Modeling the R-ratio and hadronic contributions to $$g-2$$ with a Treed Gaussian process
Andrew Fowlie (Department of Physics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, China); Qiao Li (Department of Physics, Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu, 210023, China)
The BNL and FNAL measurements of the anomalous magnetic moment of the muon disagree with the Standard Model (SM) prediction by more than $$4\sigma $$ . 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 ).
