Hadronic Vacuum Polarisation Contributions to g-2 and other precision observables

Sustained tension between the measured results of the Muon g-2 experiment at Fermilab and the theoretical prediction suggests a potential for new physics beyond the Standard Model. The precision of the Fermilab measurement has been improved by a factor of two by analysis of Run 2 and Run 3 data, and is expected to improve by the same factor again once all of the data collected has been analysed. This improvement in experimental accuracy needs to be accompanied by a comparable improvement in theoretical accuracy.
The largest source of uncertainty on the theoretical prediction comes from the Hadronic Vacuum Polarisation (HVP) contribution. While other contributions to the prediction can be calculated within the framework of perturbation theory, the HVP contribution must be calculated from dispersive or lattice QCD methods. The primary focus of this PhD is to refine the dispersive calculation of the HVP contribution, by means of developing improved methodology and including new data sets not previously available.
Among the new data sets to be considered is the n+n- data collected with the CMD-3 experiment. There is a considerable discrepancy between these results and those obtained previously by other experiments including CMD-2, which ran at the same facility. It will be necessary to determine the best way to include these data alongside prior results with which they seem incompatible.
There also exists a notable tension between the dispersive and lattice QCD predictions for the HVP contribution to g-2. When lattice QCD is used to perform the HVP calculation, a result more consistent with the experimental result is obtained. The source of this tension is as yet unknown, and is the source of much investigation. As part of this project, dispersive predictions of so-called window observables can be made and compared to those of lattice QCD groups.
The first stage of this project will be to update the program used for the KNT calculation of the HVP contribution into a more modern language. This will allow use of powerful modern software features such as relational databases and make the code more accessible. Blinding procedures will also be implemented into the calculation from the start; these are introduced with the aim of avoiding biasing the final result.
As the project progresses, the statistical methods used in the code will be refined with the aim of assigning more accurate uncertainties. The role of systematic uncertainties and correlations will also be scrutinised. New data sets will be introduced into the analysis, further increasing the precision and accuracy of the measurement. Unbiased methods of reconciling data sets in tension will be developed and applied to address outstanding potential issues. Furthermore, the handling of radiative corrections in the analysis will be improved.
The project will yield not only an updated dispersive calculation of the HVP contribution to g-2, but also updated values for other precision observables. These can be compared to the results of other precision physics experiments (such as the hyperfine splitting of muonium), or, in the case of the calculation of the running of the QCD coupling, used as inputs for further measurements. The results of the updated calculation will be compared to the final Fermilab measurement and results from lattice QCD. This project therefore will make a potentially important contribution to a major test of the Standard Model and the search for new physics.