# FeaturedA Challenges to QED from hyperfine measurements

1. May 20, 2017

### tom.stoer

Does anybody have more insights regarding

https://www.nature.com/articles/ncomms15484
High precision hyperfine measurements in Bismuth challenge bound-state strong-field QED

Does this really challange QED? Or does this mean that we miss certain contributions to QED calculations?

The authors are speculating "new effects might appear in the interaction of the electron with itself, the vacuum or the nuclear fields in this regime, that is, the hyperfine interaction might be affected by the existence of new particles not included yet in the current standard model and therefore not considered in state-of-the-art QED calculations."

Does this mean "new physics" or just standard model effects not taken into account so far, e.g. heavier particles like Myon, tau, W, Z, ...?

2. May 20, 2017

### A. Neumaier

From the main text:
• Assuming that all the atomic structure calculations are correct, one can extract the required size of the nuclear moment that is in accordance with our result. However, at this point we refrain from doing so, as an independent test of the underlying theory should be carried out first.
• [...] the overdue re-determination of the nuclear magnetic moment of 209Bi
Thus it probably just means that the uncertainties in the approximate calculations and in the nuclear form factors were not estimated correctly. Nothing relevant for heavier elementary particles or beyond the standard model.

3. May 20, 2017

### tom.stoer

Thanks, that was my conclusion as well. So I was wondering why mentioning "new particles" and why writing

http://www.pro-physik.de/details/news/10531640/Experiment_zeigt_Grenzen_der_QED.html
Experiment zeigt Grenzen der QED

Do you know the QED calculations? What they might exclude or miss?

Starting with some solutions for the Dirac equation as background field in QED might be problematic. We know that it fails for Z > 137, but of course this indicates that it might fail for smaller Z as well.

4. May 21, 2017

### A. Neumaier

I only know the principles behind this kind of computations. A modified Dirac equation is expected from theory as the correct effective theory; see https://www.physicsoverflow.org/23626 . The terms in it are determined from the form factors and the self-energy of the electron, which depend on its environment, in the present case on properties of the 209Bi nucleus. From the modified Dirac equation one can the compute the hyperfine splitting by standard, reliable methods.

Thus the only question is getting the effective Dirac equation correct. Its computation involves QED with nonstandard corrections by the nontrivial nuclear form factors. Details are messy and hence error prone; also there is an element of art involved as it is not so obvious which terms in the approximation schemes to keep and which ones to neglect. I wouldn't want to try checking the calculations.

5. May 23, 2017

### hilbert2

I didn't even know that someone's doing QED calculations for something with that large atomic number... You've probably heard about the "proton radius puzzle" where the muonic helium hyperfine structure shows signs of smaller than expected proton charge radius. In the bismuth atom, the inner electrons are close to the nucleus (an in strong electric field) because of the large nuclear charge while the muon is close to the nucleus of muonic helium because of its large mass. I remember someone has proposed the idea that the $\mu$-He anomaly is a result of some new physics, too.

EDIT: Oh, it was done for a Bi ion that has only a small number of electrons left. Then it makes sense.

6. May 23, 2017

### vanhees71

Was the radius measurement done with helium too now? I'm only aware of muonic hydrogen and the deuteron. Both leads to proton charge radii significantly smaller to the CODATA value from electronic hydrogen spectroscopy and electron-proton scattering. For a recent talk in our Nuclear Physics Colloquium, see

http://th.physik.uni-frankfurt.de/~hees/np-colloquium/index.html

(talk on last Friday, May 19).

7. May 24, 2017

### hilbert2

Sorry, I remembered wrong that they did it with helium already. It was muonic hydrogen and there was a short mention somewhere that they were planning to do the same experiment with muonic helium.

8. May 24, 2017

### vanhees71

Yes, and one should also emphasize that the new Bi results do not challenge QED per se but of course the theorists to better understand the electromagnetic form factors of the nucleus and the hadronic/QCD corrections. The latter is an obstacle even for much more fundamental questions like the anomalous magnetic moment of the muon. Although the muon is an elementary Dirac Fermion (within the Standard Model of course), the largest theoretical uncertainty are due to strong-interaction corrections. There's a major joint experimental and theoretical effort under way to get this under better control. The question of all this finally is to decide whether there is really some "physics beyond the Standard Model" seen or whether the observations can be explained within the Standard Model.

9. May 25, 2017

### tom.stoer

Thanks.

So the conclusion is that it's not a challenge to QED as a theory but to the mathematical methods to solve QED.

That was my interpretation as well.

10. May 28, 2017

### bitstreamout

In my humble opinion, this conclusion should be substinate with some calculations as the statement its self, even if likely true, should be checked out to be true