Particle Physics


What is the Shape of a Proton?

Picture a proton.

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.

Image: Flickr user Tomasz Stasiuk, adapted under a Creative Commons license.

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.

Tell us what you think on Twitter, Facebook, or email.


Matthew Francis

    Matthew R. Francis is a science writer, physicist, public speaker, educator, and frequent wearer of jaunty hats. He contributes a weekly column about astronomy and space to The Daily Beast. His writing has also appeared in Ars Technica, Slate, Nautilus, Aeon, and a variety of other publications. A former college professor and planetarium director, he holds a PhD in physics and astronomy from Rutgers University. Image courtesy of Tony Hitchcock.

    • Richard Jowsey

      Fascinating stuff!! I’m re-reading a very interesting text by Vayenas & Souentie titled “Gravity, Special Relativity and the Strong Force”, which proposes that quarks are actually ultra-relativistic neutrinos, and the strong force is gravitational. I know, sounds preposterous, but the math works. I think there’s a basic error in their SR math, namely in the derivation of gamma-cubed, but need to work it through some more to be certain. I’d appreciate your opinion on their model.

      • Richard Jowsey

        [Edit] There is, of course, no basic error in their SR math. On further delving, the gamma-cubed factor which had me puzzled actually originated in Einstein’s 1905 electrodynamics paper, in which it was termed “longitudinal” (cf “transverse”) mass. Relativistic frames of reference can be quite confusing!

    • George Raina
    • Saheed Apenaola

      I like to think of it this way. Imagine how vast our solar system is. Now imagine something that big to exist in a minute level. Now imagine the size of an electron, which is more than half the size of a proton.

    • Mike P

      If protons are made from smaller parts, how did nature make each proton identical?


      • “how did nature make each proton identical?”

        There is only one type of universal substance so of course everything is made from it and everything would have to be the same.

        The “Atom” with protons, neutrons and electrons is a fairly good model but that’s the end there are no quarks like they say.

        If you smash / collide a proton you will get pieces — actually shrapnel — all the same stuff just different amounts of it. (they think if something has a different weight (or mass) they are different things).

    • phxmarker mark

      The proton acts like a little black hole exchanging information with the vacuum. The radius.mass relationship of the proton is:

      Rp=proton Radius
      Mp=proton Mass
      L=Planck Length
      M=Planck Mass

    • Hey, you used my photo! Woot!

    • ibrahimu Ntimba
    • ~~~~~~~~~~~~

      Does anyone believe this real science below…

      They say red, blue and green quarks are shooting anti-green, anti-blue and anti-red gluons at anti-quarks and changing the color charges so that the color charge is conserved. That stuff just has to be correct!

      NOTE: It doesn’t matter how they explain “color charge”. The point is they think there are 3 different things inside a proton (or neutron) and they are held together in a specific arrangement. If you can think about it in depth you will realize that is completely impossible.
      The explanation (they give) is the only way to explain an incorrect model. But the model and the explanation are both impossible.
      And if you have an incorrect model and an incorrect explanation you can call it counterintuitive — that’s a way to allow anything, even magic.

      How do 3 quarks know that is the correct number for a proton / neutron?
      Why do not 4 quarks combine?
      Is there an instruction set / manual at that level specifically for particles?
      No! …everything has to be automatic.
      Think about it, how do quarks know to only combine in groups of three?
      The answer is… they don’t, the mainstream quark model is incorrect