Uncertainties of the hadronic corrections for electron and muon

[exponent137]

TL;DR Summary

The pie chart in the link below shows that about 99.95% of the total error of g-2 of the muon in the theoretical prediction is due to the uncertainties in the hadronic corrections. What is this number for g-2 of the electron?

https://news.fnal.gov/2020/06/physicists-publish-worldwide-consensus-of-muon-magnetic-moment-calculation/

The pie chart in this link shows that about 99.95% of the total error of g-2 of the muon in the theoretical prediction is due to the uncertainties in the hadronic corrections. What is this number for g-2 of the electron? Maybe this number exists also for tau particles?

The new value of fine structure constant was measured, 1/137.035 999 206(11), maybe this question will become important with new updates.

 

[mfb]

They get 7000*10^-11 for the total hadronic effect on a=(g-2)/2 (equation 8.5), with an uncertainty of ~1%. Generally these things tend to scale with the squared mass, so we expect contributions to the electron g-2 to be weaker by a factor ~40,000, or ~1.7*10^-12, suggesting an uncertainty of ~1.7*10^-14.

Here is a discussion of the electron g-2, and indeed they do find 1.7*10^-12 with an uncertainty of 1.6*10^-14.

The current uncertainty on the electron g-2 value is ~10^-12, largely from the uncertainty in the fine-structure constant. It's important to add the hadronic contribution but its uncertainty is negligible at the moment.

For the tau hadronic contributions are much more important, but here the measurements are worse by orders of magnitude so precise calculations don't have a high priority.

 

[exponent137]

They get 7000*10^-11 for the total hadronic effect on a=(g-2)/2 (equation 8.5), with an uncertainty of ~1%. Generally these things tend to scale with the squared mass, so we expect contributions to the electron g-2 to be weaker by a factor ~40,000, or ~1.7*10^-12, suggesting an uncertainty of ~1.7*10^-14.

Here is a discussion of the electron g-2, and indeed they do find 1.7*10^-12 with an uncertainty of 1.6*10^-14.

The current uncertainty on the electron g-2 value is ~10^-12, largely from the uncertainty in the fine-structure constant. It's important to add the hadronic contribution but its uncertainty is negligible at the moment.

For the tau hadronic contributions are much more important, but here the measurements are worse by orders of magnitude so precise calculations don't have a high priority.

Thank you for information.

But I am more interested also about this:
The current uncertainty on the electron g-2 value is ~10^-12, largely from the uncertainty in the fine-structure constant. It's important to add the hadronic contribution but its uncertainty is negligible at the moment.

I thought
https://www.scientificamerican.com/...-ever-measurement-of-fine-structure-constant/
where it is written:
In the case of the electron, the experimental measurement of the magnetic moment is 1.6 standard deviations above the theoretical prediction based on the fine-structure constant measured by the Paris group.

Let us assume that the cause for the disagreement between the theoretical and the measured magnetic moment of the muon is new physics and the same is valid in the case of the electron. (Thus we assume that E898 measurement will confirm this. )

What is your estimation how the uncertainty of the fine structure constant (0.000 000 011) should be reduced that we will obtain 5$\sigma$ tension also for the electron? Is it not enough approximately 0...011*1.6/5 in a naive estimation? (Of course the tension between Paris and Berkeley measurements should also be explained. )

 

[mfb]

1.6 standard deviation is nothing, given that you "expect" 1.
The 1.6 are a combination of experimental and "theoretical" uncertainty, so it's not a simple scaling ("theoretical" in quotes because the uncertainty comes from another measurement). To get to 5 sigma at the same central values you would need a reduction in uncertainty on both sides.

Note figure 1 in the alpha measurement: Their result is in disagreement with a 2018 measurement. They'll have to find out what went wrong in one of them.