We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a µ = (g − 2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a µ (Expt) = 11 659 208.0(5.4)(3.3) × 10 −10 , where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a µ includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ≈ 0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e + e − hadronic cross sections, lie 2.2 -2.7 standard deviations below the experimental result.

We present a new measurement of the positive muon magnetic anomaly, a µ ≡ (gµ − 2)/2, from the Fermilab Muon g −2 Experiment based on data collected in 2019 and 2020. We have analyzed more than four times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of two due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω′ p , and of the anomalous precession frequency corrected for beam dynamics effects, ωa. From the ratio ωa/ω ′ p , together with precisely determined external parameters, we determine a µ = 116 592 057(25) × 10 −11 (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a µ (FNAL) = 116 592 055(24) × 10 −11 (0.20 ppm). The new experimental world average is aµ(Exp) = 116 592 059(22) × 10 −11 (0.19 ppm), which represents a factor of two improvement in precision.

The Booster Neutrino Experiment (MiniBooNE) searches for ν µ → ν e oscillations using the O(1 GeV) neutrino beam produced by the Booster synchrotron at the Fermi National Accelerator Laboratory (FNAL). The Booster delivers protons with 8 GeV kinetic energy (8.89 GeV/c momentum) to a beryllium target, producing neutrinos from the decay of secondary particles in the beam line. We describe the Monte Carlo simulation methods used to estimate the flux of neutrinos from the beamline incident on the MiniBooNE detector for both polarities of the focusing horn. The simulation uses the Geant4 framework for propagating particles, accounting for electromagnetic processes and hadronic interactions in the beamline materials, as well as the decay of particles.The absolute double differential cross sections of pion and kaon production in the simulation have been tuned to match external measurements, as have the hadronic cross sections for nucleons and pions. The statistical precision of the flux predictions is enhanced through reweighting and resampling techniques. Systematic errors in the flux estimation have been determined by varying parameters within their uncertainties, accounting for correlations where appropriate.

A high-statistics sample of charged-current muon neutrino scattering events collected with the MiniBooNE experiment is analyzed to extract the first measurement of the double differential cross section ( d 2 σ dTµd cos θµ ) for charged-current quasielastic (CCQE) scattering on carbon. This result features minimal model dependence and provides the most complete information on this process to date. With the assumption of CCQE scattering, the absolute cross section as a function of neutrino energy (σ[Eν]) and the single differential cross section ( dσ dQ 2 ) are extracted to facilitate comparison with previous measurements. These quantities may be used to characterize an effective axial-vector form factor of the nucleon and to improve the modeling of low-energy neutrino interactions on nuclear targets. The results are relevant for experiments searching for neutrino oscillations.

This paper explores the use of L/E oscillation probability distributions to compare experimental measurements and to evaluate oscillation models. In this case, L is the distance of neutrino travel and E is a measure of the interacting neutrino's energy. While comparisons using allowed and excluded regions for oscillation model parameters are likely the only rigorous method for these comparisons, the L/E distributions are shown to give qualitative information on the agreement of an experiment's data with a simple two-neutrino oscillation model. In more detail, this paper also outlines how the L/E distributions can be best calculated and used for model comparisons. Specifically, the paper presents the L/E data points for the final MiniBooNE data samples and, in the Appendix, explains and corrects the mistaken analysis published by the ICARUS collaboration.