What are the dimensions of the proton's substructure?

I was looking over the "Visualizing the Proton" videos that MIT put out a few years ago, where the collision data from CEBAF, etc. was turned into a visual representation of quarks, gluons and the rest.

The video is nice, but there's no actual dimensions on any of it. I get that it's just a representation, and not necessarily reality, but:

1. What's the average/maximal distance between a quark and the centre of the image/proton when "X=0.3"? (22 seconds into the video)

2. What's the width of the quark itself? Do up and down quarks have different widths?

Note: I understand that the proton is a composite particle, better described as a probability space rather than a distinct "shape" like a macroscopic object (an apple, box, etc.). The MIT depiction implies that this probability distribution still has a superstructure though, and so I'm wondering specifically what the distance between components would be in this view.

Edit: This video by Vitaly Velizhanin doesn't quite answer my question, but does go through deep inelastic scattering in detail and helps dispel some misconceptions I had. It seems as though most of the depiction of the quarks and their connections in the MIT video was artistic license, and the MIT video doesn't rely on specific measurements for the distance between quarks or the probability radius of the quarks themselves.

I've also updated the title, since the original title "What is the size of the proton?" doesn't actually match up with what is being asked.

• One note, careful with the word width as that has an entirely different meaning in high energy particle physics where it is commonly used in the term "decay width" in terms of particle decay rates/lifetimes. Commented Dec 12, 2022 at 19:10
• This video goes into a bit more popular-science-level detail about what the animation is doing. Commented Dec 12, 2022 at 20:35
• The proton is not a point particle and has a charge radius a bit less than 1 fm. (The exact value of the proton radius was a bit of a puzzle a few years ago, but this was over experiments using different methods that disagreed at the few percent level.) As far as we know, the quarks inside the proton are point particles. The up and down valence quarks momentum distributions within the proton are very similar but not exactly the same; see "Understanding the Parton Distribution Functions". Commented Dec 12, 2022 at 21:15
• The distribution of quarks doesn't seem to be random though, at least in this representation. They have defined locations within the proton (or more likely the proton's charge radius?), which means their average/most likely positions should be determinable. Is the answer just to assume that the width of the circle at 22 sec is twice the proton's charge radius, then extrapolate? Commented Dec 12, 2022 at 21:36
• Accepted rms charge radius of proton is about 0.8 fm. Commented Dec 13, 2022 at 9:57