Muon g-2 has been measured to better than parts per million precision and compared to highly precise Standard Model predictions. The differences between the two main Standard Model predictions and the experimental measurements of this physical observable (the anomalous magnetic moment of the muon) are at the parts per ten million level although the differences between the two main Standard Model predictions, and between the experimentally measured value and one of those predictions, is statistically significant.
The tau lepton's anomalous magnetic moment has a quite precise (but not quite as precise as muon g-2) Standard Model predicted value of the SM prediction of 0.001 177 21 (5), which is quite close to the quite precisely measured and theoretically calculated electron g-2 value (the experimentally measured value of which is in mild 2.5 sigma tension with this value measured at a parts per hundred million level, by being too low), and the muon g-2 value (discussed at length in previous posts at this blog which is in tension with the Standard Model value in the other direction).
The ATLAS experiment's latest measurement of this quantity at the Large Hadron Collider (LHC) (like previously efforts to measure this quantity) is far less precise, mostly due to the seven orders of magnitude shorter mean lifetime of the tau lepton than its less massive, but otherwise identical cousins the muon (the electron is stable). The ATLAS measure of tau g-2 has a 95% confidence interval range of (−0.058, −0.012) ∪ (−0.006, 0.025), which includes the Standard Model predicted value in a very broad discount range of .046 and 0.31 for a combined range of 0.77 (about 2.25 times the uncertainty of the global average PDF value below), due to the imprecise measurement.
The Particle Data Group value as explained in a power point presentation providing more background on the question from 2020 is -0.018(17), which is also consistent with the Standard Model predicted value at about a 1.1 standard deviation level. Still, the uncertainty in this value is still about sixteen times the magnitude of its theoretically predicted value.
The same paper does reveal that the rate at which tau lepton pairs are produced by photo-production (i.e. creation of a tau lepton and tau anti-lepton by colliding two photons, in this case in connection with the high energy collision of two lead atoms), is right in line with the Standard Model prediction. The measured value is 1.04 times the value predicted in the Standard Model with an uncertainty of + 0.06 and - 0.05, so within about two-thirds of a standard deviation of experimental uncertainty of the predicted value.
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the W boson – has a significantly greater mass than theorized
I've blogged this at length at https://dispatchesfromturtleisland.blogspot.com/2022/04/a-new-w-boson-mass-measurement-from-cdf.html?showComment=1651627610061#c575989171971862752 with updates in the comments.
Either the central value, or the uncertainty in the measurement, or both, as reported by CDF using data from 2011 and before which has been reanalyzed, is almost surely wrong. It is in strong tension with a consistent result from eight or nine other direct measurements, and an indirect measurement from a global electroweak fit that is based mostly upon the masses of the Z boson, Higgs boson, and top quark, plus the electromagnetic and weak force coupling constants.
There is also a 20 MeV shared systemic error that makes all or most of the direct measurements too high due to a definitional issue that was neglected in early measurements when this was too small to be relevant.
A number of sources of understated error have been identified in commentary.
The CMS experiment at the LHC will be reporting its first W boson measurement this year or next year, with similar precision to the existing global average and the claimed CDF direct measurement error, and it is widely expected to come in very close to previous measurements made at the LHC at the LHCb and ATLAS experiments.
The barrage of new papers based upon a single outlier measurement of a quantity that has been precisely measured many times is absurd. There is also a thread in the HEP part of Physics Forums to which I've contributed.
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