What do subatomic particles look like?

"What do subatomic particles look like?" sounds like a pretty basic question.  But, in fact, it is not.  Many physicists would considered it ill-posed, since 'look' presupposes observation with visible light, something that is impossible, since, by any measure, these particles are far smaller than the wavelength of light.  Instead, observing subatomic particles requires far more energetic probes.  And, quantum fluctuations mean that they are ever-changing; instead of an instantaneous shape, we can only hope to observe, at best, the average shape, plus some measure of the fluctuations.   Like many larger objects, the way that they look depends on how one looks at them.

Consider the proton, the central nucleus of a hydrogen atom.   When we ask what it looks like, we can expect to learn about its size and hopefully shape.  Is it spherical?  How does its density change in going from the center to its periphery?   This begets an important question: density of what?  There are many different ways to characterize a proton.  One could measure the charge distribution, mass density, or at internal pressure, or look at where the quarks and/or gluons are within it.  One could also probe quarks or gluons within a specific momentum (Bjorken-x) range. 

Or, one could ask where its 'protonness' is.  More generally, one can ask where its baryon number is.  Baryon number is what makes protons and neutrons what they are, and distinguishes them from mesons.  In the valence quark model, protons have three quarks (as in the left drawing above). When one adds in gluons and evanescent quark-antiquark pairs, it looks more like the drawing on the right.  Then one can define baryons as having three more quarks than antiquarks.  But, this is not the only possibility.  However, sophisticated mathematics - the requirement of local gauge invariance of the proton  - points toward the existence of a baryon junction, comprising a nonperturbative localized configuration of gluons which is connected to these three quarks.  This model makes some predictions that seem to be borne out experimentally.   Another consequence is that the protonness is likely to be concentrated in the center of the nucleus.

We can probe this using a reaction that is sensitive to baryon number.  Backward photoproduction (also known as u-channel photoproduction) is one such reaction.  In it, a photon interacts with a proton, producing a meson, plus the original baryon.  Normally, as in diagram (a) above, the produced meson carries most of the momentum of the photon; the momentum transfer from the proton target is small.  But, sometimes, the proton acquires most of the photon momentum, leaving the meson nearly at rest.  This can happen if there is a large momentum transfer from the proton (diagram (c)) or if there is a small momentum transfer, but transfer also exchanges baryon number (diagram (b)).   Either way, the photon is rather directly probing the baryon number in the target.  

We use this reaction to 'image' the proton by looking at the momentum transfer in these backward production reactions.   The higher the momentum transfer, the smaller the object that is struck.  In more technical terms,  a two-dimensional Fourier transform of the transverse momentum of the outgoing meson gives us a density distribution of  baryon number within the proton.  In a preprint (arXiv:2603.03730) we (me, plus colleagues from U Washington, Livermore and UC Davis) did this for a number of different backward production reactions, along with, as a benchmark, some otherwise-matching conventional forward photoproduction reactions.  The plot below shows our results:

And there you have it - pictures of the essence of the proton - the seat of its baryon number. Here, the x axis is the radius (distance from the center of mass of the proton), in fermi; 1 fermi is 10^-15 m.   The y axis is the baryon number density.   For simplicity, we characterized these distributions by their average (rms) radius.  We found that the average transverse (after squashing the proton down to two dimensions) radius of the baryon number was 0.33 to 0.53 fm.  In comparison, a number of other measures of the proton size, based on its charge density, or parton densities, all found larger radii, at least 0.67 fm.  So, a protons protonness is concentrated near the center of the proton.  

There are caveats on this result.  If you are interested, please read the paper (click on the PDF link on the web page above), but overall it seems fairly (pardon the pun) solid.