Jester at Resonaances has a new post on a new ultraprecision measurement of the electromagnetic force coupling constant based upon a two month old paper that missed headlines when it came out because of the way that it was published and tagged. He notes:

What the Berkeley group really did was to measure the mass of the cesium-133 atom, achieving the relative accuracy of 4*10^{-10}, that is 0.4 parts par billion (ppb). . . . the measurement of the cesium mass can be translated into a 0.2 ppb measurement of the fine structure constant: 1/α=137.035999046(27). One place where precise knowledge of α is essential is in calculation of the magnetic moment of the electron. Recall that the g-factor is defined as the proportionality constant between the magnetic moment and the angular momentum. For the electron we have:

Experimentally, g_{e}is one of the most precisely determined quantities in physics, with the most recent measurement quoting a_{e}= 0.00115965218073(28), that is 0.0001 ppb accuracy on g_{e}, or 0.2 ppb accuracy on a_{e}. In the Standard Model, g_{e}is calculable as a function of α and other parameters. In the classical approximation g_{e}=2, while the one-loop correction proportional to the first power of α was already known in prehistoric times thanks to Schwinger. The dots above summarize decades of subsequent calculations, which now include O(α^5) terms, that is 5-loop QED contributions! . . . the main theoretical uncertainty for the Standard Model prediction of g_{e}is due to the experimental error on the value of α. The Berkeley measurement allows one to reduce the relative theoretical error on a_{e}down to 0.2 ppb: a_{e}= 0.00115965218161(23), which matches in magnitude the experimental error and improves by a factor of 3 the previous prediction based on the α measurement with rubidium atoms. . . .

it also provides a powerful test of the Standard Model. New particles coupled to the electron may contribute to the same loop diagrams from which g_{e}is calculated, and could shift the observed value of a_{e}away from the Standard Model predictions. In many models, corrections to the electron and muon magnetic moments are correlated. The latter famously deviates from the Standard Model prediction by 3.5 to 4 sigma, depending on who counts the uncertainties. Actually,if you bother to eye carefully the experimental and theoretical values of aSo now we have two g-2 anomalies!_{e}beyond the 10th significant digit you can see that they are also discrepant, this time at the 2.5 sigma level.

FWIW, I calculate the discrepancy to be 2.43 sigma, and not 2.5.

Jester has a pretty chart that illustrates the discrepancies, but it does more to obscure than reveal what is going on to the uninitiated. Words, which I will paraphrase below for even greater clarity, are more clear in this case.

As Jester explains, the direction of the discrepancy is important.

Jester has a pretty chart that illustrates the discrepancies, but it does more to obscure than reveal what is going on to the uninitiated. Words, which I will paraphrase below for even greater clarity, are more clear in this case.

As Jester explains, the direction of the discrepancy is important.

New physics fixes that treat electrons and muons the same, in general, don't work, because the electron g-2 calls for a negative contribution to the theoretically calculated value, while the muon g-2 needs a positive contribution to the theoretically calculated value.

So, new physics can't solve both discrepancies without violating lepton universality, which is tightly constrained by other measurements that seem to contradict evidence that this is violated in B meson decays, so this isn't possible without some sort of elaborate theoretical structure that cause it to be violated sometimes, but not others.

So, new physics can't solve both discrepancies without violating lepton universality, which is tightly constrained by other measurements that seem to contradict evidence that this is violated in B meson decays, so this isn't possible without some sort of elaborate theoretical structure that cause it to be violated sometimes, but not others.

On the other hand, discrepancies in the opposite directions in measurements of two quantities that are extremely analogous to each other in the Standard Model, and in different magnitudes, are exactly what you would expect to see if there is theoretical or experimental error in either of the measurement. If you assume that lepton universality is not violated and pool the results for electron g-2 and muon g-2 in a statistically sound way, the discrepancies tend to cancel each other other producing a global average that is closer to the Standard Model prediction.

More experimental data regarding these measurements is coming soon.

The muon g-2 experiment in Fermilab should soon deliver first results which may confirm or disprove the muon anomaly. Further progress with the electron g-2 and fine-structure constant measurements is also expected in the near future. The biggest worry is that, if the accuracy improves by another two orders of magnitude, we will need to calculate six loop QED corrections...

**QED v. QCD**

It is also worth pausing for just a moment to compare the state of QED (the Standard Model theory of the electromagnetic force) with QCD (the Standard Model theory of the strong force).

The

**strong force coupling constant**discussed in my previous post at this blog is known with a precision of**7 parts per 1000**, which may be overestimated and actually be closer to 4 parts per 1000. This is based on NNLO calculations (i.e. three loops).
The

**electromagnetic force coupling constant**, which is proportionate to the fine structure constant, α, is known with a precision of**0.2 parts per billion**, and the electron g-2 is calculated to five loops. So, we know the electromagnetic coupling constant to a precision 2-4 million times greater than we know the strong force coupling constant.
For sake of completeness, we know the

**weak force coupling constant**(which is proportional to the Fermi coupling constant) to a precision of about**2 parts per million**. This is about 10,000 times less precise than the electromagnetic coupling constant, but about 2000-4000 times more precisely than the strong force coupling constant.
We know the

**gravitational coupling constant**(i.e. Newton's constant G) which isn't strictly analogous to the three Standard Model coupling constants since it doesn't run with energy scale in General Relativity and isn't dimensionless, to a precision of about**2 parts per 10,000**. This is about 20-40 times more precise than the precision with which we have measured the strong force coupling constant (even incorporating my conjecture that the uncertainty in the strong force coupling constant's global average value is significantly overestimated), is about 100 times less precise than our best measurement of the weak force coupling constant, and is about a million times less precise than our best measurement of the electromagnetic coupling constant.
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