If quarks had internal structure (contradicting current beliefs), what is the lowest upper bound on their "radius" based on current experimental results?

If possible, I'd prefer to only consider experiments which probe protons and neutrons (not other shorter-lived particles since their interpretations get biased more by the standard model).

My only understanding is that this radius must be less than roughly 0.2 fm since spacings are found to be 2 fm in high-energy proton scattering experiments. I imagine "higher-energy scattering experiments" and "excited angular momentum experiments" have probed this further, but am not familiar with any other results. Or, is there some other reason why this radius must be zero? Honestly, with the surprise of quarks 10,000x smaller than the electron cloud, it wouldn't be surprising if we found some internal structure after another 10,000x zoom.

  • $\begingroup$ Note that the current bound of the electron radius is of order $10^{-18}\text{ m} = 10^{-3}\text{ fm}$. The size of he electron cloud in a atom is a representation of the electrostatic potential between the electron and the nucleus, not a fundamental property of the electron. $\endgroup$ Jul 20, 2012 at 19:06
  • $\begingroup$ sorry, I meant to write cloud, not could, so I now changed that one word $\endgroup$
    – bobuhito
    Jul 20, 2012 at 20:10
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    $\begingroup$ I understood the could/cloud wordo, but the point is that you shouldn't compare the intrinsic size (if any) of the quark to the size of a atomic electron cloud, but to the intrinsic size (if any) of the electron. $\endgroup$ Jul 20, 2012 at 20:11
  • $\begingroup$ I agree with your point, but I was just trying to point out that every 100 years we zoom in further and get surprised. Thank you for the bound on the electron radius; that is something else I've wondered about. By the way, I think I need to abandon my "probe protons and neutrons" hope since the gluons "cloud" the magnified region in some similar sense (so the standard model already has internal structure around the quarks which any probe would probably interact with). $\endgroup$
    – bobuhito
    Jul 20, 2012 at 20:56
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    $\begingroup$ Related: physics.stackexchange.com/questions/24001/…, although that deals with electrons rather than quarks. $\endgroup$
    – David Z
    Jul 21, 2012 at 0:10

1 Answer 1


As I mentioned in another answer, what people actually report these days is not really an upper bound on the radius of a particle. Instead, what you'll find is a lower bound on what is sometimes called the "contact interaction scale" - the energy at which you start to see effects of interactions among the constituents of a quark, if they exist.

For example, the most recent information I can find is this paper from the CMS experiment. It presents lower bounds on the contact interaction scale ranging from $7.5\text{ TeV}$ to $14.5\text{ TeV}$, depending on which model of substructure you're looking at. (In order to extract a lower bound from the data you get out of the detector, you need to make some assumptions about what kind of substructure you might be looking for.) So roughly speaking, we're reasonably sure that the types of substructure considered in the paper do not have any effect at processes involving less than $7.5\text{ TeV}$ of energy.

You can convert these limits into distances using the formula $\lambda = h c/E$, which tells you the wavelength corresponding to a particle with that limiting energy. This is just a rough order-of-magnitude bound, but it's as close as you can get to declaring an upper bound on the quark's radius with the knowledge we have today. Based on the values in the paper, it's $1.6\times 10^{-19}\text{ m}$.


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