I New proton radius measurement with electrons favors "muon value"

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Previously most measurements using electrons favored a larger value while measurements with muons found a smaller value for the radius. Now a second electron measurement measured a result that agrees with the muon-based measurements.
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It looks increasingly like something is wrong with the older electron-based results. The story of "with electrons you measure one thing, with muons another" doesn't work any more. Is that a good thing (there might be some conclusion what the radius is in the next years) or a bad thing (no new physics)? I guess it depends on your point of view. A Frequentist would highlight that we only discover what was true anyway, a Bayesian would point out that our best knowledge about it changed.

Edit: Someone pointed me to this paper arguing that most electron measurements have a bias, and taking that into account would bring them closer to the muon measurements.

Key figure from the publication:

F5.large.jpg
 
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ohwilleke

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Good catch. I have done a blog post with a bit more background inspired by this post and a review of some additional related papers.
 
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vanhees71

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What I didn't understand about the nice experiment is, why it comes to a different value in this Lamb-shift measurement than the previous ones. Some time ago there was also a Lamb-shift measurement, where the authors also came closer to the "muon value", and the reason was the use of some more detailed fit procedure taking into account resonances and their interference in the Lambshift measurements of electronic hydrogen.

https://science.sciencemag.org/content/358/6359/79.abstract
 

ohwilleke

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What I didn't understand about the nice experiment is, why it comes to a different value in this Lamb-shift measurement than the previous ones. Some time ago there was also a Lamb-shift measurement, where the authors also came closer to the "muon value", and the reason was the use of some more detailed fit procedure taking into account resonances and their interference in the Lambshift measurements of electronic hydrogen.

https://science.sciencemag.org/content/358/6359/79.abstract
In the electron case there has always had to be considerable theoretical adjustment to the raw data in order to get the proton charge radius from the Lamb shift, while the muon measurement is much more direct and requires far less theoretical manipulation.

My understanding is that the part of the different (maybe most of it) in the muon-like measurements involve making an adjustment in the process of converting raw measurements to a proton charge radius that previous studies had omitted, probably erroneously or thinking that it was negligible when it was not.

But, while that is the gist of it as I understand it, I don't have a specialist PhD's command of all the details to evaluate it except by reading other people's discussions of it and reading it to make sure that it seems to generally reflect what other people are saying.
 

vanhees71

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Interesting. So it's an example for the sociological "bandwagon phenomenon": Whenever there's "considerable theoretical adjustment to the raw data" necessary and there is a previous supposedly very accurate result the theoretical adjustment is tending to be iterated such to come close to this previous value. How can we be now sure that the same doesn't apply to the new measurement(s), i.e., that now the understanding is that the muon measurements are less "theory dependent" and thus give "a better value" so that now one tends to do the "theoretical adjustments" to the effect to come closer to the "muon value"?
 

hilbert2

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I remember how I read about the proton radius problem with fascination in the summer 2010. Have been following it quite closely since then.
 

ohwilleke

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Interesting. So it's an example for the sociological "bandwagon phenomenon": Whenever there's "considerable theoretical adjustment to the raw data" necessary and there is a previous supposedly very accurate result the theoretical adjustment is tending to be iterated such to come close to this previous value. How can we be now sure that the same doesn't apply to the new measurement(s), i.e., that now the understanding is that the muon measurements are less "theory dependent" and thus give "a better value" so that now one tends to do the "theoretical adjustments" to the effect to come closer to the "muon value"?
It isn't purely a bandwagon phenomena. The whole point of the scientific method is to favor theories that conform to experimental results.

For example, it would have been easy in the development of QED to rule out amplitudes deriving from paths at which a photon travels at more than the speed of light or less so, which would have produced slightly different theoretical predictions. But, including those adjustments produces more accurate results so we include those virtual path amplitudes in making our predictions and that is pretty much now universally accepted as the right way to the QED calculations.

