Why is QED being blamed for the discrepancy in proton radius measurements?

[PAllen]

Radius of proton due to QED??

In one account of the new findings of smaller proton radius, the claim was repeated several times that the radius of a proton was predicted by QED, in conflict with the new measurement. Why QED? I would think, within a proton, QCD is orders of magnitude more important. Of course the quarks are charged, but why would QED dominate?

Thanks for any explanation.

 

[humanino]

QED is the relevant interaction when probing the proton by lepton (say electron or muon) scattering, or when calculating the energy levels of a bound state such as hydrogen or muonic hydrogen.

The findings are certainly important. To find out whether they are experimental errors, the experiment must be repeated by an independent group. Whether they have forgotten an ingredient in calculation is quite possible. Once the community feels those possibilities have been excluded, they would call the findings "new physics".

 

[PAllen]

QED is the relevant interaction when probing the proton by lepton (say electron or muon) scattering, or when calculating the energy levels of a bound state such as hydrogen or muonic hydrogen.

The findings are certainly important. To find out whether they are experimental errors, the experiment must be repeated by an independent group. Whether they have forgotten an ingredient in calculation is quite possible. Once the community feels those possibilities have been excluded, they would call the findings "new physics".

To clarify, it's clear that leptons interact with the charged quarks by QED, but why doesn't QCD have a lot to say about the 'where the quarks are', e.g. what radius of asymptotic freedom is? Does this somehow have nothing to do with radius measured by lepton scattering, and, if not, why not?

 

[humanino]

QCD have a lot to say about the 'where the quarks are'

Sure, most certainly. As you correctly point out, the question requires 'quotes', that is to say a better definition. In particular

what radius of asymptotic freedom is?

This is not the definition used in this case. The definition used for the radius is related to the slope of the electric form factor at the real photon point. These form factors appear in the QED (virtual-)photon/nucleon vertex.

In principle, one could calculate these form factors in the standard model (QCD+QED+weak) but in practice this is difficult. For instance, with a heavy pion, your nucleon will shrink and the form factor will flatten. I do not have reference right now, but I suspect this is especially hard to determine the slope at 0.

 

[PAllen]

Sure, most certainly. As you correctly point out, the question requires 'quotes', that is to say a better definition. In particularThis is not the definition used in this case. The definition used for the radius is related to the slope of the electric form factor at the real photon point. These form factors appear in the QED (virtual-)photon/nucleon vertex.

In principle, one could calculate these form factors in the standard model (QCD+QED+weak) but in practice this is difficult. For instance, with a heavy pion, your nucleon will shrink and the form factor will flatten. I do not have reference right now, but I suspect this is especially hard to determine the slope at 0.

If the experiment is confirmed, is it possible that no change to the standard model is actually needed? Instead, could this just be evidence that the intractable QCD+QED calcution is required to get the right answer? I guess I am asking, how strong are theoretical arguments that QCD should be ingorable at the level precision measured here?

 

[humanino]

If the experiment is confirmed, is it possible that no change to the standard model is actually needed? Instead, could this just be evidence that the intractable QCD+QED calcution is required to get the right answer? I guess I am asking, how strong are theoretical arguments that QCD should be ingorable at the level precision measured here?

Yes, this is quite a possible outcome. We have seen in the past that the difficulty of this kind of calculation can be underestimated. However, I have only a superficial knowledge of these results, so I can not point out to specific possible limitations.

Since I should have done that while ago, I printed the article. Hopefully I can find some time to study it soon.

 

[Sleuth]

I studied the problem a little bit in my master thesis...
The problem is that the proton radius is only a simple constant which does not have any real physical meaning, just because as you said the proton is not an elementary particle and it would make no sense talking about its "physical" radius.

Nevertheless, when you use QED to compute energy levels of an Hydrogenlike atom, you obtain that you can parametrize your result in function of some constants like the fine structure constant \alpha, and the proton radius... this is just a definition...

now the point is that the accepted proton radius Rp value is obtained through spectroscopy in hydrogen like atoms, which compared with the theoretical predictions expressed in terms of Rp allow to obtain a certain value for this Rp.

The problem is that if you use the lamb shift, the shift between 2S and 2P_1/2, you still have a theoretical prediction for the lamb shift which depends on Rp, and an experimental value... these together allow you to obtain again the Rp, and surprise... they are different of about 3-5 standard deviations!

The reason is not known but, a reasonable explanation could be in some error in the theoretical evaluation of the lamb shift... I don't know if you ever went through it, but it's a quite lengthy and cumbersome procedure, not very rigorous... infact you perform two independent calculations, one for the soft photons, and the other for the hard photons, using two different formulae which are well defined respectively for the soft and hard regime, and then you more or less match them together...

now this procedure is far from rigorous, and can obviously work only at the first order, because you immediately lose the understanding of what you are doing if you try to go further in the perturbative expansion...

what is believed now is that a new treatment of the lamb shift could be the answer, as far as i know :)

bye

Sleuth

 

[humanino]

QED confronts the proton's radius

Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other.
Three reasons justify a further look at this subject:

• (1) There is an apparent error in [1] in solving a cubic equation. This error is equivalent to a shift of the proton's radius by 3.4 of the standard deviations of [1], in the "right" direction of data-reconciliation.
• (2) One of the approximations used in [1] is not valid for muonic hydrogen. This amounts to an extra $\sim 3\sigma$ in the same direction.
  In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius "runs", much as the QCD coupling "constant" does.
• (3) The result of [1] requires a choice of the "third Zemach moment". Its published independent determination is based on an analysis with a $p$-value --the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis-- of $3.92\times 10^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of "tension" between muonic- and ordinary-hydrogen results, currently at most $\sim 3.5\sigma$.

There is no tension between the results of [1] and the proton radius determined with help of the analyticity of its form factors.

 

[negru]

I fail to understand why a bunch of ill approximations and mixing and matching were Nature material. Like if I wrote a paper on the value of g computed by throwing rocks from a tower. If I got a different answer no one would even have to read my abstract to know it's just wrong.

But then again for some time now Nature calls any wrong physics "new physics".

If there's any new physics within QED we would have seen other effects by now. This is getting way too much attention.