The Muon g-2 Issue In A Nutshell

The introduction of a new paper by authors who describe themselves by the first initials of their surnames (KNTW) nicely sums of the state of the efforts to compare experimental measurements of muon g-2 with predictions of its value using the Standard Model of Particle Physics.

The anomalous magnetic moment of the muon, aµ, and its potential for discovering new physics stand at a crossroads. The accuracy and precision of the Standard Model (SM) prediction, a(SM)µ, relies on resolving significant tensions in evaluations of the hadronic vacuum polarization (HVP) contributions, a(HVP)µ . Data-driven evaluations of the HVP using e+e− → hadrons cross section data as input result in a value for a(SM)µ that is ∼ 5σ below the most recent experimental measurement from the Muon g−2 Experiment at Fermilab, a(exp)µ. With an unprecedented 200 parts-per-billion (ppb) precision, confirmation of previous measurements, and final results (expected in 2025) projected to improve the experimental precision by another factor of two, the measurements of aµ appear to be on solid ground.<1> However, high-precision lattice QCD calculations (incorporating QED corrections) and the most recent experimental measurement of the dominant e+e− → π+π− cross section from the CMD-3 experiment result in independent, but consistent values for aHVP that are >4σ larger than previous data-driven evaluations. They therefore generate values for a(SM)µ that are consistent with a(exp)µ and support a no-new-physics scenario in the muon g−2, whilst leaving an unexplained discrepancy with the vast catalogue of previously measured hadronic cross section data. 

The KNT (now KNTW) data-driven determinations of a(HVP)µ are crucial inputs to previous and future community-approved predictions for a(SM)µ from the Muon g−2 Theory Initiative. With multiple, independent lattice QCD evaluations of a(HVP)µ becoming significantly competitive only in recent years, it was one of only a few data-driven HVP evaluations which exclusively formed the value for a(HVP) lattice QCD and updated data-driven evaluations, with KNTW being a key input to the latter. An alternative approach to determine a(HVP)µ by experimentally measuring the spacelike vacuum polarization is under preparation at the MUonE Experiment. 

The KNTW procedure for evaluating the total hadronic cross section and a(HVP)µ (plus other precision observables which depend on hadronic effects) is undergoing a major overhaul and modernization of the analysis framework. The aim of this revamp is to make use of sophisticated analysis tools, perform new evaluations of various contributions, incorporate handles in the analysis structure that result in flexible and robust ways to test various systematic effects, improve determinations of corresponding systematic uncertainties and ultimately produce a new state-of-the-art in the determination of these quantities. These changes will be described in detail in the next full KNTW update. 

Such future data-driven evaluations of a(HVP)µ depend largely on new experimentally measured hadronic cross section data, particularly for the π+π− final state. These require increased precision and a more robust understanding of higher-order radiative corrections, which are currently being studied in detail within the STRONG2020 program and The RadioMonteCarlow 2 Effort. Whilst a discussion of these improvements is outside the scope of this letter, such future results have been announced from the BaBar, Belle II, BESIII, CMD-3, KLOE and SND experiments within the next few years. These new measurements could either fundamentally adjust the previous data-driven evaluations of a(HVP)µ used in the SM prediction that exhibits the ∼ 5σ discrepancy with a(exp)µ. Future SM predictions are expected to incorporate both to bring them more in line with e.g. the recent CMD-3 π+π− measurement or make the current tensions even worse if new measurements confirm lower cross section values with increased precision. 

Importantly, and as will be discussed in the next section, analysis choices in how to use these data can produce significantly different results. With this being the case, the future of a(HVP)µ and a(SM)µ being so uncertain, and the crossroads in the current tensions ultimately suggesting either a discovery of new physics or a multi-method confirmation of the SM, analysis blinding for data-driven determinations of the HVP is now paramount. 

<1> Alternative future measurements of aµ are also planned at JPARC and PSI.