Are there any ideas for why a proton's radius is smaller than predicted?

This isn’t exactly news since the first experiment to indicate a discrepancy was done in 2010. However the new experiment, done by the same group is even more precise and uses a different technique that should allow even more precise measurements in the future.

Briefly, previous measurements of the proton’s charge radius involved using normal hydrogen with a single proton for the nucleus and a single electron. The new technique as well as the one in 2010 used a muon in place of an electron. Since a muon is 200 times heavier, it changes the dynamics considerably. However since muons also have a half life of about 2 millionths of a second, doing the measurements is a little tricky.

The bottom line is that the muon measurement deviates from the standard measurements by 5 standard deviations which is a bit off to say the least and at present seems to present a problem for the best tested aspect of the standard model which is QED

I would expect the proton’s radius to depend much more on QCD (quantum chromodynamics) effects than on QED, and QCD is much more poorly understood. So a result like this is a bit surprising, but not shocking.

Except that they measured the charge radius not the physical radius. I think they use that as a proxy for the physical radius.

Their is no physical radius. Charge defines matter as we feel it.

The charge is in the quarks, and the typical spacing between quarks surely depends on the color force, about which we know so little.

It’s not really that we don’t understand so much about the colour force, it’s just that one of the things we imagine we do understand is that the colour force works the same way in a proton with an electron hanging around as it does in a proton with a muon hanging around.

At the moment my bet is a systemic error in the way the radius is determined from the raw data. It’s a very indirect chain of inference.

Well, that’s sort of true about everything when you get down to the quantum level. Boundaries start to get sort of fuzzy, so fuzzy that you get phenomena like quantum tunneling where particles can appear in places that it’s technically impossible for them to get to.

Interesting fun fact: did you know that the nuclear fusion that powers the sun would be impossible without quantum tunneling? Our sun isn’t massive enough to get the job done purely with the brute force of heat and pressure. And since the concept applies to both energy barriers as well as physical barriers, if you have enough hydrogen nuclei in the same place, the odds are that you will get enough of them to spontaneously tunnel through the barrier to give you sustained fusion.

Another interesting fact as I was reading up on the proton in wikipedia is that the resting mass of the 3 quarks that make up a proton only account for 1% of its mass. The rest is made up of gluons which have no mass.

And if that isn’t bad enough, some part of the proton is composed of ghost particles from the quantum vacuum known as “sea quarks” that continuously pop in and out of existence.

If you mean the strong force, I thought we knew a fair amount about that it being unified with electro-weak and all. But I think the idea is that it shouldn’t be influenced by whether an electron is in orbit around the proton or a muon. If that sort of influence were accounted for by the standard model, I don’t think this would be such a big deal.

I think this is incorrect. The proton is massive enough that the uncertainty principle doesn’t relegate it to a “cloud” the way it does for an electron.

Isaac Asimov, in an essay entitled “The Proton-Reckoner,” mentioned that the proton is massive enough to have an appreciable diameter (and volume, as his intent was to calculate how many protons it would take to fill the observable cosmos.)

Charge defines ordinary physical matter at our scale. Wood, water, plastic, granite, and so on. But at the level of the proton, mass is also a fundamental measure of matter, and some larger masses (the nucleus of the atom, for instance) have meaningful diameters.

I think it’s less because of its mass and more because it’s a composite particle and therefore has multiple wave functions? I think that’s what I read someplace.

Matt Strasser’s take on the issue here.

A couple of points from that article:

[ul]
[li]This is not a “predicted vs. measured” problem. It’s a “measured one way vs. measured a couple of other ways” problem. Two previous classes of experiment – doing the same experiment with standard hydrogen and direct scattering experiments – give the “book” number for proton size. It’s just the muonic hydrogen measurements that disagree. There is, to my knowledge, no accepted “theoretical” number.[/li][li]The chance that the proton actually changes size is quite low. An unobserved force strong enough to fuck with the colour force would not remain unobserved for long. If experimental error is ruled out, a more likely resolution is that there is a subtle way the relationship between the observed transitions and proton size works.[/li][/ul]

He does however admit that the issue is outside his area of expertise whereas the people publishing this work have been living it for the past 3 years. For example towards the end, about muonic hydrogen he says.

What he said. When any science is in the realm of the theoretical, the math is always wrong, or it wouldn’t be theoretical.

The strong force is just a sort of residual leftover effect of the color force, which almost entirely cancels out over distances longer than the radius of a proton or so. It’s sort of like the relationship between the van der Waals force and the electromagnetic force. And while there is strong circumstantial evidence that the color force can be unified with the electroweak force, nobody’s quite sure how to do it, and our usual methods for studying the electroweak force don’t work in most color-force applications.

Chronos: I was reading a little about that yesterday and the color force seems especially bizarre. Apparently it has infinite range with no decrease in intensity as distance increases. From wikipedia entry on the strong force:

So essentially, 2 free quarks could be on opposite ends of the universe and would still be attracted to one another.

And yet somehow, when joined together with gluons and other quarks, the residual force can barely be felt beyond the width of an atomic nucleus. For some reason this strikes me as one of those ‘just so’ stories. I understand that things have been greatly simplified to allow for an explanation comprehensible to lay people, but still.

This cancellation is just like with the electromagnetic force. A positive proton and a negative electron can attract each other to form a neutral entity that no longer exerts electric force (except via higher-order effects). Analogously, a quark and antiquark can form a strong-force-neutral entity. The only difference is that you can’t separate the quarks without putting so much energy in that you just create additional quarks/antiquarks that immediately bind up to the original ones.

The mental image you are creating – two free quarks far away from each other and pulling unboundedly hard on each other – is analogous to trying to put two electrons arbitrarily close together. While in the quark case it’s large separations that are hard and in the electron case it’s close separations that are hard, the two cases are on the same footing, weirdness wise. You can’t construct either system without putting in the energy to do so, and in trying to do so for either system, you will end up creating new particles. In the quark case, there is just the added feature that the new particles will tightly bind to the original particles to create colorless hadrons.

Regarding understanding the strong force or not: I wouldn’t say at all that we don’t understand the strong force. On the contrary, we can use QCD to make predictions like these:

Masses of hadrons as predicted by QCD and as measured(*)

The points are various predictions for the masses of the indicated hadrons, and the black lines are the observed masses. The figure includes mesons and baryons and includes ground states and excited states. Rather impressive agreement!

The trouble is that QCD is tremendously hard to do calculations with. In most cases, calculational limitations still swamp experimental uncertainties.

This isn’t to say there aren’t deep questions (for instance, why doesn’t the strong force violate CP symmetry when it very well can), but these sorts of deep questions in the Standard Model aren’t unique to the strong force.
(*) arXiv:1203.1204

Except that unlike the electromagnetic force, QCD specifically states that the range is infinite.

Also the strong nuclear force is the residual force that is left over when quarks and gluons bind - no? So why isn’t the strong force also infinite?

Because of those cancellations. If there’s, say, a meson at one point and some other particle at another, you can have one of the quarks in the meson pulling that particle toward it with a ton of force, and the other one pushing it away with a ton of force, and the two forces cancel out. It’s only when you’re really close, such that one or the other of the forces isn’t quite up to a ton yet, that there’s a net force.

And incidentally, I love the fact that I can use the word “ton” here literally.

I’m not seeing how that answers the question though. It’s still that residual force that holds a nucleus together right? So why doesn’t the residual force have the same infinite range?

Because at the scale of a nucleus, it doesn’t cancel out completely.