Also, it is worth recalling that almost no SM calculations are made to absolute exact analytical precision. We intentionally omit terms from infinite series and estimate the uncertainty introduced by doing so.

Mathematical physics is less rigorous than purely theoretical mathematics.

In that context, the possibility that initial results could have omitted a term that is theoretically well justified and has an impact only on the 0.03 fm scale in the final result that it turns out was material enough that it should have been factored in to get a result closer to experiment (without disputing any of the adjustments that actually were made), isn't just sociology, or at least, isn't sociology that is likely to lead the establishment astray.

Honestly, in the face of different measurements and predictions that shouldn't theoretically be different, but are, like the charge radius of the proton on the ordinary hydrogen and muonic hydrogen cases, using the more precise measurement as a pointer towards the direction and magnitude of something that is likely to be wrong in the less precise measurement or prediction should usually be the first instinct, instead of looking for BSM explanations. A situation like this is a bit like the practical and common issue in accounting of trying to reconcile two discrepant results from the same source documents that are produced using different approaches to calculate them. It is a trouble shooting process.

And, keep in mind, as hilbert2 implies, this is not a super old problem. It took a while for people qualified to evaluate the issue closely enough look to properly evaluate it. Many of the other biggest unsolved problems in physics have been around for many decades long than this one, and the tensions involved in some of them have greater statistical significance. Likewise, solved problems also took longer from discovery of the problem to resolution. It took more than eight or nine years, for example, to solve the Pioneer 2 anomaly.

If anything, the sociological bandwagon has been the effort to throw BSM theories at the discrepancy prematurely before more prosaic explanations for the discrepancy were throughly vetted. These efforts are blowing back against that now well developed trend to look for a BSM theory to explain every anomaly that results from a scientific culture in which coming up with a theory first, before it is a sure thing, is the path to fame and full professorship.

I am far more concerned about the bandwagon thinking that keep scientists working on programs like supersymmetry and theories based upon WIMP cold dark matter particles even when experimental and observational evidence hasn't provided anything to favor supersymmetry, and has done nothing to favor WIMP CDM over alternatives to it, for many years.
 
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Is it a completely dumb question to ask whether a proton actually has a fixed radius? Or alternatively what is actually meant by the word 'radius' in this context ? Are we still envisaging the proton as a spherical object with the electron in 'orbit' (planetary type model) ?
 

vanhees71

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Of course, a proton is not a little classical bullet. It has for sure a fuzzy "boundary". What we are discussing here is the charge radius, as operationally defined by measuring the socalled form factor. The latter quantity is defined by scattering processes, and electron scattering this is indeed one type of measurements done to measure this "charge radius of the proton". A collection of such experiments enters the "CODATA value". Another way is to measure the Lamb shift of em. transitions, and this is done with both the usual "electronic hydrogen atoms" (in some trap) and "muonic hydrogen atoms". For some years the muonic-atom measurements show a significant deviation from the CODATA value, and this triggered a big "hype" about it because it could be indication of "physics beyond the Standard Model", but that's a bold claim and thus one has to make sure that the experiments are correctly analyzed, and there are indications for some time that there might be something wrong with the evaluation of the electron measurments. The here discussed newest measurement of the Lambshift in electronic hydrogen atoms now finds a value in accordance with the muonic hydrogen measurements, though it seems not to be clear what's the reason for the discrepancy. As I wrote above, other experiments of the same kind also come to the conclusion that the "muonic result" is the correct one, and the reason for the "wrong result" of the other experiment was the negligence of interference effects of two close resonances in the evaluation of the experiments.

I think, there's still work to do to clarify clearly, where the discrepancies come from, but as it looks now more and more evidence has it that again the Standard Model prevailed, and the hoped deviation from it cannot be confirmed :-(.
 
