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ohwilleke

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- New research shows many strong tensions between the data driven Theory Initiative calculation of the SM value of muon g-2 and other calculations and data. Research to resolve these tensions is underway.

The E989 experiment at Fermilab recently made a high precision measurement of the anomalous magnetic moment of the muon (muon g-2), an observable quantity which can in principal be calculated using the Standard Model for the electron, the muon, and the tau lepton, respectively. The upshot of this measurement was that the new high precision experimental measurement confirmed the results of a previous high precision experimental measurement.

But it wasn't clear which of two leading calculations of the Standard Model prediction of what muon g-2 should be was correct. The "official" Muon g-2 Theory Initiative determination of what the Standard Model predicted that muon g-2 should be (published in Nature and heavily overlapping pre-print here) was 4.2 sigma different from the actual measurement of muon g-2. But, a competing the lattice QCD estimate by the BMW group was consistent with the actual measurement of muon g-2 at the 1.5 sigma level.

The two groups differed solely in how they calculated the Standard Model prediction for the hadronic vacuum polarization part of the calculation of the Standard Model prediction of muon g-2 which is the source of 83% of the uncertainty in the final prediction. This is unsurprising since QCD calculations (i.e. calculations implicating the Standard Model strong force) are almost always much less precise than calculations involving the electromagnetic and weak forces in the Standard Model. Calculations in QCD are also almost always much more difficult to conduct than comparable electroweak calculations.

The Theory Initiative 2020 Working Paper, in part, used experimental data from electron-positron collisions in lieu of first principles calculations in a "data driven" model, while the BMW group calculation was the most precise "first principles only" calculation of the key portion of the Standard Model muon g-2 calculation.

The conclusion in the body text of a new paper quoted below reviews the work that has been done on determining the correct Standard Model prediction of since the most recent experimental muon g-2 measurement, documenting myriad tensions driving the two very different Standard Model predictions for muon g-2 from the Theory Initiative and the BMW group respectively. It states:

A previous puzzle in the high energy physics community, the Muonic Hydrogen Proton Radius Puzzle, which appeared to show a large discrepancy between the size of a proton in an ordinary hydrogen atom compared to a proton in muonic hydrogen in which the electron in ordinary hydrogen was replaced by a muon, was ultimately resolved when issues with the existing state of the art measurement of the proton radius in ordinary non-muonic hydrogen came to light. In the end, the new muonic hydrogen measurement of the proton radius was found to be the correct one and matched improved measurements of the proton radius in ordinary hydrogen containing an electron rather than a muon.

It could be that there is a similar issue with the electron-positron data used as an input in the Theory Initiative calculation.

Another possibility is that the way that the electron-positron data was incorporated into the Theory Initiative calculation was flawed.

A third-possibility is that the BMW calculation is flawed in a way shared with other lattice QCD calculations by non-BWM scientists, and that the measured value of muon g-2 actually is very significantly different from what the Standard Model predicts that it should be, thus pointing to new physics.

At first glance, this update on the tensions seen so far seems to favor the first of these three possible explanations, although not unequivocally.

But it wasn't clear which of two leading calculations of the Standard Model prediction of what muon g-2 should be was correct. The "official" Muon g-2 Theory Initiative determination of what the Standard Model predicted that muon g-2 should be (published in Nature and heavily overlapping pre-print here) was 4.2 sigma different from the actual measurement of muon g-2. But, a competing the lattice QCD estimate by the BMW group was consistent with the actual measurement of muon g-2 at the 1.5 sigma level.

The two groups differed solely in how they calculated the Standard Model prediction for the hadronic vacuum polarization part of the calculation of the Standard Model prediction of muon g-2 which is the source of 83% of the uncertainty in the final prediction. This is unsurprising since QCD calculations (i.e. calculations implicating the Standard Model strong force) are almost always much less precise than calculations involving the electromagnetic and weak forces in the Standard Model. Calculations in QCD are also almost always much more difficult to conduct than comparable electroweak calculations.

The Theory Initiative 2020 Working Paper, in part, used experimental data from electron-positron collisions in lieu of first principles calculations in a "data driven" model, while the BMW group calculation was the most precise "first principles only" calculation of the key portion of the Standard Model muon g-2 calculation.

The conclusion in the body text of a new paper quoted below reviews the work that has been done on determining the correct Standard Model prediction of since the most recent experimental muon g-2 measurement, documenting myriad tensions driving the two very different Standard Model predictions for muon g-2 from the Theory Initiative and the BMW group respectively. It states:

An unambiguous interpretation of the new measurement of the muon g−2 by the E989 experiment at Fermilab is impeded by several tensions that have been exposed since the publication of the 2020 White Paper: (1) There is a tension of 2.1σ between a single lattice calculation and the WP-recommended value for a_{µ}^{hvp,LO}, based on e+e− cross section data published prior to 2023; (2) There is a tension of almost 4σ between several lattice calculations and the corresponding dispersive estimate based on the same e+e− data; (3) There is a tension of 2−3σ in the hadronic running of α, as estimated by two lattice calculations and e+e− data; (4) There is a slight tension of 1−2σ in the Adler function determined from lattice and perturbative QCD on the one hand, and e+e−data on the other; (5) Finally, there is a tension of 2.7σ in the dominant π+π−channel between BaBar and KLOE, as well as a tension of about 4σ between CMD-3 and all other experiments.

In this context, it is important to realise that a larger SM prediction for a_{µ}is not in contradiction with global electroweak constraints, at least at the current level of precision.

The race is now on to determine why these two facially valid ways of calculating muon g-2 conducted by esteemed and well qualified groups of physicists have come up with such different results, and to determine which calculation is correct.Obviously, an independent cross-check of the BMW lattice result for a_{µ}^{hvp,LO}, with sub-percent precision is badly needed. Furthermore, the tension among e+e−data must be elucidated, a task for which the alternative determination of the R-ratio from τ decays could be useful. These activities are currently in progress. The Muon g−2 Theory Initiative is preparing an update of the original WP, which will thoroughly address the issues that have come to the fore since 2020.

A previous puzzle in the high energy physics community, the Muonic Hydrogen Proton Radius Puzzle, which appeared to show a large discrepancy between the size of a proton in an ordinary hydrogen atom compared to a proton in muonic hydrogen in which the electron in ordinary hydrogen was replaced by a muon, was ultimately resolved when issues with the existing state of the art measurement of the proton radius in ordinary non-muonic hydrogen came to light. In the end, the new muonic hydrogen measurement of the proton radius was found to be the correct one and matched improved measurements of the proton radius in ordinary hydrogen containing an electron rather than a muon.

It could be that there is a similar issue with the electron-positron data used as an input in the Theory Initiative calculation.

Another possibility is that the way that the electron-positron data was incorporated into the Theory Initiative calculation was flawed.

A third-possibility is that the BMW calculation is flawed in a way shared with other lattice QCD calculations by non-BWM scientists, and that the measured value of muon g-2 actually is very significantly different from what the Standard Model predicts that it should be, thus pointing to new physics.

At first glance, this update on the tensions seen so far seems to favor the first of these three possible explanations, although not unequivocally.

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