The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the eleven separate determinations of \omega_a, and the systematic uncertainties on the result.

Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment

The Fermilab Muon g −2 experiment recently reported its first measurement of the anomalous magnetic moment $$ {a}_{\mu}^{\mathrm{FNAL}} $$
 , which is in full agreement with the previous BNL measurement and pushes the world average deviation $$ \Delta {a}_{\mu}^{2021} $$
 from the Standard Model to a significance of 4.2σ. Here we provide an extensive survey of its impact on beyond the Standard Model physics. We use state-of-the-art calculations and a sophisticated set of tools to make predictions for aμ, dark matter and LHC searches in a wide range of simple models with up to three new fields, that represent some of the few ways that large ∆aμ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large ∆aμ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the aμ result can only be explained by rather small masses and/or large couplings and enhanced chirality flips, which can lead to conflicts with limits from LHC and dark matter experiments. Our results show that the new measurement excludes a large number of models and provides crucial constraints on others. Two-Higgs doublet and leptoquark models provide viable explanations of aμ only in specific versions and in specific parameter ranges. Among all models with up to three fields, only models with chirality enhancements can accommodate aμ and dark matter simultaneously. The MSSM can simultaneously explain aμ and dark matter for Bino-like LSP in several coannihilation regions. Allowing under abundance of the dark matter relic density, the Higgsino- and particularly Wino-like LSP scenarios become promising explanations of the aμ result.

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New physics explanations of aμ in light of the FNAL muon g − 2 measurement

Atom interferometers have been developed in the last three decades as new powerful tools to investigate gravity. They were used for measuring the gravity acceleration, the gravity gradient, and the gravity-field curvature, for the determination of the gravitational constant, for the investigation of gravity at microscopic distances, to test the equivalence principle of general relativity and the theories of modified gravity, to probe the interplay between gravitational and quantum physics and to test quantum gravity models, to search for dark matter and dark energy, and they were proposed as new detectors for the observation of gravitational waves. Here I describe past and ongoing experiments with an outlook on what I think are the main prospects in this field and the potential to search for new physics.

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Testing gravity with cold atom interferometry: Results and prospects.

We perform a model-exhaustive analysis of all possible beyond Standard Model (BSM) solutions to the $(g-2)_\mu$ anomaly to study production of the associated new states at future muon colliders, and formulate a no-lose theorem for the discovery of new physics if the anomaly is confirmed and weakly coupled solutions below the GeV scale are excluded. Our goal is to find the highest possible mass scale of new physics subject only to perturbative unitarity, and optionally the requirements of minimum flavour violation (MFV) and/or naturalness. We prove that a 3 TeV muon collider is guaranteed to discover all BSM scenarios in which $\Delta a_\mu$ is generated by SM singlets with masses above $\sim $ GeV; lighter singlets will be discovered by upcoming low-energy experiments. If new states with electroweak quantum numbers contribute to $(g-2)_\mu$, the minimal requirements of perturbative unitarity guarantee new charged states below $\mathcal{O}(100 {\rm TeV})$, but this is strongly disfavoured by stringent constraints on charged lepton flavour violating (CLFV) decays. Reasonable BSM theories that satisfy CLFV bounds by obeying Minimal Flavour Violation (MFV) and avoid generating two new hierarchy problems require the existence of at least one new charged state below $\sim 10 - 20$ TeV. This strongly motivates the construction of high-energy muon colliders, which are guaranteed to discover new physics: either by producing these new charged states directly, or by setting a strong lower bound on their mass, which would empirically prove that the universe is fine-tuned and violates the assumptions of MFV while somehow not generating large CLFVs. The former case is obviously the desired outcome, but the latter scenario would perhaps teach us even more about the universe by profoundly revising our understanding of naturalness, cosmological vacuum selection, and the SM flavour puzzle.

A No-Lose Theorem for Discovering the New Physics of $(g-2)_\mu$ at Muon Colliders

New neutral heavy gauge bosons (Z′) are predicted within many extensions of the Standard Model. While in case they couple to quarks the LHC bounds are very stringent, leptophilic Z′ bosons (even with sizable couplings) can be much lighter and therefore lead to interesting quantum effects in precision observables (like (g − 2)μ) and generate flavour violating decays of charged leptons. In particular, $$ \mathrm{\ell}\to \mathrm{\ell}^{\prime }v\overline{v} $$
 decays, anomalous magnetic moments of charged leptons, l → l′γ and l → 3l′ decays place stringent limits on leptophilic Z′ bosons. Furthermore, in case of mixing Z′ with the SM Z, Z pole observables are affected. In light of these many observables we perform a global fit to leptophilic Z′ models with the main goal of finding the bounds for the Z′ couplings to leptons. To this end we consider a number of scenarios for these couplings. While in generic scenarios correlations are weak, this changes once additional constraints on the couplings are imposed. In particular, if one considers an Lμ − Lτ symmetry broken only by left-handed rotations, or considers the case of τ − μ couplings only. In the latter setup, on can explain the (g − 2)μ anomaly and the hint for lepton flavour universality violation in $$ \tau \to \mu v\overline{v}/\tau \to ev\overline{v} $$
 without violating bounds from electroweak precision observables.

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Global analysis of leptophilic Z′ bosons

The standard model of particle physics is remarkably successful because it is consistent with (almost) all experimental results. However, it fails to explain dark matter, dark energy and the imbalance between matter and antimatter in the Universe. Because discrepancies between standard-model predictions and experimental observations may provide evidence of new physics, an accurate evaluation of these predictions requires highly precise values of the fundamental physical constants. Among them, the fine-structure constant α is of particular importance because it sets the strength of the electromagnetic interaction between light and charged elementary particles, such as the electron and the muon. Here we use matter-wave interferometry to measure the recoil velocity of a rubidium atom that absorbs a photon, and determine the fine-structure constant α−1 = 137.035999206(11) with a relative accuracy of 81 parts per trillion. The accuracy of eleven digits in α leads to an electron g factor1,2—the most precise prediction of the standard model—that has a greatly reduced uncertainty. Our value of the fine-structure constant differs by more than 5 standard deviations from the best available result from caesium recoil measurements3. Our result modifies the constraints on possible candidate dark-matter particles proposed to explain the anomalous decays of excited states of 8Be nuclei4 and paves the way for testing the discrepancy observed in the magnetic moment anomaly of the muon5 in the electron sector6. The fine-structure constant is determined with an accuracy of 81 parts per trillion using matter-wave interferometry to measure the rubidium atom recoil velocity.

Léo Morel

Papers

Determination of the fine-structure constant with an accuracy of 81 parts per trillion