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

TL;DR

This paper employs a treed Gaussian process to model the $R$-ratio in order to better understand its role in the hadronic vacuum polarization contributions to the muon g-2 anomaly, providing a data-driven uncertainty quantification.

Contribution

It introduces a treed Gaussian process approach for modeling the $R$-ratio, enabling principled uncertainty quantification and addressing modeling tensions in HVP contributions.

Findings

No evidence of previous $R$-ratio mis-modeling.

Method yields results consistent with prior estimates.

Advances modeling techniques for the $R$-ratio.

Abstract

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.