https://doi.org/10.1140/epjc/s10052-023-12110-9
Regular Article – Theoretical Physics
Modeling the R-ratio and hadronic contributions to 
with a Treed Gaussian process
1
Department of Physics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, 215123, Suzhou, China
2
Department of Physics, Institute of Theoretical Physics, Nanjing Normal University, 210023, Nanjing, Jiangsu, China
Received:
4
July
2023
Accepted:
4
October
2023
Published online:
19
October
2023
The BNL and FNAL measurements of the anomalous magnetic moment of the muon disagree with the Standard Model (SM) prediction by more than 
. The hadronic vacuum polarization (HVP) contributions are the dominant source of uncertainty in the SM prediction. There are, however, tensions between different estimates of the HVP contributions, including data-driven estimates based on measurements of the R-ratio. To investigate that tension, we modeled the unknown R-ratio as a function of CM energy with a treed Gaussian process (TGP). This is a principled and general method grounded in data-science that allows complete uncertainty quantification and automatically balances over- and under-fitting to noisy data. Our tool yields exploratory results are similar to previous ones and we find no indication that the R-ratio was previously mismodeled. Whilst we advance some aspects of modeling the R-ratio and develop new tools for doing so, a competitive estimate of the HVP contributions requires domain-specific expertise and a carefully curated database of measurements (github, https://github.com/qiao688/TGP_for_g-2).
© The Author(s) 2023
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