A 2015 review of supersymmetry prospects (J. Ellis, arXiv:1510.06204) posed as its foremost open question the origin of the discrepancy between the measured muon anomalous magnetic moment a_mu = (g−2)/2 and its Standard Model prediction: an unknown theoretical uncertainty in the SM calculation, an unrecognized experimental systematic, or genuine new physics at the TeV scale — noting that the answer crucially conditions the plausibility of the low-mass supersymmetric spectra favored by pMSSM10 global fits. A decade of later literature has transformed but not settled the question. On the experimental side, the Fermilab E989 experiment confirmed the Brookhaven E821 measurement, and the final world average (2025) is a_mu = 1165920715(145)×10⁻¹² (124 ppb), largely closing the experimental-systematic branch. On the theory side, the specific hadronic light-by-light uncertainty flagged in 2015 has been halved, while the entire discrepancy now hinges on the leading-order hadronic vacuum polarization (HVP) contribution: data-driven dispersive evaluations from e+e−→hadrons cross sections have become mutually incompatible (CMD-3 versus legacy datasets), and lattice-QCD determinations point to a prediction consistent with experiment — in the 2025 Theory Initiative update, a_mu(SM) = 116592033(62)×10⁻¹¹ and Δa_mu = 38(63)×10⁻¹¹, i.e. no significant tension. The problem therefore remains open with a sharper core: establish the HVP contribution — and hence the SM prediction for a_mu — at the precision of the final experimental measurement, so that it can be decided whether any residual discrepancy exists and whether new physics, such as the light smuons and charginos favored by supersymmetric global fits, is indicated by this observable.

Background

The magnetic moment of the muon is written as μ = gμ(e/2mμ)S, and the small deviation of the dimensionless factor gμ from 2 defines the anomalous magnetic moment aμ = (gμ − 2)/2. In the Standard Model (SM), aμ receives contributions from pure QED (evaluated through fifth order in the fine-structure constant with negligible uncertainty), from the electroweak interaction (known to better than 1%), and from strong-interaction effects that cannot be computed perturbatively and now dominate the theoretical uncertainty. The two hadronic contributions are the leading-order hadronic vacuum polarization (HVP) — a quark–antiquark loop inserted into the photon propagator, entering at order α² — and the hadronic light-by-light (HLbL) contribution, a four-photon loop with hadronic substructure entering at order α³. The HVP is evaluated either ab initio with lattice QCD (the numerical, discretized formulation of quantum chromodynamics) or through a dispersion relation, in which it is expressed as an integral of the measured e+e− → hadrons cross section weighted by a known kernel; the HLbL term is evaluated with dispersive methods constrained by measured scattering data and by lattice QCD.

The Brookhaven E821 experiment's final measurement (G. W. Bennett et al., 2006) exceeded contemporaneous SM evaluations by roughly 3σ, and this discrepancy was, around 2015, one of the longest-standing hints of possible TeV-scale new physics. In supersymmetry (SUSY), loops of sleptons (scalar partners of leptons; the smuon is the muon's partner) and of charginos/neutralinos (mixed fermion partners of the electroweak gauge and Higgs bosons) can raise aμ, so the discrepancy pulls global fits toward light electroweak-scale superpartners. The source of this candidate, a 2015 review by J. Ellis, analyzed the constrained MSSM (CMSSM — the minimal supersymmetric Standard Model with universal soft SUSY-breaking parameters at a high scale), its NUHM1/2 variants (allowing non-universal soft contributions to the Higgs masses), and the pMSSM10 — a phenomenological MSSM scan over ten soft SUSY-breaking parameters (gaugino masses, first/second- and third-generation squark masses, a common slepton mass, a common trilinear mixing parameter, the Higgs mixing parameter μ, the pseudoscalar Higgs mass, and tanβ, the ratio of the two Higgs vacuum expectation values), fitted with ≈1.2×10⁹ sampled points to precision electroweak data, Higgs measurements, flavor observables, LHC sparticle searches, and dark matter constraints (K. J. de Vries et al., 2015). In those fits the (g−2) likelihood was the single strongest pull, favoring small smuon and chargino masses, and the review posed as its foremost open question whether the discrepancy arises from an unknown SM theoretical uncertainty — it specifically mentioned the HLbL contribution — from an unrecognized experimental effect, or from new physics, noting that settling this is crucial for judging the plausibility of the low-mass SUSY spectra the fits favored, and that the Fermilab E989 experiment would remeasure aμ with far greater precision. The same review listed related open issues — whether the SM vacuum is metastable (the SM Higgs quartic coupling runs negative at high field values, with the instability scale depending critically on the top-quark mass and the strong coupling; D. Buttazzo et al., 2013, is the benchmark calculation), the extension of LHC searches for long-lived charged sparticles beyond chargino–neutralino near-degeneracy to the stau case, the dependence of the fit conclusions on the chosen parameterization, and whether even a 100 TeV collider could cover multi-TeV coannihilation endpoints — which are related motivation and testing questions but separable research lines.

