Modeling the R-ratio and hadronic contributions to g- 2 with a Treed Gaussian process

The BNL and FNAL measurements of the anomalous magnetic moment of the muon disagree with the Standard Model (SM) prediction by more than 4 σ . 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).