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Thanks - I googled a little on search terms "proton charge radius" and "atomic form factor" and concluded that this topic is perhaps a tad out of depth for me!
 

ohwilleke

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Is it a completely dumb question to ask whether a proton actually has a fixed radius? Or alternatively what is actually meant by the word 'radius' in this context ? Are we still envisaging the proton as a spherical object with the electron in 'orbit' (planetary type model) ?
As explained by vanhees71, the radius of a proton is well defined in this context, although in a way a bit more complex than an orbit.

It isn't a completely dumb question to ask whether a proton actually has a fixed radius. The muonic hydrogen result lead to hundreds if not thousands of papers by PhDs in physics pondering a theoretical way that this could be the case.

But, while there are lots of reasons (in general) that a proton radius might plausibly vary (e.g. the context of other hadrons in a nucleus or due to temperature, for example), the notion that a proton radius might vary based upon having a muon rather than an electron in its vicinity would be truly stunning within the context of the Standard Model or any other plausible extension of the Standard Model that wouldn't have been discovered in previous experiments up to and including the LHC.

This is because electrons and muons have the same properties except mass (e.g. the same EM charge and no strong force interactions) so their impact shouldn't be that different, and because the proton radius is believed based upon very solid reasoning and evidence to be overwhelmingly a function (1) at first order of strong force bonds between its quarks, and (2) at second order of electromagnetic interactions between its quarks. The EM effects between quarks in a proton should be much, much greater than that with an electron or muon in the same atom, since the distance between them is much shorter than the distance between a proton and an electron or muon that is part of the same atom, because EM forces decline as a function of 1/r^2. The average distance of a muon from a proton in muonic hydrogen might be a bit different from the average distance of an electron from a proton in ordinary hydrogen due to their mass difference which might slightly impact the pull of the charged lepton in hydrogen on the proton, but not very much, in a third order or lower factor. A fuller exposition of this can be found at http://www.sjsu.edu/faculty/watkins/muonicH2.htm

The magnitude of the experimentally measured size difference is about 4%. A third or lower order factor, if it has any effect, shouldn't have nearly that strong an effect. Hence, the source would have to be either "new physics" or some error in determining the quantities that are being compared.
 
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But, while there are lots of reasons (in general) that a proton radius might plausibly vary (e.g. the context of other hadrons in a nucleus or due to temperature, for example), the notion that a proton radius might vary based upon having a muon rather than an electron in its vicinity would be truly stunning within the context of the Standard Model or any other plausible extension of the Standard Model that wouldn't have been discovered in previous experiments up to and including the LHC.
Just to avoid confusion for other readers: The models made to explain the difference didn't focus on a changing proton radius. The raw measurement value is the energy difference between different states. Any new interaction between muons and protons can change the energy levels and therefore the difference. The proton radius is a tiny correction to these energy levels, so even a relatively weak interaction can make a difference large enough to appear like a 4% smaller proton radius.
 

ohwilleke

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Just to avoid confusion for other readers: The models made to explain the difference didn't focus on a changing proton radius. The raw measurement value is the energy difference between different states. Any new interaction between muons and protons can change the energy levels and therefore the difference. The proton radius is a tiny correction to these energy levels, so even a relatively weak interaction can make a difference large enough to appear like a 4% smaller proton radius.
I don't disagree. But, the difference observed was still way out of line in magnitude what any Standard Model prediction of how muonic hydrogen and ordinary hydrogen should differ, because the differences should be due more or less entirely to QED effects, which we understand to absurd precision.
 

vanhees71

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That's unfortunately not true. The main theoretical uncertainty in the Lamb-shift calculation (and btw. also in context of the muon anomalous magnetic moment, which is also under investigation right now with the BNL apparatus shipped to Fermilab some years ago) are the QCD corrections.
 

ohwilleke

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That's unfortunately not true. The main theoretical uncertainty in the Lamb-shift calculation (and btw. also in context of the muon anomalous magnetic moment, which is also under investigation right now with the BNL apparatus shipped to Fermilab some years ago) are the QCD corrections.
Interesting. I did not know that and it is quite surprising. I'll have to go read some of the Lamb-shift calculations more carefully.
 

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