We present a new measurement of the positive muon magnetic anomaly, $a_{\mu }\equiv (g_{\mu }-2)/2$, from the Fermilab Muon $g-2$ Experiment using data collected in 2019 and 2020. We have analyzed more than 4 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 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ${\tilde{\omega }}_p^{\prime }$, and of the anomalous precession frequency corrected for beam dynamics effects, ${\omega }_a$. From the ratio ${\omega }_a/{\tilde{\omega }}_p^{\prime }$, together with precisely determined external parameters, we determine $a_{\mu }=116592057(25)\times {10}^{-11}$ (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain $a_{\mu }(\mathrm{FNAL})=116592055(24)\times {10}^{-11}$ (0.20 ppm). The new experimental world average is $a_{\mu }(\exp )=116592059(22)\times {10}^{-11}$ (0.19 ppm), which represents a factor of 2 improvement in precision.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

A new measurement of the magnetic anomaly a μ of the positive muon is presented based on data taken from 2020 to 2023 by the Muon g − 2 Experiment at Fermi National Accelerator Laboratory (FNAL). This dataset contains over 2.5 times the total statistics of our previous results. From the ratio of the precession frequencies for muons and protons in our storage ring magnetic field, together with precisely known ratios of fundamental constants, we determine a μ = 1 165 920 710 ( 162 ) × 10 − 12 (139 ppb) for the new datasets, and a μ = 1 165 920 705 ( 148 ) × 10 − 12 (127 ppb) when combined with our previous results. The new experimental world average, dominated by the measurements at FNAL, is a μ ( exp ) = 1 165 920 715 ( 145 ) × 10 − 12 (124 ppb). The measurements at FNAL have improved the precision on the world average by over a factor of 4.

We present details on a new measurement of the muon magnetic anomaly, $a_{\mu }=(g_{\mu }-2)/2$. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses $3.1\mathrm{GeV}/c$ polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of $a_{\mu }$ is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure $a_{\mu }=116592057(25)\times {10}^{-11}$ (0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield $a_{\mu }(\mathrm{FNAL})=116592055(24)\times {10}^{-11}$ (0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is $a_{\mu }(\exp )=116592059(22)\times {10}^{-11}$ (0.19 ppm).

A next step of energy increase of hadron colliders beyond the LHC requires high-field superconducting magnets capable of providing a dipolar field in the range of 16 T in a 50-mm aperture with accelerator quality. These characteristics could meet the requirements for an upgrade of the LHC to twice the present beam energy or for a 100-TeV center of mass energy future circular collider. This paper summarizes the activities and plans for the development of these magnets, in particular within the 16 T Magnet Technology Program, the WP5 of the EuroCirCol, and the U.S. Magnet Development Program.