Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon $g-2$ Experiment for the positive muon magnetic anomaly $a_{\mu }\equiv (g_{\mu }-2)/2$. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ${\omega }_a$ between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ${\tilde{\omega }}_p^{\prime }$ in a spherical water sample at $34.7°\mathrm{C}$. The ratio ${\omega }_a/{\tilde{\omega }}_p^{\prime }$, together with known fundamental constants, determines $a_{\mu }(\mathrm{FNAL})=116\hspace{0.17em}592\hspace{0.17em}040(54)\times {10}^{-11}$ (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both ${\mu }^{+}$ and ${\mu }^{-}$, the new experimental average of $a_{\mu }(\mathrm{Exp})=116\hspace{0.17em}592\hspace{0.17em}061(41)\times {10}^{-11}$ (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

Figure 1

Feynman diagrams of representative SM contributions to the muon anomaly. From left to right: first-order QED and weak processes, leading-order hadronic (H) vacuum polarization, and hadronic light-by-light contributions.

Figure 2

Fourier transform of the residuals from a time-series fit following Eq. (5) but neglecting betatron motion and muon loss (red dashed), and from the full fit (black). The peaks correspond to the neglected betatron frequencies and muon loss. Inset: asymmetry-weighted $e^{+}$ time spectrum (black) from the Run-1c run group fit with the full fit function (red) overlaid.

Figure 3

Azimuthally averaged magnetic field contours ${\omega }_p^{\prime }(x,y)$ overlaid on the time and azimuthally averaged muon distribution $M(x,y)$.

Figure 4

From top to bottom: experimental values of $a_{\mu }$ from BNL E821, this measurement, and the combined average. The inner tick marks indicate the statistical contribution to the total uncertainties. The Muon $g-2$ Theory Initiative recommended value [13] for the standard model is also shown.