Muon g-2: Review of Theory and Experiment

TL;DR

The paper surveys the experimental determination and Standard Model calculation of the muon anomalous magnetic moment $a_\mu=(g-2)/2$, highlighting the Brookhaven E821 measurement and the dominant hadronic uncertainties. It details the experimental setup, including the magic $\gamma$ condition, storage-ring magnetic-field mapping, and high-rate calorimeter timing, as well as the analysis framework for extracting $\omega_p$ and $\omega_a$ with a blind approach. The review then synthesizes QED, hadronic vacuum polarization, hadronic light-by-light scattering, and electroweak contributions, presenting the current SM prediction and the 3.4 sigma tension with experiment, which motivates future work such as the E969 program. The work underscores the muon g-2 as a sensitive probe of new physics and a stringent constraint on beyond-Standard-Model scenarios, with significant implications for electroweak and hadronic dynamics and for guiding next-generation precision tests at colliders.

Abstract

A review of the experimental and theoretical determinations of the anomalous magnetic moment of the muon is given. The anomaly is defined by a=(g-2)/2, where the Landé g-factor is the proportionality constant that relates the spin to the magnetic moment. For the muon, as well as for the electron and tauon, the anomaly a differs slightly from zero (of order 10^{-3}) because of radiative corrections. In the Standard Model, contributions to the anomaly come from virtual `loops' containing photons and the known massive particles. The relative contribution from heavy particles scales as the square of the lepton mass over the heavy mass, leading to small differences in the anomaly for e, μ, and τ. If there are heavy new particles outside the Standard Model which couple to photons and/or leptons, the relative effect on the muon anomaly will be \sim (m_μ/ m_e)^2 \approx 43\times 10^3 larger compared with the electron anomaly. Because both the theoretical and experimental values of the muon anomaly are determined to high precision, it is an excellent place to search for the effects of new physics, or to constrain speculative extensions to the Standard Model. Details of the current theoretical evaluation, and of the series of experiments that culminates with E821 at the Brookhaven National Laboratory are given. At present the theoretical and the experimental values are known with a similar relative precision of 0.5 ppm. There is, however, a 3.4 standard deviation difference between the two, strongly suggesting the need for continued experimental and theoretical study

Figures (51)

• Figure 1: The Feynman graphs for: (a) $g=2$; (b) the lowest-order radiative correction first calculated by Schwinger; and (c) the vacuum polarization contribution, which is an example of the next-order term. The * emphasizes that in the loop the muon is off-shell.
• Figure 2: Number of decay electrons per unit energy, N (arbitrary units), value of the asymmetry $A$, and relative figure of merit $NA^2$ (arbitrary units) as a function of electron energy. Detector acceptance has not been incorporated, and the polarization is unity. For the third CERN experiment and E821, $E_{max}\approx 3.1$ GeV ($p_\mu = 3.094$ GeV/c) in the laboratory frame.
• Figure 3: The integral $N$, $A$, and $NA^2$ (arbitrary units) for a single energy-threshold as a function of the threshold energy; (a) in the laboratory frame, not including and (b) including the effects of detector acceptance and energy resolution for the E821 calorimeters discussed below. For the third CERN experiment and E821, $E_{max}\approx 3.1$ GeV ($p_\mu = 3.094$ GeV/c) in the laboratory frame.
• Figure 4: The E821 beamline and storage ring. Pions produced at $0^{\circ}$ are collected by the quadrupoles Q1-Q2 and the momentum is selected by the collimators K1-K2. The pion decay channel is 72 m in length. Forward muons at the magic momentum are selected by the collimators K3-K4.
• Figure 5: (a) A plan view of the inflector-storage-ring geometry. The dot-dash line shows the central muon orbit at 7112 mm. The beam enters through a hole in the back of the magnet yoke, then passes into the inflector. The inflector cryostat has a separate vacuum from the beam chamber, as can be seen in the cross sectional view. The cryogenic services for the inflector are provided through a radial penetration through the yoke at the upstream end of the inflector. (b) A cross-sectional view of the pole pieces, the outer-radius coil-cryostat arrangement, and the downstream end of the superconducting inflector. The muon beam direction at the inflector exit is into the page. The center of the storage ring is to the right. The outer-radius coils which excite the storage-ring magnetic field are shown, but the inner-radius coils are omitted.