getting a full pot in return. Says Accardi, “Spin is a very basic property of the proton, and we need to understand it from a microscopic point of view if we are to claim we understand the underlying theory” governing proton structure. The solution to this mystery, and the riddle of the proton’s true size, could be provided by the Electron-Ion Collider (EIC), a possible future United States particle physics experiment which Accardi is hoping will be funded. The EIC would send electrons and protons or atomic nuclei around a tunnel in opposite directions at close to light speed. During collisions, the electrons pry apart the protons or nuclei without themselves being destroyed. The result could reveal true parton configurations, solving problems of how quarks and gluons produce the total proton behavior.

Scientists love mysteries: they’re signs we have more to discover, to keep us interested. By peering inside protons, we may find new states of matter—proposals with names like gluon condensates or color glass—or even unsuspected particles. That such things could come from something so familiar as a proton is all the more exciting.

Go Deeper
Editor’s picks for further reading

arXiv: Muonic hydrogen and the proton radius puzzle
A technical review of the proton size puzzle and its possible resolutions.

Jefferson Lab: Questions and Answers
In this archive of accessible Q&A features, Jefferson Lab scientists explain what we know about atoms and their structure and how we know it.

Of Particular Significance: What’s a Proton, Anyway?
Blogger and theoretical physicist Matthew Strassler (figuratively) dives inside the proton.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.