A decade of subsequent work has sharply reframed the question. The 2020 Muon g−2 Theory Initiative White Paper (T. Aoyama et al.) established the data-driven SM prediction aμ(SM) = 116591810(43)×10⁻¹¹, which stood 3.7σ below the Brookhaven measurement and 4.2σ below the early Fermilab average. The Fermilab E989 experiment then confirmed E821 (2021 and 2023 results) and delivered a final world average aμ(exp) = 1165920715(145)×10⁻¹² (124 ppb) in 2025 — so two independent storage-ring experiments agree and the experimental branch is essentially closed. On the theory side, a lattice-QCD calculation of the HVP by the BMW collaboration (S. Borsanyi et al., Nature 2021, 0.8% total uncertainty) significantly reduced the tension, and the CMD-3 measurement of the dominant e+e− → π+π− cross section (F. V. Ignatov et al., 2024) pushed the dispersive prediction upward — but at the price of revealing that the e+e− datasets are mutually incompatible. The 2025 Theory Initiative update (R. Aliberti et al., 235 authors) concluded that the tensions among data-driven dispersive evaluations "have increased to a level that makes it impossible to combine the results in a meaningful way", adopted a consolidated lattice-QCD average for the HVP (0.9%), and obtained aμ(SM) = 116592033(62)×10⁻¹¹ (530 ppb) with Δaμ = aμ(exp) − aμ(SM) = 38(63)×10⁻¹¹ — no significant tension — while explicitly identifying the resolution of the dispersive tensions as the key open element and the E989 precision (127 ppb) as the target of future theory efforts. The theoretical uncertainty now exceeds the experimental one by more than a factor of four: the answer to the 2015 question has been funneled into a single, still-open battleground, the leading-order HVP contribution.

Problem Statement

The origin of the discrepancy between the measured muon anomalous magnetic moment and its Standard Model prediction was posed in the 2015 review of supersymmetry prospects as a three-branch question: does the difference arise from (i) an unknown systematic uncertainty in the Standard Model calculation (the review specifically flagged the hadronic light-by-light contribution), (ii) an unrecognized experimental effect, or (iii) genuine new physics at the TeV scale — with the answer crucially conditioning the plausibility of the low-mass supersymmetric spectra favored by pMSSM-type global fits? That 2015 three-branch question remains the objective. The evidence accumulated since then (see Background) has largely resolved the experimental branch (ii) and much reduced the hadronic-light-by-light uncertainty singled out within branch (i), but branch (i) — the Standard Model hadronic uncertainty — is not closed: it now resides in the leading-order hadronic vacuum polarization, which remains the unresolved element.

Updated by a decade of evidence, the open question is whether the leading-order hadronic vacuum polarization contribution — and hence the Standard Model prediction for aμ — can be determined to a precision matching the final experimental world average aμ(exp) = 1165920715(145)×10⁻¹² (124 ppb, dominated by Fermilab E989), leaving a value of Δaμ = aμ(exp) − aμ(SM) that differs from zero at a statistically significant level (taken as ≥3σ) — and whether this observable therefore indicates new physics, such as the light smuons and charginos toward which supersymmetric global fits are pulled.

References

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