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

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.

arXiv comment23 pages, 5 figures

References in corpus (29)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• Rank-normalization, folding, and localization: An improved $\hat{R}$ for assessing convergence of MCMC
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• Fast and scalable Gaussian process modeling with applications to astronomical time series
• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\alpha }({\mathbf{m}}_{\mathbf{Z}}^2)$
• High-statistics measurement of the pion form factor in the rho-meson energy range with the CMD-2 detector
• New physics explanations of $a_{\mu }$ in light of the FNAL muon $g-2$ measurement
• Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions
• Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• The $e^{+}{e}^{-}\to 2({\pi }^{+}{\pi }^{-}){\pi }^0$, 2(π^+π^-)η$,$K^+ K^-π^+π^-π^0$and$K^+ K^-π^+π^-η$ Cross Sections Measured with Initial-State Radiation
• Reevaluation of the hadronic contribution to the muon magnetic anomaly using new e+e- -> pi+pi- cross section data from BABAR
• On the extraction of spectral densities from lattice correlators
• Update of g-2 of the muon and Delta alpha
• Efficient modeling of correlated noise II. A flexible noise model with fast and scalable methods
• Study of the reaction $e^{+}{e}^{-}\to {\pi }^0\gamma$ with the SND detector at the VEPP-2M collider
• Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ using initial state radiation
• Probing the energy-smeared R-ratio on the lattice
• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ cross section using initial-state radiation at BaBar
• Hadronic Uncertainties versus New Physics for the $W$ boson Mass and Muon $g-2$ Anomalies
• Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\eta$ in the c.m. energy range 1394--2005 MeV with the CMD-3 detector
• Study of the reactions $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0{\pi }^0\gamma$ and ${\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0\eta \gamma$ at center-of-mass energies from threshold to 4.35 GeV using initial-state radiation
• Fast Automatic Bayesian Cubature Using Lattice Sampling
• Approximate Inference for Nonstationary Heteroscedastic Gaussian process Regression
• Study of the process $e^{+}{e}^{-}\to 3({\pi }^{+}{\pi }^{-}){\pi }^0$ in the C.M. Energy range 1.6--2.0 GeV with the CMD-3 detector