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.

The Fermilab Muon g −2 experiment recently reported its first measurement of the anomalous magnetic moment $$ {a}_{\mu}^{\mathrm{FNAL}} $$a μ FNAL , which is in full agreement with the previous BNL measurement and pushes the world average deviation $$ \Delta {a}_{\mu}^{2021} $$∆ a μ 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 a_μ, 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 ∆a_μ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large ∆a_μ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the a_μ 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 a_μ only in specific versions and in specific parameter ranges. Among all models with up to three fields, only models with chirality enhancements can accommodate a_μ and dark matter simultaneously. The MSSM can simultaneously explain a_μ 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 a_μ result.

We present FlexibleEFTHiggs, a method for calculating the SM-like Higgs pole mass in SUSY (and even non-SUSY) models, which combines an effective field theory approach with a diagrammatic calculation. It thus achieves an all order resummation of leading logarithms together with the inclusion of all non-logarithmic 1-loop contributions. We implement this method into FlexibleSUSY and study its properties in the MSSM, NMSSM, E₆SSM and MRSSM. In the MSSM, it correctly interpolates between the known results of effective field theory calculations in the literature for a high SUSY scale and fixed- order calculations in the full theory for a sub-TeV SUSY scale. We compare our MSSM results to those from public codes and identify the origin of the most significant deviations between the \( \overline{\mathrm{DR}} \) programs. We then perform a similar comparison in the remaining three non-minimal models. For all four models we estimate the theoretical uncertainty of Flex- ibleEFTHiggs and the fixed-order \( \overline{\mathrm{DR}} \) programs thereby finding that the former becomes more precise than the latter for a SUSY scale above a few TeV. Even for sub-TeV SUSY scales, FlexibleEFTHiggs maintains the uncertainty estimate around 2–3 GeV, remaining a competitive alternative to existing fixed-order computations.

We complete the two-loop calculation of β-functions for vacuum expectation values (VEVs) in gauge theories by the missing \( \mathcal{O} \)(g ⁴)-terms. The full two-loop results are presented for generic and supersymmetric theories up to two-loop level in arbitrary R _ξ -gauge. The results are obtained by means of a scalar background field, identical to our previous analysis. As a by-product, the two-loop scalar anomalous dimension for generic supersymmetric theories is presented. As an application we compute the β-functions for VEVs and tan β in the MSSM, NMSSM, and E₆SSM.