## Thursday, November 21, 2013

### Accuracy of Muon g-2 Theoretical Prediction Improved

The previous state of the art prediction for the anomalous magnetic moment of the muon (g-2) was:

(154 ± 1 ± 2) × 10−11

where the ﬁrst error was due to electroweak hadronic uncertainties, but the second, larger uncertainty was due to the unknown Higgs boson mass.

A new paper incorporating new fundamental constant measurements, most importantly, the Higgs boson mass, has essentially eliminated the uncertainty due to the Higgs boson mass uncertainty from the theoretically predicted value of muon g-2, leading to a new world's best estimate of:

(153.6 ± 1.0) × 10−11

The new estimate is approximately 55% more precise than the previous one.
The ﬁnal theory error of these contributions dominated by the electroweak hadronic and three-loop uncertainties . . . . It is enlarged to the conservative value ±1.0 × 10−11 . . . . The parametric uncertainty due to the input parameters MW, mt, and particularly MH is negligible. The precision of the result is by far suﬃcient for the next generation of aµ measurements. Clearly, the full Standard Model theory error remains dominated by the non-electroweak hadronic contributions.
In other words, as is often the case, the difficulty associated with doing QCD calculations prevents the theoretical estimate from being more precise.

Precision muon g-2 theoretical expectations are important because the current experimentally measured value of this constant is about three standard deviations from the theoretically expected value and greater precision on both the theoretical and experimental fronts can clarify if this discrepancy is real, or just a product of inaccurate theoretical predictions and experimental values.

UPDATE: I am not entirely clear how the conversion of the figures above to the muon g-2 figures below in the Snowmass on the Mississippi Charge Lepton paper at Equations 4.3-4.5 on page 35 is accomplished.  This sets forth a discrepancy between theory from a pair of 2011 papers and experiment from BNL E821 (2006) of: 287(80)*10^-11, with the theoretical prediction being slightly lower than the experimentally valued at a roughly three sigma level.

Using a root of the sum of squares methods to combine error estimates, the theoretical error is 49*10^-11, the experimental error is 63*10^-11 and the combined theoretical and experimental error, as shown, is 80*10^-11.

A review of the paper paper in my original post is looking at only a portion of the muon g-2 theoretical estimate (the electroweak contributions to muon g-2 rather than the entire muon g-2), producing a -0.4*10^-11 adjustment in the mean theoretical value, and a 1.2*10^-11 reduction in the combined theoretical error estimate, a less impressive improvement that previously suggested.  The precision improvement in the overall muon g-2 estimate from knowledge of the Higgs boson mass is actually only about 2%.